add basegear and keep feature.py

This reverts commit 878811ae54.

.github/workflows/pylint.yml

@@ -0,0 +1,23 @@
+name: Pylint
+
+on: [push]
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: ["3.8", "3.9", "3.10"]
+    steps:
+    - uses: actions/checkout@v3
+    - name: Set up Python ${{ matrix.python-version }}
+      uses: actions/setup-python@v3
+      with:
+        python-version: ${{ matrix.python-version }}
+    - name: Install dependencies
+      run: |
+        python -m pip install --upgrade pip
+        pip install pylint
+    - name: Analysing the code with pylint
+      run: |
+        pylint $(git ls-files '*.py')

.gitignore

@@ -53,7 +53,7 @@ docs/_build/
 # PyBuilder
 target/
 
-#costum
+#custom
 *.kdev4
 *.lyx~
 .ipynb_checkpoints/

LICENSE

@@ -1,281 +1,622 @@
-GNU GENERAL PUBLIC LICENSE
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+                       Version 3, 29 June 2007
 
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+
+  However, if you cease all violation of this License, then your
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+your receipt of the notice.
+
+  Termination of your rights under this section does not terminate the
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+material under section 10.
+
+  9. Acceptance Not Required for Having Copies.
+
+  You are not required to accept this License in order to receive or
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+occurring solely as a consequence of using peer-to-peer transmission
+to receive a copy likewise does not require acceptance.  However,
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+
+  10. Automatic Licensing of Downstream Recipients.
+
+  Each time you convey a covered work, the recipient automatically
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+  An "entity transaction" is a transaction transferring control of an
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+
+  11. Patents.
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+  A "contributor" is a copyright holder who authorizes use under this
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+work thus licensed is called the contributor's "contributor version".
+
+  A contributor's "essential patent claims" are all patent claims
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+  If, pursuant to or in connection with a single transaction or
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+
+  A patent license is "discriminatory" if it does not include within
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+or that patent license was granted, prior to 28 March 2007.
+
+  Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+  12. No Surrender of Others' Freedom.
+
+  If conditions are imposed on you (whether by court order, agreement or
 otherwise) that contradict the conditions of this License, they do not
-excuse you from the conditions of this License.  If you cannot
+excuse you from the conditions of this License.  If you cannot convey a
-distribute so as to satisfy simultaneously your obligations under this
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+License and any other pertinent obligations, then as a consequence you may
-may not distribute the Program at all.  For example, if a patent
+not convey it at all.  For example, if you agree to terms that obligate you
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-all those who receive copies directly or indirectly through you, then
+the Program, the only way you could satisfy both those terms and this
-the only way you could satisfy both it and this License would be to
+License would be to refrain entirely from conveying the Program.
-refrain entirely from distribution of the Program.
 
-If any portion of this section is held invalid or unenforceable under
+  13. Use with the GNU Affero General Public License.
-any particular circumstance, the balance of the section is intended to
-apply and the section as a whole is intended to apply in other
-circumstances.
 
-It is not the purpose of this section to induce you to infringe any
+  Notwithstanding any other provision of this License, you have
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+License will continue to apply to the part which is the covered work,
-generous contributions to the wide range of software distributed
+but the special requirements of the GNU Affero General Public License,
-through that system in reliance on consistent application of that
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-system; it is up to the author/donor to decide if he or she is willing
+combination as such.
-to distribute software through any other system and a licensee cannot
-impose that choice.
 
-This section is intended to make thoroughly clear what is believed to
+  14. Revised Versions of this License.
-be a consequence of the rest of this License.
 
-  8. If the distribution and/or use of the Program is restricted in
+  The Free Software Foundation may publish revised and/or new versions of
-certain countries either by patents or by copyrighted interfaces, the
+the GNU General Public License from time to time.  Such new versions will
-original copyright holder who places the Program under this License
-may add an explicit geographical distribution limitation excluding
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-
-  9. The Free Software Foundation may publish revised and/or new versions
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 address new problems or concerns.
 
-Each version is given a distinguishing version number.  If the Program
+  Each version is given a distinguishing version number.  If the
-specifies a version number of this License which applies to it and "any
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-later version", you have the option of following the terms and conditions
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-either of that version or of any later version published by the Free
+option of following the terms and conditions either of that numbered
-Software Foundation.  If the Program does not specify a version number of
+version or of any later version published by the Free Software
-this License, you may choose any version ever published by the Free Software
+Foundation.  If the Program does not specify a version number of the
-Foundation.
+GNU General Public License, you may choose any version ever published
+by the Free Software Foundation.
 
-  10. If you wish to incorporate parts of the Program into other free
+  If the Program specifies that a proxy can decide which future
-programs whose distribution conditions are different, write to the author
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+public statement of acceptance of a version permanently authorizes you
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+to choose that version for the Program.
-make exceptions for this.  Our decision will be guided by the two goals
-of preserving the free status of all derivatives of our free software and
-of promoting the sharing and reuse of software generally.
 
-                            NO WARRANTY
+  Later license versions may give you additional or different
+permissions.  However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
 
-  11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
+  15. Disclaimer of Warranty.
-FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW.  EXCEPT WHEN
-OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
-PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
-OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
-MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.  THE ENTIRE RISK AS
-TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU.  SHOULD THE
-PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
-REPAIR OR CORRECTION.
 
-  12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
-WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
+APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
-REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
-INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
-OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
-TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
+PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
-YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
+IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
-PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
-POSSIBILITY OF SUCH DAMAGES.
+
+  16. Limitation of Liability.
+
+  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
 
                      END OF TERMS AND CONDITIONS
 
@@ -287,15 +628,15 @@ free software which everyone can redistribute and change under these terms.
 
   To do so, attach the following notices to the program.  It is safest
 to attach them to the start of each source file to most effectively
-convey the exclusion of warranty; and each file should have at least
+state the exclusion of warranty; and each file should have at least
 the "copyright" line and a pointer to where the full notice is found.
 
-    {description}
+    <one line to give the program's name and a brief idea of what it does.>
-    Copyright (C) {year}  {fullname}
+    Copyright (C) <year>  <name of author>
 
-    This program is free software; you can redistribute it and/or modify
+    This program is free software: you can redistribute it and/or modify
     it under the terms of the GNU General Public License as published by
-    the Free Software Foundation; either version 2 of the License, or
+    the Free Software Foundation, either version 3 of the License, or
     (at your option) any later version.
 
     This program is distributed in the hope that it will be useful,
@@ -303,37 +644,31 @@ the "copyright" line and a pointer to where the full notice is found.
     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     GNU General Public License for more details.
 
-    You should have received a copy of the GNU General Public License along
+    You should have received a copy of the GNU General Public License
-    with this program; if not, write to the Free Software Foundation, Inc.,
+    along with this program.  If not, see <https://www.gnu.org/licenses/>.
-    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 
 Also add information on how to contact you by electronic and paper mail.
 
-If the program is interactive, make it output a short notice like this
+  If the program does terminal interaction, make it output a short
-when it starts in an interactive mode:
+notice like this when it starts in an interactive mode:
 
-    Gnomovision version 69, Copyright (C) year name of author
+    <program>  Copyright (C) <year>  <name of author>
-    Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
     This is free software, and you are welcome to redistribute it
     under certain conditions; type `show c' for details.
 
 The hypothetical commands `show w' and `show c' should show the appropriate
-parts of the General Public License.  Of course, the commands you use may
+parts of the General Public License.  Of course, your program's commands
-be called something other than `show w' and `show c'; they could even be
+might be different; for a GUI interface, you would use an "about box".
-mouse-clicks or menu items--whatever suits your program.
 
-You should also get your employer (if you work as a programmer) or your
+  You should also get your employer (if you work as a programmer) or school,
-school, if any, to sign a "copyright disclaimer" for the program, if
+if any, to sign a "copyright disclaimer" for the program, if necessary.
-necessary.  Here is a sample; alter the names:
+For more information on this, and how to apply and follow the GNU GPL, see
+<https://www.gnu.org/licenses/>.
 
-  Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+  The GNU General Public License does not permit incorporating your program
-  `Gnomovision' (which makes passes at compilers) written by James Hacker.
+into proprietary programs.  If your program is a subroutine library, you
-
+may consider it more useful to permit linking proprietary applications with
-  {signature of Ty Coon}, 1 April 1989
+the library.  If this is what you want to do, use the GNU Lesser General
-  Ty Coon, President of Vice
+Public License instead of this License.  But first, please read
-
+<https://www.gnu.org/licenses/why-not-lgpl.html>.
-This General Public License does not permit incorporating your program into
-proprietary programs.  If your program is a subroutine library, you may
-consider it more useful to permit linking proprietary applications with the
-library.  If this is what you want to do, use the GNU Lesser General
-Public License instead of this License.

README.md

@@ -1,38 +1,57 @@
-# A Gear module for FreeCAD
+## A Gear module for FreeCAD
-
+[![Liberapay](http://img.shields.io/liberapay/patrons/looooo.svg?logo=liberapay)](https://liberapay.com/looooo/donate) 
-[![Liberapay](http://img.shields.io/liberapay/patrons/looooo.svg?logo=liberapay)](https://liberapay.com/looooo/donate)
 
 ## Requirements
-FreeCAD > v0.16
+FreeCAD > v0.16  
+__python > 3 (for python2 use branch py2)__
 
-# Screenshots
-![gear](examples/spiral.png)
-![gear1](examples/animated_spiral.gif)
 
 ## Supported gear-types
 
 ### Cylindric Involute
-#### Shifting
+* Shifting
-#### Helical
+* Helical
-#### Double Helical
+* Double Helical
-#### Undercut
+* Undercut  
+
+![involute-gear](examples/involute-double-helical-gear.png)
+
 
 ### Involute Rack
+![involute-rack](examples/involute-rack.png)
 
 ### Cylindric Cycloid
-#### Helical
+* Helical
-#### Double Helical
+* Double Helical
+
+![cycloid-gear](examples/cycloid-gear.png)
+
+### Cycloid Rack
+
+![cycloid-rack](examples/cycloid-rack.png)
 
 ### Spherical Involute Bevel-Gear
-#### Spiral
+* Spiral  
+
+![bevel-gear](examples/bevel-gear.png)
 
 ### Crown-Gear
+![crown-gear](examples/crown-gear.png)
+
+### Worm-Gear
+![worm-gear](examples/worm-gear.png)
+
+### Timing-Gear
+![timing-gear](examples/timing-gear.png)
+
+### Lantern-Gear
+![lantern-gear](examples/lantern-gear.png)
 
 ---------------------------
 
 ## Installation
 
-### Addon Manger  
+### Addon Manager  
 Starting from v0.17 it's possible to use the built-in FreeCAD [Addon Manager](https://github.com/FreeCAD/FreeCAD-addons#1-builtin-addon-manager)
 located in the `Tools` > `Addon Manager` dropdown menu.
 
@@ -79,4 +98,4 @@ by browsing this repositories [issue queue](https://github.com/looooo/freecad.ge
 * "FC Gears: Feedback thread" ([thread](https://forum.freecadweb.org/viewtopic.php?f=8&t=27626))  
 
 # License
-GNU General Public License v2.0
+GNU General Public License v3.0

TODO.md

@@ -0,0 +1,6 @@
+#TODO:
+
+## refactoring
+
+- [ ] fp.gear.z -> fp.gear.num_teeth
+- [ ] fp.teeth  -> fp.gear.num_teeth

examples/animation.py

@@ -1,11 +1,11 @@
 # script for bevel-gear animation
 
-from PySide import QtGui, QtCore
+from PySide import QtCore
-import FreeCADGui as Gui
+import FreeCAD as app
+import FreeCADGui as gui
 import numpy as np
-import imageio
 
-doc = App.ActiveDocument
+doc = app.ActiveDocument
 g2 = doc.Common
 g1 = doc.Common001
 
@@ -15,12 +15,9 @@ def make_pics():
     n = 30
     for i in range(n):
         phi = np.pi * 2 / 30 / n
-    	g1.Placement.Rotation.Angle += phi * 2
+        g1.Placement.Rotation.Angle += phi * 2
-    	g2.Placement.Rotation.Angle -= phi
+        g2.Placement.Rotation.Angle -= phi
-        Gui.activeDocument().activeView().saveImage('/home/lo/Schreibtisch/animated_gear/gear_{}.png'.format(i) ,300,300,'Current')
+        gui.activeDocument().activeView().saveImage('/home/lo/Schreibtisch/animated_gear/gear_{}.png'.format(i) ,300,300,'Current')
-
-def make_animated_gif():
-
 
 def update(*args):
     print("time")

examples/worm_cutting_tool/cutting_tool_worm_assembly.ipynb

@@ -0,0 +1,434 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "5e24589a-461d-46b5-8141-37f948dcf4dc",
+   "metadata": {},
+   "source": [
+    "# cutting tool for a worm gear\n",
+    "\n",
+    "1. idea 1:  \n",
+    "\n",
+    "<img src=\"../../docs/computing a profile_from_a_given_rack.jpg\">"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "7eacf041-aa83-49e2-9cbe-066f177197f6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import sympy as sp\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "980417d0-c79d-4501-a7cc-9725b3bbea83",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def symbolic_transformation(angle, axis, translation=np.array([0., 0., 0.])):\n",
+    "    \"\"\"\n",
+    "        see http://en.wikipedia.org/wiki/SO%284%29#The_Euler.E2.80.93Rodrigues_formula_for_3D_rotations\n",
+    "        sympy enabled transformation\n",
+    "        angle: angle of rotation\n",
+    "        axis: the axis of the rotation\n",
+    "        translation: translation of transformation\n",
+    "    \"\"\"\n",
+    "    assert len(axis) == 3\n",
+    "    a = sp.cos(angle / 2)\n",
+    "    axis_normalized = axis / sp.sqrt(axis.dot(axis))\n",
+    "    (b, c, d) = -axis_normalized * sp.sin(angle / 2)\n",
+    "    mat = sp.Matrix(\n",
+    "        [\n",
+    "            [\n",
+    "                a**2 + b**2 - c**2 - d**2,\n",
+    "                2 * (b * c - a * d),\n",
+    "                2 * (b * d + a * c),\n",
+    "                translation[0],\n",
+    "            ],\n",
+    "            [\n",
+    "                2 * (b * c + a * d),\n",
+    "                a**2 + c**2 - b**2 - d**2,\n",
+    "                2 * (c * d - a * b),\n",
+    "                translation[1],\n",
+    "            ],\n",
+    "            [\n",
+    "                2 * (b * d - a * c),\n",
+    "                2 * (c * d + a * b),\n",
+    "                a**2 + d**2 - b**2 - c**2,\n",
+    "                translation[2],\n",
+    "            ],\n",
+    "            [0.0, 0.0, 0.0, 1.0],\n",
+    "        ]\n",
+    "    )\n",
+    "    return sp.simplify(mat)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "5852aa56-e66b-4f3c-a50d-0cb4cb21abd2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t = sp.Symbol(\"t\")\n",
+    "T1 = symbolic_transformation(np.pi / 2.,\n",
+    "                             np.array([1., 0., 0.]),\n",
+    "                             np.array([12.5,0., 1.15]))\n",
+    "T2 = symbolic_transformation(-t / 7.5,\n",
+    "                             np.array([0., 0., 1.]),\n",
+    "                             np.array([0., 0., 0.]))\n",
+    "T3 = symbolic_transformation(0.,\n",
+    "                             np.array([1., 0., 0.]),\n",
+    "                             np.array([0., 0., t]))\n",
+    "\n",
+    "T = sp.nsimplify(T2.inv() @ T1.inv() @ T3, tolerance=10e-16)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "7c9837b8-caf7-4447-bf0d-eba9085197a5",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[ 0.        ,  0.        , -0.13333333,  0.15333333],\n",
+       "       [-0.13333333,  0.        ,  0.        ,  0.66666667],\n",
+       "       [ 0.        ,  0.        ,  0.        ,  0.        ],\n",
+       "       [ 0.        ,  0.        ,  0.        ,  0.        ]])"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "T_fn = sp.lambdify(t, T)\n",
+    "dT_fn = sp.lambdify(t, T.diff(t))\n",
+    "dT_fn(0.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4354a36-409a-40a6-8f4f-bb5a6c84f3b7",
+   "metadata": {},
+   "source": [
+    "Diese Methode funktioniert nicht, weil die Bedingung zur Bestimmung des Kontaktpunktes falsch ist.\n",
+    "Eine Bedingung für die generierung einer konstanten Übersetzung ist, dass die Normale auf die Kontaktfläche (Zahnstange) immer durch den Punkt p (Eingriffspunkt für Ersatzzahnrad (Zylinder) und Ersatzzahnstange (Quader) gehen muss.\n",
+    "Gesucht sind also Punkte auf der Fläche S welche verbunden mit P normal auf die Fläche stehen. Dies kann auch als minimaler Abstand von P zur Fläche gesehen werden.\n",
+    "\n",
+    "für jedes u: min(norm(S(u,v)-P)) -> d(norm(S(u,v)-P)/dv = 0\n",
+    "die Änderung des Abstands ist 0 -> die Gerade steht normal auf die Fläche\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "43f00b65-c05c-4734-8c5a-e7845a6f4dff",
+   "metadata": {},
+   "source": [
+    "## Vorgehensweise\n",
+    "\n",
+    "1. approximate the surface by a BSplineSurface\n",
+    "\n",
+    "- Erstellen eines \"Cross-Sektion\" objekts aus dem \"Werkzeug\"\n",
+    "\n",
+    "<img src=\"cross_section.png\">  \n",
+    "\n",
+    "- Draft downgrade um Kanten zu bekommen\n",
+    "das Cross-section Objekt beinhaltet nicht die anfangs und end Kanten. Diese müssen zusätzlich vom Werkzeug extrahiert werden\n",
+    "\n",
+    "- Part Loft zum erstellen einer schönen BSplinefläche\n",
+    "\n",
+    "<img src=\"loft_bspline_flaechen.png\"> \n",
+    "\n",
+    "3. Loft -> Surface\n",
+    "\n",
+    "```python\n",
+    "# select the cutting faces\n",
+    "face_1 = App.ActiveDocument.Loft.Shape.Faces[0].copy()\n",
+    "face_2 = App.ActiveDocument.Loft001.Shape.Faces[0].copy()\n",
+    "\n",
+    "# compute the contact curve:\n",
+    "bsp_1 = face_1.Surface\n",
+    "bsp_2 = face_2.Surface\n",
+    "\n",
+    "```\n",
+    "\n",
+    "4. Minimierung des Abstands zum \"Pitch-Punkt\"\n",
+    "\n",
+    "```python\n",
+    "import scipy as scp\n",
+    "point = App.Vector(5., 0., 1.15 - time) \n",
+    "xyz_1 = []\n",
+    "for v in np.linspace(0, 1, 5):\n",
+    "        def dist_1(u):\n",
+    "            distance = bsp_1.value(u, v) - point\n",
+    "            return distance.x ** 2 + distance.z ** 2\n",
+    "        u_1 = scp.optimize.minimize(dist_1, 0.5, tol=1e-6).x[0]\n",
+    "        xyz_1.append(bsp_1.value(u_1, v))\n",
+    "```\n",
+    "\n",
+    "5. erstellen einer B-Spline Kurve welche durch die Kinematik T transformiert wird\n",
+    "\n",
+    "```python\n",
+    "c_1 = Part.BSplineCurve()\n",
+    "c_1.interpolate(Points=xyz_1)\n",
+    "c_1 = c_1.toShape()\n",
+    "\n",
+    "Part.show(c_1.transformShape(T))\n",
+    "```\n",
+    "\n",
+    "6. Loft anwenden auf die erstellten BSpline Kurven\n",
+    "\n",
+    "<img src=\"loft_of_generated_bsplines.png\">\n",
+    "\n",
+    "7. Array für das Zahnrad\n",
+    "\n",
+    "<img src=\"gear_assembly.png\">"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "cfd8026b-5a84-4882-a1de-63580776a579",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import sympy as sp\n",
+    "t, x, z = sp.symbols([\"t\", \"x\", \"z\"], real=True)\n",
+    "s, alpha, n_t, y = sp.symbols([\"s\", \"alpha\", \"n_t\", \"y\"], real=True, positiv=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "65bb90d7-0f5b-410e-9a3a-0f9953a4d846",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(\\frac{n_{t} t}{\\pi} \\right)} & \\sin{\\left(\\frac{n_{t} t}{\\pi} \\right)} & 0 & 0\\\\- \\sin{\\left(\\frac{n_{t} t}{\\pi} \\right)} & \\cos{\\left(\\frac{n_{t} t}{\\pi} \\right)} & 0 & 0\\\\0 & 0 & 1 & n_{t} t\\\\0 & 0 & 0 & 1.0\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[ cos(n_t*t/pi), sin(n_t*t/pi), 0,     0],\n",
+       "[-sin(n_t*t/pi), cos(n_t*t/pi), 0,     0],\n",
+       "[             0,             0, 1, n_t*t],\n",
+       "[             0,             0, 0,   1.0]])"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "T_spiral = symbolic_transformation(t * n_t / sp.pi, np.array([0, 0, 1]), np.array([0, 0, t * n_t]))\n",
+    "T_spiral"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "0f305b8b-0fb5-4b71-80b6-9a2b43b59e26",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}0\\\\s \\cos{\\left(\\alpha \\right)}\\\\s \\sin{\\left(\\alpha \\right)}\\\\1\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[           0],\n",
+       "[s*cos(alpha)],\n",
+       "[s*sin(alpha)],\n",
+       "[           1]])"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "l = sp.Matrix([0, s * sp.cos(alpha), s * sp.sin(alpha), 1])\n",
+    "l"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "da3c8575-99ad-4258-8734-c165ea65b014",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}s \\sin{\\left(\\frac{n_{t} t}{\\pi} \\right)} \\cos{\\left(\\alpha \\right)}\\\\s \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\frac{n_{t} t}{\\pi} \\right)}\\\\n_{t} t + s \\sin{\\left(\\alpha \\right)}\\\\1.0\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[s*sin(n_t*t/pi)*cos(alpha)],\n",
+       "[s*cos(alpha)*cos(n_t*t/pi)],\n",
+       "[      n_t*t + s*sin(alpha)],\n",
+       "[                       1.0]])"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "spiral = (T_spiral @ l)\n",
+    "spiral"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "e47eb83b-6e89-4246-a82a-bd5629aedc2a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\frac{\\pi \\operatorname{asin}{\\left(\\frac{x}{s \\cos{\\left(\\alpha \\right)}} \\right)}}{n_{t}}$"
+      ],
+      "text/plain": [
+       "pi*asin(x/(s*cos(alpha)))/n_t"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "x_cross_section = sp.simplify(sp.solve(spiral[0] - x, t)[1])\n",
+    "x_cross_section  # parameter s"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "c2954b39-eea0-4e27-987f-07a5d0dedaad",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}x\\\\s \\sqrt{1 - \\frac{x^{2}}{s^{2} \\cos^{2}{\\left(\\alpha \\right)}}} \\cos{\\left(\\alpha \\right)}\\\\s \\sin{\\left(\\alpha \\right)} + \\pi \\operatorname{asin}{\\left(\\frac{x}{s \\cos{\\left(\\alpha \\right)}} \\right)}\\\\1.0\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[                                               x],\n",
+       "[s*sqrt(1 - x**2/(s**2*cos(alpha)**2))*cos(alpha)],\n",
+       "[        s*sin(alpha) + pi*asin(x/(s*cos(alpha)))],\n",
+       "[                                             1.0]])"
+      ]
+     },
+     "execution_count": 33,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "spiral_x = sp.simplify(spiral.subs({t: x_cross_section}))\n",
+    "spiral_x"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "id": "268c6302-4e7d-45e0-be28-1b64cf8b766e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\frac{\\sqrt{x^{2} + y^{2}}}{\\cos{\\left(\\alpha \\right)}}$"
+      ],
+      "text/plain": [
+       "sqrt(x**2 + y**2)/cos(alpha)"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "y_cross_section = sp.simplify(sp.solve(spiral_x[1]- y, s)[0])\n",
+    "y_cross_section"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "id": "7284bd6a-b47b-483c-8e9f-79fcaecce5e3",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}x\\\\\\left|{y}\\right|\\\\\\sqrt{x^{2} + y^{2}} \\tan{\\left(\\alpha \\right)} + \\pi \\operatorname{asin}{\\left(\\frac{x}{\\sqrt{x^{2} + y^{2}}} \\right)}\\\\1.0\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[                                                          x],\n",
+       "[                                                     Abs(y)],\n",
+       "[sqrt(x**2 + y**2)*tan(alpha) + pi*asin(x/sqrt(x**2 + y**2))],\n",
+       "[                                                        1.0]])"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "spiral_xy = sp.simplify(spiral_x.subs({s: y_cross_section}))\n",
+    "spiral_xy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "82e6880a-7240-44a4-a346-4fc45e24971b",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

freecad/__init__.py

@@ -1 +0,0 @@
-__path__ = __import__('pkgutil').extend_path(__path__, __name__)

freecad/gears/__init__.py

@@ -1,2 +1,21 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
 import pygears
+
 __version__ = pygears.__version__

freecad/gears/basegear.py

@@ -0,0 +1,672 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import os
+import sys
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+import math
+from pygears import __version__
+from pygears.involute_tooth import InvoluteTooth, InvoluteRack
+from pygears.cycloid_tooth import CycloidTooth
+from pygears.bevel_tooth import BevelTooth
+from pygears._functions import (
+    rotation3D,
+    rotation,
+    reflection,
+    arc_from_points_and_center,
+)
+
+
+def fcvec(x):
+    if len(x) == 2:
+        return App.Vector(x[0], x[1], 0)
+    else:
+        return App.Vector(x[0], x[1], x[2])
+
+
+class ViewProviderGear(object):
+    def __init__(self, obj, icon_fn=None):
+        # Set this object to the proxy object of the actual view provider
+        obj.Proxy = self
+        self._check_attr()
+        dirname = os.path.dirname(__file__)
+        self.icon_fn = icon_fn or os.path.join(dirname, "icons", "involutegear.svg")
+
+    def _check_attr(self):
+        """Check for missing attributes."""
+        if not hasattr(self, "icon_fn"):
+            setattr(
+                self,
+                "icon_fn",
+                os.path.join(os.path.dirname(__file__), "icons", "involutegear.svg"),
+            )
+
+    def attach(self, vobj):
+        self.vobj = vobj
+
+    def getIcon(self):
+        self._check_attr()
+        return self.icon_fn
+
+    if sys.version_info[0] == 3 and sys.version_info[1] >= 11:
+
+        def dumps(self):
+            self._check_attr()
+            return {"icon_fn": self.icon_fn}
+
+        def loads(self, state):
+            if state and "icon_fn" in state:
+                self.icon_fn = state["icon_fn"]
+    else:
+
+        def __getstate__(self):
+            self._check_attr()
+            return {"icon_fn": self.icon_fn}
+
+        def __setstate__(self, state):
+            if state and "icon_fn" in state:
+                self.icon_fn = state["icon_fn"]
+
+
+class BaseGear(object):
+    def __init__(self, obj):
+        obj.addProperty(
+            "App::PropertyString", "version", "version", "freecad.gears-version", 1
+        )
+        obj.version = __version__
+        self.make_attachable(obj)
+
+    def make_attachable(self, obj):
+        # Needed to make this object "attachable",
+        # aka able to attach parameterically to other objects
+        # cf. https://wiki.freecadweb.org/Scripted_objects_with_attachment
+        if int(App.Version()[1]) >= 19:
+            obj.addExtension("Part::AttachExtensionPython")
+        else:
+            obj.addExtension("Part::AttachExtensionPython", obj)
+        # unveil the "Placement" property, which seems hidden by default in PartDesign
+        obj.setEditorMode("Placement", 0)  # non-readonly non-hidden
+
+    def execute(self, fp):
+        # checksbackwardcompatibility:
+        if not hasattr(fp, "positionBySupport"):
+            self.make_attachable(fp)
+        fp.positionBySupport()
+        gear_shape = self.generate_gear_shape(fp)
+        if hasattr(fp, "BaseFeature") and fp.BaseFeature != None:
+            # we're inside a PartDesign Body, thus need to fuse with the base feature
+            gear_shape.Placement = (
+                fp.Placement
+            )  # ensure the gear is placed correctly before fusing
+            result_shape = fp.BaseFeature.Shape.fuse(gear_shape)
+            result_shape.transformShape(
+                fp.Placement.inverse().toMatrix(), True
+            )  # account for setting fp.Shape below moves the shape to fp.Placement, ignoring its previous placement
+            fp.Shape = result_shape
+        else:
+            fp.Shape = gear_shape
+
+    def generate_gear_shape(self, fp):
+        """
+        This method has to return the TopoShape of the gear.
+        """
+        raise NotImplementedError("generate_gear_shape not implemented")
+
+    if sys.version_info[0] == 3 and sys.version_info[1] >= 11:
+
+        def loads(self, state):
+            pass
+
+        def dumps(self):
+            pass
+    else:
+
+        def __setstate__(self, state):
+            pass
+
+        def __getstate__(self):
+            pass
+
+
+class LanternGear(BaseGear):
+    def __init__(self, obj):
+        super(LanternGear, self).__init__(obj)
+        obj.addProperty(
+            "App::PropertyInteger", "teeth", "gear_parameter", "number of teeth"
+        )
+        obj.addProperty("App::PropertyLength", "module", "base", "module")
+        obj.addProperty(
+            "App::PropertyLength",
+            "bolt_radius",
+            "base",
+            "the bolt radius of the rack/chain",
+        )
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+        obj.addProperty(
+            "App::PropertyInteger",
+            "num_profiles",
+            "accuracy",
+            "number of profiles used for loft",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head",
+            "tolerance",
+            "head * module = additional length of head",
+        )
+
+        obj.teeth = 15
+        obj.module = "1. mm"
+        obj.bolt_radius = "1 mm"
+
+        obj.height = "5. mm"
+        obj.num_profiles = 10
+
+        self.obj = obj
+        obj.Proxy = self
+
+    def generate_gear_shape(self, fp):
+        m = fp.module.Value
+        teeth = fp.teeth
+        r_r = fp.bolt_radius.Value
+        r_0 = m * teeth / 2
+        r_max = r_0 + r_r + fp.head * m
+
+        phi_max = (r_r + np.sqrt(r_max**2 - r_0**2)) / r_0
+
+        def find_phi_min(phi_min):
+            return r_0 * (
+                phi_min**2 * r_0
+                - 2 * phi_min * r_0 * np.sin(phi_min)
+                - 2 * phi_min * r_r
+                - 2 * r_0 * np.cos(phi_min)
+                + 2 * r_0
+                + 2 * r_r * np.sin(phi_min)
+            )
+
+        try:
+            import scipy.optimize
+
+            phi_min = scipy.optimize.root(
+                find_phi_min, (phi_max + r_r / r_0 * 4) / 5
+            ).x[0]  # , r_r / r_0, phi_max)
+        except ImportError:
+            App.Console.PrintWarning(
+                "scipy not available. Can't compute numerical root. Leads to a wrong bolt-radius"
+            )
+            phi_min = r_r / r_0
+
+        # phi_min = 0 # r_r / r_0
+        phi = np.linspace(phi_min, phi_max, fp.num_profiles)
+        x = r_0 * (np.cos(phi) + phi * np.sin(phi)) - r_r * np.sin(phi)
+        y = r_0 * (np.sin(phi) - phi * np.cos(phi)) + r_r * np.cos(phi)
+        xy1 = np.array([x, y]).T
+        p_1 = xy1[0]
+        p_1_end = xy1[-1]
+        bsp_1 = Part.BSplineCurve()
+        bsp_1.interpolate(list(map(fcvec, xy1)))
+        w_1 = bsp_1.toShape()
+
+        xy2 = xy1 * np.array([1.0, -1.0])
+        p_2 = xy2[0]
+        p_2_end = xy2[-1]
+        bsp_2 = Part.BSplineCurve()
+        bsp_2.interpolate(list(map(fcvec, xy2)))
+        w_2 = bsp_2.toShape()
+
+        p_12 = np.array([r_0 - r_r, 0.0])
+
+        arc = Part.Arc(
+            App.Vector(*p_1, 0.0), App.Vector(*p_12, 0.0), App.Vector(*p_2, 0.0)
+        ).toShape()
+
+        rot = rotation(-np.pi * 2 / teeth)
+        p_3 = rot(np.array([p_2_end]))[0]
+        # l = Part.LineSegment(fcvec(p_1_end), fcvec(p_3)).toShape()
+        l = part_arc_from_points_and_center(
+            p_1_end, p_3, np.array([0.0, 0.0])
+        ).toShape()
+        w = Part.Wire([w_2, arc, w_1, l])
+        wires = [w]
+
+        rot = App.Matrix()
+        for _ in range(teeth - 1):
+            rot.rotateZ(np.pi * 2 / teeth)
+            wires.append(w.transformGeometry(rot))
+
+        wi = Part.Wire(wires)
+        if fp.height.Value == 0:
+            return wi
+        else:
+            return Part.Face(wi).extrude(App.Vector(0, 0, fp.height))
+
+
+class HypoCycloidGear(BaseGear):
+
+    """parameters:
+    pressure_angle:  pressureangle,   10-30°
+    pitch_angle:  cone angle,      0 < pitch_angle < pi/4
+    """
+
+    def __init__(self, obj):
+        super(HypoCycloidGear, self).__init__(obj)
+        obj.addProperty(
+            "App::PropertyFloat",
+            "pin_circle_radius",
+            "gear_parameter",
+            "Pin ball circle radius(overrides Tooth Pitch",
+        )
+        obj.addProperty(
+            "App::PropertyFloat", "roller_diameter", "gear_parameter", "Roller Diameter"
+        )
+        obj.addProperty(
+            "App::PropertyFloat", "eccentricity", "gear_parameter", "Eccentricity"
+        )
+        obj.addProperty(
+            "App::PropertyAngle",
+            "pressure_angle_lim",
+            "gear_parameter",
+            "Pressure angle limit",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "pressure_angle_offset",
+            "gear_parameter",
+            "Offset in pressure angle",
+        )
+        obj.addProperty(
+            "App::PropertyInteger",
+            "teeth_number",
+            "gear_parameter",
+            "Number of teeth in Cam",
+        )
+        obj.addProperty(
+            "App::PropertyInteger",
+            "segment_count",
+            "gear_parameter",
+            "Number of points used for spline interpolation",
+        )
+        obj.addProperty(
+            "App::PropertyLength",
+            "hole_radius",
+            "gear_parameter",
+            "Center hole's radius",
+        )
+
+        obj.addProperty(
+            "App::PropertyBool", "show_pins", "Pins", "Create pins in place"
+        )
+        obj.addProperty("App::PropertyLength", "pin_height", "Pins", "height")
+        obj.addProperty(
+            "App::PropertyBool",
+            "center_pins",
+            "Pins",
+            "Center pin Z axis to generated disks",
+        )
+
+        obj.addProperty(
+            "App::PropertyBool", "show_disk0", "Disks", "Show main cam disk"
+        )
+        obj.addProperty(
+            "App::PropertyBool",
+            "show_disk1",
+            "Disks",
+            "Show another reversed cam disk on top",
+        )
+        obj.addProperty("App::PropertyLength", "disk_height", "Disks", "height")
+
+        obj.pin_circle_radius = 66
+        obj.roller_diameter = 3
+        obj.eccentricity = 1.5
+        obj.pressure_angle_lim = "50.0 deg"
+        obj.pressure_angle_offset = 0.01
+        obj.teeth_number = 42
+        obj.segment_count = 42
+        obj.hole_radius = "30. mm"
+
+        obj.show_pins = True
+        obj.pin_height = "20. mm"
+        obj.center_pins = True
+
+        obj.show_disk0 = True
+        obj.show_disk1 = True
+        obj.disk_height = "10. mm"
+
+        self.obj = obj
+        obj.Proxy = self
+
+    def to_polar(self, x, y):
+        return (x**2 + y**2) ** 0.5, math.atan2(y, x)
+
+    def to_rect(self, r, a):
+        return r * math.cos(a), r * math.sin(a)
+
+    def calcyp(self, p, a, e, n):
+        return math.atan(math.sin(n * a) / (math.cos(n * a) + (n * p) / (e * (n + 1))))
+
+    def calc_x(self, p, d, e, n, a):
+        return (
+            (n * p) * math.cos(a)
+            + e * math.cos((n + 1) * a)
+            - d / 2 * math.cos(self.calcyp(p, a, e, n) + a)
+        )
+
+    def calc_y(self, p, d, e, n, a):
+        return (
+            (n * p) * math.sin(a)
+            + e * math.sin((n + 1) * a)
+            - d / 2 * math.sin(self.calcyp(p, a, e, n) + a)
+        )
+
+    def calc_pressure_angle(self, p, d, n, a):
+        ex = 2**0.5
+        r3 = p * n
+        rg = r3 / ex
+        pp = rg * (ex**2 + 1 - 2 * ex * math.cos(a)) ** 0.5 - d / 2
+        return math.asin((r3 * math.cos(a) - rg) / (pp + d / 2)) * 180 / math.pi
+
+    def calc_pressure_limit(self, p, d, e, n, a):
+        ex = 2**0.5
+        r3 = p * n
+        rg = r3 / ex
+        q = (r3**2 + rg**2 - 2 * r3 * rg * math.cos(a)) ** 0.5
+        x = rg - e + (q - d / 2) * (r3 * math.cos(a) - rg) / q
+        y = (q - d / 2) * r3 * math.sin(a) / q
+        return (x**2 + y**2) ** 0.5
+
+    def check_limit(self, x, y, maxrad, minrad, offset):
+        r, a = self.to_polar(x, y)
+        if (r > maxrad) or (r < minrad):
+            r = r - offset
+            x, y = self.to_rect(r, a)
+        return x, y
+
+    def generate_gear_shape(self, fp):
+        b = fp.pin_circle_radius
+        d = fp.roller_diameter
+        e = fp.eccentricity
+        n = fp.teeth_number
+        p = b / n
+        s = fp.segment_count
+        ang = fp.pressure_angle_lim
+        c = fp.pressure_angle_offset
+
+        q = 2 * math.pi / float(s)
+
+        # Find the pressure angle limit circles
+        minAngle = -1.0
+        maxAngle = -1.0
+        for i in range(0, 180):
+            x = self.calc_pressure_angle(p, d, n, i * math.pi / 180.0)
+            if (x < ang) and (minAngle < 0):
+                minAngle = float(i)
+            if (x < -ang) and (maxAngle < 0):
+                maxAngle = float(i - 1)
+
+        minRadius = self.calc_pressure_limit(p, d, e, n, minAngle * math.pi / 180.0)
+        maxRadius = self.calc_pressure_limit(p, d, e, n, maxAngle * math.pi / 180.0)
+        # unused
+        # Part.Wire(Part.makeCircle(minRadius,App.Vector(-e, 0, 0)))
+        # Part.Wire(Part.makeCircle(maxRadius,App.Vector(-e, 0, 0)))
+
+        App.Console.PrintMessage("Generating cam disk\r\n")
+        # generate the cam profile - note: shifted in -x by eccentricicy amount
+        i = 0
+        x = self.calc_x(p, d, e, n, q * i / float(n))
+        y = self.calc_y(p, d, e, n, q * i / n)
+        x, y = self.check_limit(x, y, maxRadius, minRadius, c)
+        points = [App.Vector(x - e, y, 0)]
+        for i in range(0, s):
+            x = self.calc_x(p, d, e, n, q * (i + 1) / n)
+            y = self.calc_y(p, d, e, n, q * (i + 1) / n)
+            x, y = self.check_limit(x, y, maxRadius, minRadius, c)
+            points.append([x - e, y, 0])
+
+        wi = make_bspline_wire([points])
+        wires = []
+        mat = App.Matrix()
+        mat.move(App.Vector(e, 0.0, 0.0))
+        mat.rotateZ(2 * np.pi / n)
+        mat.move(App.Vector(-e, 0.0, 0.0))
+        for _ in range(n):
+            wi = wi.transformGeometry(mat)
+            wires.append(wi)
+
+        cam = Part.Face(Part.Wire(wires))
+        # add a circle in the center of the cam
+        if fp.hole_radius.Value:
+            centerCircle = Part.Face(
+                Part.Wire(Part.makeCircle(fp.hole_radius.Value, App.Vector(-e, 0, 0)))
+            )
+            cam = cam.cut(centerCircle)
+
+        to_be_fused = []
+        if fp.show_disk0 == True:
+            if fp.disk_height.Value == 0:
+                to_be_fused.append(cam)
+            else:
+                to_be_fused.append(cam.extrude(App.Vector(0, 0, fp.disk_height.Value)))
+
+        # secondary cam disk
+        if fp.show_disk1 == True:
+            App.Console.PrintMessage("Generating secondary cam disk\r\n")
+            second_cam = cam.copy()
+            mat = App.Matrix()
+            mat.rotateZ(np.pi)
+            mat.move(App.Vector(-e, 0, 0))
+            if n % 2 == 0:
+                mat.rotateZ(np.pi / n)
+            mat.move(App.Vector(e, 0, 0))
+            second_cam = second_cam.transformGeometry(mat)
+            if fp.disk_height.Value == 0:
+                to_be_fused.append(second_cam)
+            else:
+                to_be_fused.append(
+                    second_cam.extrude(App.Vector(0, 0, -fp.disk_height.Value))
+                )
+
+        # pins
+        if fp.show_pins == True:
+            App.Console.PrintMessage("Generating pins\r\n")
+            pins = []
+            for i in range(0, n + 1):
+                x = p * n * math.cos(2 * math.pi / (n + 1) * i)
+                y = p * n * math.sin(2 * math.pi / (n + 1) * i)
+                pins.append(Part.Wire(Part.makeCircle(d / 2, App.Vector(x, y, 0))))
+
+            pins = Part.Face(pins)
+
+            z_offset = -fp.pin_height.Value / 2
+            if fp.center_pins == True:
+                if fp.show_disk0 == True and fp.show_disk1 == False:
+                    z_offset += fp.disk_height.Value / 2
+                elif fp.show_disk0 == False and fp.show_disk1 == True:
+                    z_offset += -fp.disk_height.Value / 2
+            # extrude
+            if z_offset != 0:
+                pins.translate(App.Vector(0, 0, z_offset))
+            if fp.pin_height != 0:
+                pins = pins.extrude(App.Vector(0, 0, fp.pin_height.Value))
+
+            to_be_fused.append(pins)
+
+        if to_be_fused:
+            return Part.makeCompound(to_be_fused)
+
+
+def part_arc_from_points_and_center(p_1, p_2, m):
+    p_1, p_12, p_2 = arc_from_points_and_center(p_1, p_2, m)
+    return Part.Arc(
+        App.Vector(*p_1, 0.0), App.Vector(*p_12, 0.0), App.Vector(*p_2, 0.0)
+    )
+
+
+def helicalextrusion(face, height, angle, double_helix=False):
+    """
+    A helical extrusion using the BRepOffsetAPI
+    face -- the face to extrude (may contain holes, i.e. more then one wires)
+    height -- the height of the extrusion, normal to the face
+    angle -- the twist angle of the extrusion in radians
+
+    returns a solid
+    """
+    pitch = height * 2 * np.pi / abs(angle)
+    radius = 10.0  # as we are only interested in the "twist", we take an arbitrary constant here
+    cone_angle = 0
+    direction = bool(angle < 0)
+    if double_helix:
+        spine = Part.makeHelix(pitch, height / 2.0, radius, cone_angle, direction)
+        spine.translate(App.Vector(0, 0, height / 2.0))
+        face = face.translated(
+            App.Vector(0, 0, height / 2.0)
+        )  # don't transform our argument
+    else:
+        spine = Part.makeHelix(pitch, height, radius, cone_angle, direction)
+
+    def make_pipe(path, profile):
+        """
+        returns (shell, last_wire)
+        """
+        mkPS = Part.BRepOffsetAPI.MakePipeShell(path)
+        mkPS.setFrenetMode(
+            True
+        )  # otherwise, the profile's normal would follow the path
+        mkPS.add(profile, False, False)
+        mkPS.build()
+        return (mkPS.shape(), mkPS.lastShape())
+
+    shell_faces = []
+    top_wires = []
+    for wire in face.Wires:
+        pipe_shell, top_wire = make_pipe(spine, wire)
+        shell_faces.extend(pipe_shell.Faces)
+        top_wires.append(top_wire)
+    top_face = Part.Face(top_wires)
+    shell_faces.append(top_face)
+    if double_helix:
+        origin = App.Vector(0, 0, height / 2.0)
+        xy_normal = App.Vector(0, 0, 1)
+        mirror_xy = lambda f: f.mirror(origin, xy_normal)
+        bottom_faces = list(map(mirror_xy, shell_faces))
+        shell_faces.extend(bottom_faces)
+        # TODO: why the heck is makeShell from this empty after mirroring?
+        # ... and why the heck does it work when making an intermediate compound???
+        hacky_intermediate_compound = Part.makeCompound(shell_faces)
+        shell_faces = hacky_intermediate_compound.Faces
+    else:
+        shell_faces.append(face)  # the bottom is what we extruded
+    shell = Part.makeShell(shell_faces)
+    # shell.sewShape() # fill gaps that may result from accumulated tolerances. Needed?
+    # shell = shell.removeSplitter() # refine. Needed?
+    return Part.makeSolid(shell)
+
+
+def make_face(edge1, edge2):
+    v1, v2 = edge1.Vertexes
+    v3, v4 = edge2.Vertexes
+    e1 = Part.Wire(edge1)
+    e2 = Part.LineSegment(v1.Point, v3.Point).toShape().Edges[0]
+    e3 = edge2
+    e4 = Part.LineSegment(v4.Point, v2.Point).toShape().Edges[0]
+    w = Part.Wire([e3, e4, e1, e2])
+    return Part.Face(w)
+
+
+def make_bspline_wire(pts):
+    wi = []
+    for i in pts:
+        out = Part.BSplineCurve()
+        out.interpolate(list(map(fcvec, i)))
+        wi.append(out.toShape())
+    return Part.Wire(wi)
+
+
+def points_to_wire(pts):
+    wire = []
+    for i in pts:
+        if len(i) == 2:
+            # straight edge
+            out = Part.LineSegment(*list(map(fcvec, i)))
+        else:
+            out = Part.BSplineCurve()
+            out.interpolate(list(map(fcvec, i)))
+        wire.append(out.toShape())
+    return Part.Wire(wire)
+
+
+def rotate_tooth(base_tooth, num_teeth):
+    rot = App.Matrix()
+    rot.rotateZ(2 * np.pi / num_teeth)
+    flat_shape = [base_tooth]
+    for t in range(num_teeth - 1):
+        flat_shape.append(flat_shape[-1].transformGeometry(rot))
+    return Part.Wire(flat_shape)
+
+
+def fillet_between_edges(edge_1, edge_2, radius):
+    # assuming edges are in a plane
+    # extracting vertices
+    try:
+        from Part import ChFi2d
+    except ImportError:
+        App.Console.PrintWarning(
+            "Your freecad version has no python bindings for 2d-fillets"
+        )
+        return [edge_1, edge_2]
+
+    api = ChFi2d.FilletAPI()
+    p1 = edge_1.valueAt(edge_1.FirstParameter)
+    p2 = edge_1.valueAt(edge_1.LastParameter)
+    p3 = edge_2.valueAt(edge_2.FirstParameter)
+    p4 = edge_2.valueAt(edge_2.LastParameter)
+    t1 = p2 - p1
+    t2 = p4 - p3
+    n = t1.cross(t2)
+    pln = Part.Plane(edge_1.valueAt(edge_1.FirstParameter), n)
+    api.init(edge_1, edge_2, pln)
+    if api.perform(radius) > 0:
+        p0 = (p2 + p3) / 2
+        fillet, e1, e2 = api.result(p0)
+        return Part.Wire([e1, fillet, e2]).Edges
+    else:
+        return None
+
+
+def insert_fillet(edges, pos, radius):
+    assert pos < (len(edges) - 1)
+    e1 = edges[pos]
+    e2 = edges[pos + 1]
+    if radius > 0:
+        fillet_edges = fillet_between_edges(e1, e2, radius)
+        if not fillet_edges:
+            raise RuntimeError("fillet not possible")
+    else:
+        fillet_edges = [e1, None, e2]
+    output_edges = []
+    for i, edge in enumerate(edges):
+        if i == pos:
+            output_edges += fillet_edges
+        elif i == (pos + 1):
+            pass
+        else:
+            output_edges.append(edge)
+    return output_edges

freecad/gears/bevelgear.py

@@ -0,0 +1,206 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+from pygears.bevel_tooth import BevelTooth
+from pygears._functions import rotation3D
+
+from .basegear import BaseGear, fcvec, make_bspline_wire
+
+
+class BevelGear(BaseGear):
+
+    """parameters:
+    pressure_angle:  pressureangle,   10-30°
+    pitch_angle:  cone angle,      0 < pitch_angle < pi/4
+    """
+
+    def __init__(self, obj):
+        super(BevelGear, self).__init__(obj)
+        self.bevel_tooth = BevelTooth()
+        obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+        obj.addProperty("App::PropertyAngle", "pitch_angle", "involute", "pitch_angle")
+        obj.addProperty(
+            "App::PropertyAngle",
+            "pressure_angle",
+            "involute_parameter",
+            "pressure_angle",
+        )
+        obj.addProperty("App::PropertyLength", "module", "base", "module")
+        obj.addProperty("App::PropertyFloat", "clearance", "tolerance", "clearance")
+        obj.addProperty(
+            "App::PropertyInteger",
+            "numpoints",
+            "precision",
+            "number of points for spline",
+        )
+        obj.addProperty(
+            "App::PropertyBool",
+            "reset_origin",
+            "base",
+            "if value is true the gears outer face will match the z=0 plane",
+        )
+        obj.addProperty(
+            "App::PropertyLength",
+            "backlash",
+            "tolerance",
+            "The arc length on the pitch circle by which the tooth thicknes is reduced.",
+        )
+        obj.addProperty("App::PropertyPythonObject", "gear", "base", "test")
+        obj.addProperty(
+            "App::PropertyAngle", "beta", "helical", "angle used for spiral bevel-gears"
+        )
+        obj.addProperty("App::PropertyLength", "dw", "computed", "The pitch diameter.")
+        obj.setExpression(
+            "dw", "teeth * module"
+        )  # calculate via expression to ease usage for placement
+        obj.setEditorMode(
+            "dw", 1
+        )  # set read-only after setting the expression, else it won't be visible. bug?
+        obj.addProperty(
+            "App::PropertyAngle",
+            "angular_backlash",
+            "computed",
+            "The angle by which this gear can turn without moving the mating gear.",
+        )
+        obj.setExpression(
+            "angular_backlash", "backlash / dw * 360° / pi"
+        )  # calculate via expression to ease usage for placement
+        obj.setEditorMode(
+            "angular_backlash", 1
+        )  # set read-only after setting the expression, else it won't be visible. bug?
+        obj.gear = self.bevel_tooth
+        obj.module = "1. mm"
+        obj.teeth = 15
+        obj.pressure_angle = "20. deg"
+        obj.pitch_angle = "45. deg"
+        obj.height = "5. mm"
+        obj.numpoints = 6
+        obj.backlash = "0.00 mm"
+        obj.clearance = 0.1
+        obj.beta = "0 deg"
+        obj.reset_origin = True
+        self.obj = obj
+        obj.Proxy = self
+
+    def generate_gear_shape(self, fp):
+        fp.gear.z = fp.teeth
+        fp.gear.module = fp.module.Value
+        fp.gear.pressure_angle = (90 - fp.pressure_angle.Value) * np.pi / 180.0
+        fp.gear.pitch_angle = fp.pitch_angle.Value * np.pi / 180
+        max_height = fp.gear.module * fp.teeth / 2 / np.tan(fp.gear.pitch_angle)
+        if fp.height >= max_height:
+            App.Console.PrintWarning(
+                "height must be smaller than {}".format(max_height)
+            )
+        fp.gear.backlash = fp.backlash.Value
+        scale = (
+            fp.module.Value * fp.gear.z / 2 / np.tan(fp.pitch_angle.Value * np.pi / 180)
+        )
+        fp.gear.clearance = fp.clearance / scale
+        fp.gear._update()
+        pts = list(fp.gear.points(num=fp.numpoints))
+        rot = rotation3D(2 * np.pi / fp.teeth)
+        # if fp.beta.Value != 0:
+        #     pts = [np.array([self.spherical_rot(j, fp.beta.Value * np.pi / 180.) for j in i]) for i in pts]
+
+        rotated_pts = pts
+        for i in range(fp.gear.z - 1):
+            rotated_pts = list(map(rot, rotated_pts))
+            pts.append(np.array([pts[-1][-1], rotated_pts[0][0]]))
+            pts += rotated_pts
+        pts.append(np.array([pts[-1][-1], pts[0][0]]))
+        wires = []
+        if not "version" in fp.PropertiesList:
+            scale_0 = scale - fp.height.Value / 2
+            scale_1 = scale + fp.height.Value / 2
+        else:  # starting with version 0.0.2
+            scale_0 = scale - fp.height.Value
+            scale_1 = scale
+        if fp.beta.Value == 0:
+            wires.append(make_bspline_wire([scale_0 * p for p in pts]))
+            wires.append(make_bspline_wire([scale_1 * p for p in pts]))
+        else:
+            for scale_i in np.linspace(scale_0, scale_1, 20):
+                # beta_i = (scale_i - scale_0) * fp.beta.Value * np.pi / 180
+                # rot = rotation3D(beta_i)
+                # points = [rot(pt) * scale_i for pt in pts]
+                angle = (
+                    fp.beta.Value
+                    * np.pi
+                    / 180.0
+                    * np.sin(np.pi / 4)
+                    / np.sin(fp.pitch_angle.Value * np.pi / 180.0)
+                )
+                points = [
+                    np.array([self.spherical_rot(p, angle) for p in scale_i * pt])
+                    for pt in pts
+                ]
+                wires.append(make_bspline_wire(points))
+        shape = Part.makeLoft(wires, True)
+        if fp.reset_origin:
+            mat = App.Matrix()
+            mat.A33 = -1
+            mat.move(fcvec([0, 0, scale_1]))
+            shape = shape.transformGeometry(mat)
+        return shape
+        # return self.create_teeth(pts, pos1, fp.teeth)
+
+    def create_tooth(self):
+        w = []
+        scal1 = (
+            self.obj.m.Value
+            * self.obj.gear.z
+            / 2
+            / np.tan(self.obj.pitch_angle.Value * np.pi / 180)
+            - self.obj.height.Value / 2
+        )
+        scal2 = (
+            self.obj.m.Value
+            * self.obj.gear.z
+            / 2
+            / np.tan(self.obj.pitch_angle.Value * np.pi / 180)
+            + self.obj.height.Value / 2
+        )
+        s = [scal1, scal2]
+        pts = self.obj.gear.points(num=self.obj.numpoints)
+        for j, pos in enumerate(s):
+            w1 = []
+
+            def scale(x):
+                return fcvec(x * pos)
+
+            for i in pts:
+                i_scale = list(map(scale, i))
+                w1.append(i_scale)
+            w.append(w1)
+        surfs = []
+        w_t = zip(*w)
+        for i in w_t:
+            b = Part.BSplineSurface()
+            b.interpolate(i)
+            surfs.append(b)
+        return Part.Shape(surfs)
+
+    def spherical_rot(self, point, phi):
+        new_phi = np.sqrt(np.linalg.norm(point)) * phi
+        return rotation3D(new_phi)(point)

freecad/gears/commands.py

@@ -1,28 +1,44 @@
-#***************************************************************************
+# -*- coding: utf-8 -*-
-#*                                                                         *
+# ***************************************************************************
-#*   This program is free software; you can redistribute it and/or modify  *
+# *                                                                         *
-#*   it under the terms of the GNU Lesser General Public License (LGPL)    *
+# * This program is free software: you can redistribute it and/or modify    *
-#*   as published by the Free Software Foundation; either version 2 of     *
+# * it under the terms of the GNU General Public License as published by    *
-#*   the License, or (at your option) any later version.                   *
+# * the Free Software Foundation, either version 3 of the License, or       *
-#*   for detail see the LICENCE text file.                                 *
+# * (at your option) any later version.                                     *
-#*                                                                         *
+# *                                                                         *
-#*   This program is distributed in the hope that it will be useful,       *
+# * This program is distributed in the hope that it will be useful,         *
-#*   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
-#*   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
-#*   GNU Library General Public License for more details.                  *
+# * GNU General Public License for more details.                            *
-#*                                                                         *
+# *                                                                         *
-#*   You should have received a copy of the GNU Library General Public     *
+# * You should have received a copy of the GNU General Public License       *
-#*   License along with this program; if not, write to the Free Software   *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
-#*   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  *
+# *                                                                         *
-#*   USA                                                                   *
+# ***************************************************************************
-#*                                                                         *
-#***************************************************************************
 
 import os
 import FreeCAD
 import FreeCADGui as Gui
-from .features import ViewProviderGear, involute_gear, involute_gear_rack
+
-from .features import cycloide_gear, bevel_gear, crown_gear
+from .basegear import (
+    ViewProviderGear,
+    HypoCycloidGear,
+    BaseGear,
+)
+from .timinggear_t import TimingGearT
+from .involutegear import InvoluteGear
+from .internalinvolutegear import InternalInvoluteGear
+from .involutegearrack import InvoluteGearRack
+from .cycloidgearrack import CycloidGearRack
+from .crowngear import CrownGear
+from .cycloidgear import CycloidGear
+from .bevelgear import BevelGear
+from .wormgear import WormGear
+from .timinggear import TimingGear
+from .lanterngear import LanternGear
+
+
+from .connector import GearConnector, ViewProviderGearConnector
 
 
 class BaseCommand(object):
@@ -41,54 +57,161 @@ class BaseCommand(object):
 
     def Activated(self):
         Gui.doCommandGui("import freecad.gears.commands")
-        Gui.doCommandGui("freecad.gears.commands.{}.create()".format(self.__class__.__name__))
+        Gui.doCommandGui(
+            "freecad.gears.commands.{}.create()".format(self.__class__.__name__)
+        )
         FreeCAD.ActiveDocument.recompute()
         Gui.SendMsgToActiveView("ViewFit")
 
     @classmethod
     def create(cls):
-        obj = FreeCAD.ActiveDocument.addObject("Part::FeaturePython", cls.NAME)
+        if FreeCAD.GuiUp:
-        cls.GEAR_FUNCTION(obj)
+            # borrowed from threaded profiles
-        ViewProviderGear(obj.ViewObject)
+            # puts the gear into an active container
+            body = Gui.ActiveDocument.ActiveView.getActiveObject("pdbody")
+            part = Gui.ActiveDocument.ActiveView.getActiveObject("part")
+
+            if body:
+                obj = FreeCAD.ActiveDocument.addObject(
+                    "PartDesign::FeaturePython", cls.NAME
+                )
+            else:
+                obj = FreeCAD.ActiveDocument.addObject("Part::FeaturePython", cls.NAME)
+            ViewProviderGear(obj.ViewObject, cls.Pixmap)
+            cls.GEAR_FUNCTION(obj)
+
+            if body:
+                body.addObject(obj)
+            elif part:
+                part.Group += [obj]
+        else:
+            obj = FreeCAD.ActiveDocument.addObject("Part::FeaturePython", cls.NAME)
+            cls.GEAR_FUNCTION(obj)
         return obj
 
     def GetResources(self):
-        return {'Pixmap': self.Pixmap, 
+        return {
-                'MenuText': self.MenuText, 
+            "Pixmap": self.Pixmap,
-                'ToolTip': self.ToolTip}
+            "MenuText": self.MenuText,
+            "ToolTip": self.ToolTip,
+        }
 
 
 class CreateInvoluteGear(BaseCommand):
     NAME = "InvoluteGear"
-    GEAR_FUNCTION = involute_gear
+    GEAR_FUNCTION = InvoluteGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'involutegear.svg')
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "involutegear.svg")
-    MenuText = 'involute gear'
+    MenuText = "Involute Gear"
-    ToolTip = 'involute gear'
+    ToolTip = "Create an external involute gear"
+
+
+class CreateInternalInvoluteGear(BaseCommand):
+    NAME = "InternalInvoluteGear"
+    GEAR_FUNCTION = InternalInvoluteGear
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "internalinvolutegear.svg")
+    MenuText = "Internal Involute Gear"
+    ToolTip = "Create an internal involute gear"
+
 
 class CreateInvoluteRack(BaseCommand):
     NAME = "InvoluteRack"
-    GEAR_FUNCTION = involute_gear_rack
+    GEAR_FUNCTION = InvoluteGearRack
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'involuterack.svg')
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "involuterack.svg")
-    MenuText = 'involute rack'
+    MenuText = "Involute Rack"
-    ToolTip = 'involute rack'
+    ToolTip = "Create an Involute rack"
+
+
+class CreateCycloidRack(BaseCommand):
+    NAME = "CycloidRack"
+    GEAR_FUNCTION = CycloidGearRack
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "cycloidrack.svg")
+    MenuText = "Cycloid Rack"
+    ToolTip = "Create an Cycloid rack"
+
 
 class CreateCrownGear(BaseCommand):
     NAME = "CrownGear"
-    GEAR_FUNCTION = crown_gear
+    GEAR_FUNCTION = CrownGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'crowngear.svg')
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "crowngear.svg")
-    MenuText = 'crown gear'
+    MenuText = "Crown Gear"
-    ToolTip = 'crown gear'
+    ToolTip = "Create a Crown gear"
 
-class CreateCycloideGear(BaseCommand):
+
+class CreateCycloidGear(BaseCommand):
     NAME = "CycloidGear"
-    GEAR_FUNCTION = cycloide_gear
+    GEAR_FUNCTION = CycloidGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'cycloidegear.svg')
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "cycloidgear.svg")
-    MenuText = 'cycloide gear'
+    MenuText = "Cycloid Gear"
-    ToolTip = 'cycloide gear'
+    ToolTip = "Create a Cycloid gear"
+
 
 class CreateBevelGear(BaseCommand):
     NAME = "BevelGear"
-    GEAR_FUNCTION = bevel_gear
+    GEAR_FUNCTION = BevelGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'bevelgear.svg')
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "bevelgear.svg")
-    MenuText = 'bevel gear'
+    MenuText = "Bevel Gear"
-    ToolTip = 'bevel gear'
+    ToolTip = "Create a Bevel gear"
+
+
+class CreateHypoCycloidGear(BaseCommand):
+    NAME = "HypocycloidGear"
+    GEAR_FUNCTION = HypoCycloidGear
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "hypocycloidgear.svg")
+    MenuText = "HypoCycloid Gear"
+    ToolTip = "Create a HypoCycloid gear with its pins"
+
+
+class CreateWormGear(BaseCommand):
+    NAME = "WormGear"
+    GEAR_FUNCTION = WormGear
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "wormgear.svg")
+    MenuText = "Worm Gear"
+    ToolTip = "Create a Worm gear"
+
+
+class CreateTimingGearT(BaseCommand):
+    NAME = "TimingGearT"
+    GEAR_FUNCTION = TimingGearT
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "timinggear_t.svg")
+    MenuText = "Timing Gear T-shape"
+    ToolTip = "Create a Timing gear T-shape"
+
+
+class CreateTimingGear(BaseCommand):
+    NAME = "TimingGear"
+    GEAR_FUNCTION = TimingGear
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "timinggear.svg")
+    MenuText = "Timing Gear"
+    ToolTip = "Create a Timing gear"
+
+
+class CreateLanternGear(BaseCommand):
+    NAME = "LanternGear"
+    GEAR_FUNCTION = LanternGear
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "lanterngear.svg")
+    MenuText = "Lantern Gear"
+    ToolTip = "Create a Lantern gear"
+
+
+class CreateGearConnector(BaseCommand):
+    NAME = "GearConnector"
+    GEAR_FUNCTION = GearConnector
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "gearconnector.svg")
+    MenuText = "Combine two gears"
+    ToolTip = "Combine two gears"
+
+    def Activated(self):
+        gear1 = Gui.Selection.getSelection()[0]
+        assert isinstance(gear1.Proxy, BaseGear)
+
+        gear2 = Gui.Selection.getSelection()[1]
+        assert isinstance(gear2.Proxy, BaseGear)
+
+        # check if selected objects are beams
+
+        obj = FreeCAD.ActiveDocument.addObject("Part::FeaturePython", self.NAME)
+        GearConnector(obj, gear1, gear2)
+        ViewProviderGearConnector(obj.ViewObject)
+
+        FreeCAD.ActiveDocument.recompute()
+        return obj

freecad/gears/connector.py

@@ -0,0 +1,208 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import os
+import sys
+import numpy as np
+import FreeCAD
+from pygears import __version__
+
+from .involutegear import InvoluteGear
+from .internalinvolutegear import InternalInvoluteGear
+from .involutegearrack import InvoluteGearRack
+from .cycloidgear import CycloidGear
+from .cycloidgearrack import CycloidGearRack
+from pygears.computation import compute_shifted_gears
+
+
+class ViewProviderGearConnector(object):
+    def __init__(self, vobj, icon_fn=None):
+        # Set this object to the proxy object of the actual view provider
+        vobj.Proxy = self
+        dirname = os.path.dirname(__file__)
+        self.icon_fn = icon_fn or os.path.join(dirname, "icons", "gearconnector.svg")
+
+    def attach(self, vobj):
+        self.vobj = vobj
+
+    def getIcon(self):
+        return self.icon_fn
+
+    if sys.version_info[0] == 3 and sys.version_info[1] >= 11:
+
+        def dumps(self):
+            return {"icon_fn": self.icon_fn}
+
+        def loads(self, state):
+            self.icon_fn = state["icon_fn"]
+    else:
+
+        def __getstate__(self):
+            return {"icon_fn": self.icon_fn}
+
+        def __setstate__(self, state):
+            self.icon_fn = state["icon_fn"]
+
+
+class GearConnector(object):
+    def __init__(self, obj, master_gear, slave_gear):
+        obj.addProperty(
+            "App::PropertyString", "version", "version", "freecad.gears-version", 1
+        )
+        obj.addProperty("App::PropertyLink", "master_gear", "gear", "master gear", 1)
+        obj.addProperty("App::PropertyLink", "slave_gear", "gear", "slave gear", 1)
+        obj.addProperty(
+            "App::PropertyAngle",
+            "angle1",
+            "gear",
+            "angle at which second gear is placed",
+            0,
+        )
+        obj.addProperty(
+            "App::PropertyAngle",
+            "angle2",
+            "gear",
+            "angle at which second gear is placed",
+            1,
+        )
+        obj.version = __version__
+        obj.master_gear = master_gear
+        obj.slave_gear = slave_gear
+        obj.angle1 = 0
+        obj.angle2 = 0
+        obj.Proxy = self
+
+    def onChanged(self, fp, prop):
+        # fp.angle2 = fp.master_gear.Placement.Rotation.Angle
+        if isinstance(fp.master_gear.Proxy, InvoluteGear) and isinstance(
+            fp.slave_gear.Proxy, InvoluteGear
+        ):
+            angle_master = fp.master_gear.Placement.Rotation.Angle * sum(
+                fp.master_gear.Placement.Rotation.Axis
+            )
+            dw_master = fp.master_gear.dw
+            dw_slave = fp.slave_gear.dw
+            dist = (dw_master + dw_slave) / 2
+            if fp.master_gear.shift != 0 or fp.slave_gear.shift != 0:
+                dist, alpha_w = compute_shifted_gears(
+                    fp.master_gear.module,
+                    np.deg2rad(fp.master_gear.pressure_angle.Value),
+                    fp.master_gear.teeth,
+                    fp.slave_gear.teeth,
+                    fp.master_gear.shift,
+                    fp.slave_gear.shift,
+                )
+
+            mat0 = FreeCAD.Matrix()  # unity matrix
+            trans = FreeCAD.Vector(dist)
+            mat0.move(trans)
+            rot = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), fp.angle1).toMatrix()
+            angle2 = dw_master / dw_slave * fp.angle1.Value
+            angle4 = dw_master / dw_slave * np.rad2deg(angle_master)
+            rot2 = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), angle2).toMatrix()
+            angle3 = abs(fp.slave_gear.teeth % 2 - 1) * 180.0 / fp.slave_gear.teeth
+            rot3 = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), angle3).toMatrix()
+            rot4 = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), -angle4).toMatrix()
+            mat1 = rot * mat0 * rot2 * rot3 * rot4
+            mat1.move(fp.master_gear.Placement.Base)
+            fp.slave_gear.Placement = mat1
+
+        if isinstance(fp.master_gear.Proxy, InternalInvoluteGear) and isinstance(
+            fp.slave_gear.Proxy, InvoluteGear
+        ):
+            angle_master = fp.master_gear.Placement.Rotation.Angle * sum(
+                fp.master_gear.Placement.Rotation.Axis
+            )
+            dw_master = fp.master_gear.dw
+            dw_slave = fp.slave_gear.dw
+            dist = (dw_master - dw_slave) / 2
+            if fp.master_gear.shift != 0 or fp.slave_gear.shift != 0:
+                dist, alpha_w = compute_shifted_gears(
+                    fp.master_gear.module,
+                    np.deg2rad(fp.master_gear.pressure_angle.Value),
+                    fp.master_gear.teeth,
+                    fp.slave_gear.teeth,
+                    fp.master_gear.shift,
+                    fp.slave_gear.shift,
+                )
+
+            mat0 = FreeCAD.Matrix()  # unity matrix
+            trans = FreeCAD.Vector(dist)
+            mat0.move(trans)
+            rot = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), fp.angle1).toMatrix()
+            angle2 = -dw_master / dw_slave * fp.angle1.Value
+            angle4 = -dw_master / dw_slave * np.rad2deg(angle_master)
+            rot2 = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), angle2).toMatrix()
+            angle3 = abs(fp.slave_gear.teeth % 2 - 1) * 180.0 / fp.slave_gear.teeth
+            rot3 = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), angle3).toMatrix()
+            rot4 = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), -angle4).toMatrix()
+            mat1 = rot * mat0 * rot2 * rot3 * rot4
+            mat1.move(fp.master_gear.Placement.Base)
+            fp.slave_gear.Placement = mat1
+
+        if (
+            isinstance(fp.master_gear.Proxy, InvoluteGear)
+            and isinstance(fp.slave_gear.Proxy, InvoluteGearRack)
+        ) or (
+            isinstance(fp.master_gear.Proxy, CycloidGear)
+            and isinstance(fp.slave_gear.Proxy, CycloidGearRack)
+        ):
+            angle_master = fp.master_gear.Placement.Rotation.Angle * sum(
+                fp.master_gear.Placement.Rotation.Axis
+            )
+            dw_master = fp.master_gear.dw.Value
+            dw_slave = 0
+            dist = -(dw_master + dw_slave) / 2
+            mat0 = FreeCAD.Matrix()  # unity matrix
+            mat0.move(FreeCAD.Vector(dist, 0, 0))
+            mat1 = FreeCAD.Matrix()
+            mat1.move(FreeCAD.Vector(0, np.deg2rad(fp.angle1.Value) * dw_master / 2, 0))
+            mat2 = FreeCAD.Matrix()
+            mat2.move(
+                FreeCAD.Vector(0, -np.deg2rad(fp.angle2.Value) * dw_master / 2, 0)
+            )
+            rot = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), fp.angle1).toMatrix()
+            mat3 = rot * mat2 * mat1 * mat0
+            mat3.move(fp.master_gear.Placement.Base)
+            fp.slave_gear.Placement = mat3
+
+        if isinstance(fp.master_gear.Proxy, CycloidGear) and isinstance(
+            fp.slave_gear.Proxy, CycloidGear
+        ):
+            angle_master = fp.master_gear.Placement.Rotation.Angle * sum(
+                fp.master_gear.Placement.Rotation.Axis
+            )
+            dw_master = fp.master_gear.dw
+            dw_slave = fp.slave_gear.dw
+            dist = (dw_master + dw_slave) / 2
+            mat0 = FreeCAD.Matrix()  # unity matrix
+            trans = FreeCAD.Vector(dist, 0, 0)
+            mat0.move(trans)
+            rot = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), fp.angle1).toMatrix()
+            angle2 = dw_master / dw_slave * fp.angle1.Value
+            angle4 = dw_master / dw_slave * np.rad2deg(angle_master)
+            rot2 = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), angle2).toMatrix()
+            angle3 = abs(fp.slave_gear.teeth % 2 - 1) * 180.0 / fp.slave_gear.teeth
+            rot3 = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), angle3).toMatrix()
+            rot4 = FreeCAD.Rotation(FreeCAD.Vector(0, 0, 1), -angle4).toMatrix()
+            mat1 = rot * mat0 * rot2 * rot3 * rot4
+            mat1.move(fp.master_gear.Placement.Base)
+            fp.slave_gear.Placement = mat1
+
+    def execute(self, fp):
+        self.onChanged(fp, None)

freecad/gears/crowngear.py

@@ -0,0 +1,143 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import os
+import sys
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+
+from .basegear import BaseGear, fcvec
+
+
+class CrownGear(BaseGear):
+    def __init__(self, obj):
+        super(CrownGear, self).__init__(obj)
+        obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
+        obj.addProperty(
+            "App::PropertyInteger",
+            "other_teeth",
+            "base",
+            "number of teeth of other gear",
+        )
+        obj.addProperty("App::PropertyLength", "module", "base", "module")
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+        obj.addProperty("App::PropertyLength", "thickness", "base", "thickness")
+        obj.addProperty(
+            "App::PropertyAngle", "pressure_angle", "involute", "pressure angle"
+        )
+        self.add_accuracy_properties(obj)
+        obj.teeth = 15
+        obj.other_teeth = 15
+        obj.module = "1. mm"
+        obj.pressure_angle = "20. deg"
+        obj.height = "2. mm"
+        obj.thickness = "5 mm"
+        obj.num_profiles = 4
+        obj.preview_mode = True
+        self.obj = obj
+        obj.Proxy = self
+
+        App.Console.PrintMessage(
+            "Gear module: Crown gear created, preview_mode = true for improved performance. "
+            "Set preview_mode property to false when ready to cut teeth."
+        )
+
+    def add_accuracy_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyInteger",
+            "num_profiles",
+            "accuracy",
+            "number of profiles used for loft",
+        )
+        obj.addProperty(
+            "App::PropertyBool",
+            "preview_mode",
+            "accuracy",
+            "if true no boolean operation is done",
+        )
+
+    def profile(self, m, r, r0, t_c, t_i, alpha_w, y0, y1, y2):
+        r_ew = m * t_i / 2
+
+        # 1: modifizierter Waelzkreisdurchmesser:
+        r_e = r / r0 * r_ew
+
+        # 2: modifizierter Schraegungswinkel:
+        alpha = np.arccos(r0 / r * np.cos(alpha_w))
+
+        # 3: winkel phi bei senkrechter stellung eines zahns:
+        phi = np.pi / t_i / 2 + (alpha - alpha_w) + (np.tan(alpha_w) - np.tan(alpha))
+
+        # 4: Position des Eingriffspunktes:
+        x_c = r_e * np.sin(phi)
+        dy = -r_e * np.cos(phi) + r_ew
+
+        # 5: oberer Punkt:
+        b = y1 - dy
+        a = np.tan(alpha) * b
+        x1 = a + x_c
+
+        # 6: unterer Punkt
+        d = y2 + dy
+        c = np.tan(alpha) * d
+        x2 = x_c - c
+
+        r *= np.cos(phi)
+        pts = [[-x1, r, y0], [-x2, r, y0 - y1 - y2], [x2, r, y0 - y1 - y2], [x1, r, y0]]
+        pts.append(pts[0])
+        return pts
+
+    def generate_gear_shape(self, fp):
+        inner_diameter = fp.module.Value * fp.teeth
+        outer_diameter = inner_diameter + fp.height.Value * 2
+        inner_circle = Part.Wire(Part.makeCircle(inner_diameter / 2.0))
+        outer_circle = Part.Wire(Part.makeCircle(outer_diameter / 2.0))
+        inner_circle.reverse()
+        face = Part.Face([outer_circle, inner_circle])
+        solid = face.extrude(App.Vector([0.0, 0.0, -fp.thickness.Value]))
+        if fp.preview_mode:
+            return solid
+
+        # cutting obj
+        alpha_w = np.deg2rad(fp.pressure_angle.Value)
+        m = fp.module.Value
+        t = fp.teeth
+        t_c = t
+        t_i = fp.other_teeth
+        rm = inner_diameter / 2
+        y0 = m * 0.5
+        y1 = m + y0
+        y2 = m
+        r0 = inner_diameter / 2 - fp.height.Value * 0.1
+        r1 = outer_diameter / 2 + fp.height.Value * 0.3
+        polies = []
+        for r_i in np.linspace(r0, r1, fp.num_profiles):
+            pts = self.profile(m, r_i, rm, t_c, t_i, alpha_w, y0, y1, y2)
+            poly = Part.Wire(Part.makePolygon(list(map(fcvec, pts))))
+            polies.append(poly)
+        loft = Part.makeLoft(polies, True)
+        rot = App.Matrix()
+        rot.rotateZ(2 * np.pi / t)
+        cut_shapes = []
+        for _ in range(t):
+            loft = loft.transformGeometry(rot)
+            cut_shapes.append(loft)
+        return solid.cut(cut_shapes)

freecad/gears/cycloidgear.py

@@ -0,0 +1,193 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+from pygears.cycloid_tooth import CycloidTooth
+from pygears._functions import rotation
+
+from .basegear import (
+    BaseGear,
+    points_to_wire,
+    insert_fillet,
+    helicalextrusion,
+    rotate_tooth,
+)
+
+
+class CycloidGear(BaseGear):
+    """FreeCAD gear"""
+
+    def __init__(self, obj):
+        super(CycloidGear, self).__init__(obj)
+        self.cycloid_tooth = CycloidTooth()
+        obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
+        obj.addProperty("App::PropertyLength", "module", "base", "module")
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+
+        obj.addProperty(
+            "App::PropertyInteger",
+            "numpoints",
+            "accuracy",
+            "number of points for spline",
+        )
+        obj.addProperty(
+            "App::PropertyPythonObject", "gear", "base", "the python object"
+        )
+
+        self.add_helical_properties(obj)
+        self.add_fillet_properties(obj)
+        self.add_tolerance_properties(obj)
+        self.add_cycloid_properties(obj)
+        self.add_computed_properties(obj)
+        obj.gear = self.cycloid_tooth
+        obj.teeth = 15
+        obj.module = "1. mm"
+        obj.setExpression(
+            "inner_diameter", "teeth / 2"
+        )  # teeth/2 makes the hypocycloid a straight line to the center
+        obj.outer_diameter = 7.5  # we don't know the mating gear, so we just set the default to mesh with our default
+        obj.beta = "0. deg"
+        obj.height = "5. mm"
+        obj.clearance = 0.25
+        obj.numpoints = 15
+        obj.backlash = "0.00 mm"
+        obj.double_helix = False
+        obj.head = 0
+        obj.head_fillet = 0
+        obj.root_fillet = 0
+        obj.Proxy = self
+
+    def add_helical_properties(self, obj):
+        obj.addProperty("App::PropertyBool", "double_helix", "helical", "double helix")
+        obj.addProperty("App::PropertyAngle", "beta", "helical", "beta")
+
+    def add_fillet_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head_fillet",
+            "fillets",
+            "a fillet for the tooth-head, radius = head_fillet x module",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "root_fillet",
+            "fillets",
+            "a fillet for the tooth-root, radius = root_fillet x module",
+        )
+
+    def add_tolerance_properties(self, obj):
+        obj.addProperty("App::PropertyFloat", "clearance", "tolerance", "clearance")
+        obj.addProperty(
+            "App::PropertyLength",
+            "backlash",
+            "tolerance",
+            "The arc length on the pitch circle by which the tooth thicknes is reduced.",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head",
+            "tolerance",
+            "head_value * modul_value = additional length of head",
+        )
+
+    def add_cycloid_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyFloat",
+            "inner_diameter",
+            "cycloid",
+            "inner_diameter divided by module (hypocycloid)",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "outer_diameter",
+            "cycloid",
+            "outer_diameter divided by module (epicycloid)",
+        )
+
+    def add_computed_properties(self, obj):
+        obj.addProperty("App::PropertyLength", "dw", "computed", "The pitch diameter.")
+        obj.setExpression(
+            "dw", "teeth * module"
+        )  # calculate via expression to ease usage for placement
+        obj.setEditorMode(
+            "dw", 1
+        )  # set read-only after setting the expression, else it won't be visible. bug?
+        obj.addProperty(
+            "App::PropertyAngle",
+            "angular_backlash",
+            "computed",
+            "The angle by which this gear can turn without moving the mating gear.",
+        )
+        obj.setExpression(
+            "angular_backlash", "backlash / dw * 360° / pi"
+        )  # calculate via expression to ease usage for placement
+        obj.setEditorMode(
+            "angular_backlash", 1
+        )  # set read-only after setting the expression, else it won't be visible. bug?
+
+    def generate_gear_shape(self, fp):
+        fp.gear.m = fp.module.Value
+        fp.gear.z = fp.teeth
+        fp.dw = fp.module * fp.teeth
+        fp.gear.z1 = fp.inner_diameter
+        fp.gear.z2 = fp.outer_diameter
+        fp.gear.clearance = fp.clearance
+        fp.gear.head = fp.head
+        fp.gear.backlash = fp.backlash.Value
+        fp.gear._update()
+
+        pts = fp.gear.points(num=fp.numpoints)
+        rot = rotation(-fp.gear.phipart)
+        rotated_pts = list(map(rot, pts))
+        pts.append([pts[-1][-1], rotated_pts[0][0]])
+        pts += rotated_pts
+        tooth = points_to_wire(pts)
+        edges = tooth.Edges
+
+        r_head = float(fp.head_fillet * fp.module)
+        r_root = float(fp.root_fillet * fp.module)
+
+        pos_head = [0, 2, 6]
+        pos_root = [4, 6]
+        edge_range = [1, 9]
+
+        for pos in pos_head:
+            edges = insert_fillet(edges, pos, r_head)
+
+        for pos in pos_root:
+            edges = insert_fillet(edges, pos, r_root)
+
+        edges = edges[edge_range[0] : edge_range[1]]
+        edges = [e for e in edges if e is not None]
+
+        tooth = Part.Wire(edges)
+
+        profile = rotate_tooth(tooth, fp.teeth)
+        if fp.height.Value == 0:
+            return profile
+        base = Part.Face(profile)
+        if fp.beta.Value == 0:
+            return base.extrude(App.Vector(0, 0, fp.height.Value))
+        else:
+            twist_angle = (
+                fp.height.Value * np.tan(fp.beta.Value * np.pi / 180) * 2 / fp.gear.d
+            )
+            return helicalextrusion(base, fp.height.Value, twist_angle, fp.double_helix)

freecad/gears/cycloidgearrack.py

@@ -0,0 +1,232 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import os
+import sys
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+
+from pygears._functions import reflection
+from .basegear import BaseGear, fcvec, points_to_wire, insert_fillet
+
+
+class CycloidGearRack(BaseGear):
+
+    """FreeCAD gear rack"""
+
+    def __init__(self, obj):
+        super(CycloidGearRack, self).__init__(obj)
+        obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+        obj.addProperty("App::PropertyLength", "thickness", "base", "thickness")
+        obj.addProperty("App::PropertyLength", "module", "involute", "module")
+        obj.addProperty(
+            "App::PropertyBool",
+            "simplified",
+            "precision",
+            "if enabled the rack is drawn with a constant number of \
+            teeth to avoid topologic renaming.",
+        )
+        obj.addProperty(
+            "App::PropertyInteger",
+            "numpoints",
+            "accuracy",
+            "number of points for spline",
+        )
+        obj.addProperty("App::PropertyPythonObject", "rack", "base", "test")
+
+        self.add_helical_properties(obj)
+        self.add_computed_properties(obj)
+        self.add_tolerance_properties(obj)
+        self.add_cycloid_properties(obj)
+        self.add_fillet_properties(obj)
+        obj.teeth = 15
+        obj.module = "1. mm"
+        obj.inner_diameter = 7.5
+        obj.outer_diameter = 7.5
+        obj.height = "5. mm"
+        obj.thickness = "5 mm"
+        obj.beta = "0. deg"
+        obj.clearance = 0.25
+        obj.head = 0.0
+        obj.add_endings = True
+        obj.simplified = False
+        obj.numpoints = 15
+        self.obj = obj
+        obj.Proxy = self
+
+    def add_helical_properties(self, obj):
+        obj.addProperty("App::PropertyAngle", "beta", "helical", "beta ")
+        obj.addProperty("App::PropertyBool", "double_helix", "helical", "double helix")
+
+    def add_computed_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyLength",
+            "transverse_pitch",
+            "computed",
+            "pitch in the transverse plane",
+            1,
+        )
+        obj.addProperty(
+            "App::PropertyBool",
+            "add_endings",
+            "base",
+            "if enabled the total length of the rack is teeth x pitch, \
+            otherwise the rack starts with a tooth-flank",
+        )
+
+    def add_tolerance_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head",
+            "tolerance",
+            "head * module = additional length of head",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "clearance",
+            "tolerance",
+            "clearance * module = additional length of root",
+        )
+
+    def add_cycloid_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyFloat",
+            "inner_diameter",
+            "cycloid",
+            "inner_diameter divided by module (hypocycloid)",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "outer_diameter",
+            "cycloid",
+            "outer_diameter divided by module (epicycloid)",
+        )
+
+    def add_fillet_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head_fillet",
+            "fillets",
+            "a fillet for the tooth-head, radius = head_fillet x module",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "root_fillet",
+            "fillets",
+            "a fillet for the tooth-root, radius = root_fillet x module",
+        )
+
+    def generate_gear_shape(self, obj):
+        numpoints = obj.numpoints
+        m = obj.module.Value
+        t = obj.thickness.Value
+        r_i = obj.inner_diameter / 2 * m
+        r_o = obj.outer_diameter / 2 * m
+        c = obj.clearance
+        h = obj.head
+        head_fillet = obj.head_fillet
+        root_fillet = obj.root_fillet
+        phi_i_end = np.arccos(1 - m / r_i * (1 + c))
+        phi_o_end = np.arccos(1 - m / r_o * (1 + h))
+        phi_i = np.linspace(phi_i_end, 0, numpoints)
+        phi_o = np.linspace(0, phi_o_end, numpoints)
+        y_i = r_i * (np.cos(phi_i) - 1)
+        y_o = r_o * (1 - np.cos(phi_o))
+        x_i = r_i * (np.sin(phi_i) - phi_i) - m * np.pi / 4
+        x_o = r_o * (phi_o - np.sin(phi_o)) - m * np.pi / 4
+        x = x_i.tolist()[:-1] + x_o.tolist()
+        y = y_i.tolist()[:-1] + y_o.tolist()
+        points = np.array([y, x]).T
+        mirror = reflection(0)
+        points_1 = mirror(points)[::-1]
+        line_1 = [points[-1], points_1[0]]
+        line_2 = [points_1[-1], np.array([-(1 + c) * m, m * np.pi / 2])]
+        line_0 = [np.array([-(1 + c) * m, -m * np.pi / 2]), points[0]]
+        tooth = points_to_wire([line_0, points, line_1, points_1, line_2])
+
+        edges = tooth.Edges
+        edges = insert_fillet(edges, 0, m * root_fillet)
+        edges = insert_fillet(edges, 2, m * head_fillet)
+        edges = insert_fillet(edges, 4, m * head_fillet)
+        edges = insert_fillet(edges, 6, m * root_fillet)
+
+        tooth_edges = [e for e in edges if e is not None]
+        p_end = np.array(tooth_edges[-2].lastVertex().Point[:-1])
+        p_start = np.array(tooth_edges[1].firstVertex().Point[:-1])
+        p_start += np.array([0, np.pi * m])
+        edge = points_to_wire([[p_end, p_start]]).Edges
+        tooth = Part.Wire(tooth_edges[1:-1] + edge)
+        teeth = [tooth]
+
+        for i in range(obj.teeth - 1):
+            tooth = tooth.copy()
+            tooth.translate(App.Vector(0, np.pi * m, 0))
+            teeth.append(tooth)
+
+        teeth[-1] = Part.Wire(teeth[-1].Edges[:-1])
+
+        if obj.add_endings:
+            teeth = [Part.Wire(tooth_edges[0])] + teeth
+            last_edge = tooth_edges[-1]
+            last_edge.translate(App.Vector(0, np.pi * m * (obj.teeth - 1), 0))
+            teeth = teeth + [Part.Wire(last_edge)]
+
+        p_start = np.array(teeth[0].Edges[0].firstVertex().Point[:-1])
+        p_end = np.array(teeth[-1].Edges[-1].lastVertex().Point[:-1])
+        p_start_1 = p_start - np.array([obj.thickness.Value, 0.0])
+        p_end_1 = p_end - np.array([obj.thickness.Value, 0.0])
+
+        line6 = [p_start, p_start_1]
+        line7 = [p_start_1, p_end_1]
+        line8 = [p_end_1, p_end]
+
+        bottom = points_to_wire([line6, line7, line8])
+
+        pol = Part.Wire([bottom] + teeth)
+
+        if obj.height.Value == 0:
+            return pol
+        elif obj.beta.Value == 0:
+            face = Part.Face(Part.Wire(pol))
+            return face.extrude(fcvec([0.0, 0.0, obj.height.Value]))
+        elif obj.double_helix:
+            beta = obj.beta.Value * np.pi / 180.0
+            pol2 = Part.Wire(pol)
+            pol2.translate(
+                fcvec([0.0, np.tan(beta) * obj.height.Value / 2, obj.height.Value / 2])
+            )
+            pol3 = Part.Wire(pol)
+            pol3.translate(fcvec([0.0, 0.0, obj.height.Value]))
+            return Part.makeLoft([pol, pol2, pol3], True, True)
+        else:
+            beta = obj.beta.Value * np.pi / 180.0
+            pol2 = Part.Wire(pol)
+            pol2.translate(
+                fcvec([0.0, np.tan(beta) * obj.height.Value, obj.height.Value])
+            )
+            return Part.makeLoft([pol, pol2], True)
+
+    def __getstate__(self):
+        return None
+
+    def __setstate__(self, state):
+        return None

freecad/gears/features.py

@@ -1,611 +1,33 @@
 # -*- coding: utf-8 -*-
-#***************************************************************************
+# ***************************************************************************
-#*                                                                         *
+# *                                                                         *
-#*   This program is free software; you can redistribute it and/or modify  *
+# * This program is free software: you can redistribute it and/or modify    *
-#*   it under the terms of the GNU Lesser General Public License (LGPL)    *
+# * it under the terms of the GNU General Public License as published by    *
-#*   as published by the Free Software Foundation; either version 2 of     *
+# * the Free Software Foundation, either version 3 of the License, or       *
-#*   the License, or (at your option) any later version.                   *
+# * (at your option) any later version.                                     *
-#*   for detail see the LICENCE text file.                                 *
+# *                                                                         *
-#*                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
-#*   This program is distributed in the hope that it will be useful,       *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
-#*   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
-#*   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
+# * GNU General Public License for more details.                            *
-#*   GNU Library General Public License for more details.                  *
+# *                                                                         *
-#*                                                                         *
+# * You should have received a copy of the GNU General Public License       *
-#*   You should have received a copy of the GNU Library General Public     *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
-#*   License along with this program; if not, write to the Free Software   *
+# *                                                                         *
-#*   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  *
+# ***************************************************************************
-#*   USA                                                                   *
+
-#*                                                                         *
+
-#***************************************************************************
+# this file is only for backwards compatibility
-
+
-from __future__ import division
+from .timinggear_t import TimingGearT
-import os
+from .involutegear import InvoluteGear
-
+from .internalinvolutegear import InternalInvoluteGear
-import numpy as np
+from .involutegearrack import InvoluteGearRack
-from pygears.involute_tooth import involute_tooth, involute_rack
+from .cycloidgearrack import CycloidGearRack
-from pygears.cycloide_tooth import cycloide_tooth
+from .crowngear import CrownGear
-from pygears.bevel_tooth import bevel_tooth
+from .cycloidgear import CycloidGear
-from pygears._functions import rotation3D, rotation
+from .bevelgear import BevelGear
-
+from .wormgear import WormGear
-
+from .timinggear import TimingGear
-import FreeCAD as App
+from .lanterngear import LanternGear
-import Part
+from .basegear import ViewProviderGear, BaseGear
-from Part import BSplineCurve, Shape, Wire, Face, makePolygon, \
-    BRepOffsetAPI, Shell, makeLoft, Solid, Line, BSplineSurface, makeCompound,\
-    show, makePolygon, makeHelix, makeShell, makeSolid
-
-
-
-
-__all__=["involute_gear",
-         "cycloide_gear",
-         "bevel_gear", 
-         "involute_gear_rack",
-         "ViewProviderGear"]
-
-def fcvec(x):
-    if len(x) == 2:
-        return(App.Vector(x[0], x[1], 0))
-    else:
-        return(App.Vector(x[0], x[1], x[2]))
-
-class ViewProviderGear(object):
-    def __init__(self, obj):
-        ''' Set this object to the proxy object of the actual view provider '''
-        obj.Proxy = self
-
-    def attach(self, vobj):
-        self.vobj = vobj
-
-    def getIcon(self):
-        __dirname__ = os.path.dirname(__file__)
-        return(os.path.join(__dirname__, "icons", "involutegear.svg"))
-
-    def __getstate__(self):
-        return None
-
-    def __setstate__(self, state):
-        return None
-
-class involute_gear(object):
-
-    """FreeCAD gear"""
-
-    def __init__(self, obj):
-        self.involute_tooth = involute_tooth()
-        obj.addProperty(
-            "App::PropertyBool", "simple", "gear_parameter", "simple")
-        obj.addProperty("App::PropertyInteger",
-                        "teeth", "gear_parameter", "number of teeth")
-        obj.addProperty(
-            "App::PropertyLength", "module", "gear_parameter", "module")
-        obj.addProperty(
-            "App::PropertyBool", "undercut", "gear_parameter", "undercut")
-        obj.addProperty(
-            "App::PropertyFloat", "shift", "gear_parameter", "shift")
-        obj.addProperty(
-            "App::PropertyLength", "height", "gear_parameter", "height")
-        obj.addProperty(
-            "App::PropertyAngle", "pressure_angle", "involute_parameter", "pressure angle")
-        obj.addProperty(
-            "App::PropertyFloat", "clearance", "gear_parameter", "clearance")
-        obj.addProperty("App::PropertyInteger", "numpoints",
-                        "gear_parameter", "number of points for spline")
-        obj.addProperty(
-            "App::PropertyAngle", "beta", "gear_parameter", "beta ")
-        obj.addProperty(
-            "App::PropertyBool", "double_helix", "gear_parameter", "double helix")
-        obj.addProperty(
-            "App::PropertyLength", "backlash", "tolerance", "backlash")
-        obj.addProperty(
-            "App::PropertyBool", "reversed_backlash", "tolerance", "backlash direction")
-        obj.addProperty(
-            "App::PropertyFloat", "head", "gear_parameter", "head_value * modul_value = additional length of head")
-        obj.addProperty("App::PropertyPythonObject", "gear", "gear_parameter", "test")
-        obj.addProperty("App::PropertyFloat", "dw", "computed", "pitch diameter", 1)
-        obj.gear = self.involute_tooth
-        obj.simple = False
-        obj.undercut = False
-        obj.teeth = 15
-        obj.module = '1. mm'
-        obj.shift = 0.
-        obj.pressure_angle = '20. deg'
-        obj.beta = '0. deg'
-        obj.height = '5. mm'
-        obj.clearance = 0.25
-        obj.head = 0.
-        obj.numpoints = 6
-        obj.double_helix = False
-        obj.backlash = '0.00 mm'
-        obj.reversed_backlash = False
-        self.obj = obj
-        obj.Proxy = self
-
-    def execute(self, fp):
-        fp.gear.double_helix = fp.double_helix
-        fp.gear.m_n = fp.module.Value
-        fp.gear.z = fp.teeth
-        fp.gear.undercut = fp.undercut
-        fp.gear.shift = fp.shift
-        fp.gear.pressure_angle = fp.pressure_angle.Value * np.pi / 180.
-        fp.gear.beta = fp.beta.Value * np.pi / 180
-        fp.gear.clearance = fp.clearance
-        fp.gear.backlash = fp.backlash.Value * (-fp.reversed_backlash + 0.5) * 2.
-        fp.gear.head = fp.head
-        fp.gear._update()
-        pts = fp.gear.points(num=fp.numpoints)
-        rotated_pts = pts
-        rot = rotation(-fp.gear.phipart)
-        for i in range(fp.gear.z - 1):
-            rotated_pts = list(map(rot, rotated_pts))
-            pts.append(np.array([pts[-1][-1], rotated_pts[0][0]]))
-            pts += rotated_pts
-        pts.append(np.array([pts[-1][-1], pts[0][0]]))
-        if not fp.simple:
-            wi = []
-            for i in pts:
-                out = BSplineCurve()
-                out.interpolate(list(map(fcvec, i)))
-                wi.append(out.toShape())
-            wi = Wire(wi)
-            if fp.beta.Value == 0:
-                sh = Face(wi)
-                fp.Shape = sh.extrude(App.Vector(0, 0, fp.height.Value))
-            else:
-                fp.Shape = helicalextrusion(
-                    wi, fp.height.Value, fp.height.Value * np.tan(fp.gear.beta) * 2 / fp.gear.d, fp.double_helix)
-        else:
-            rw = fp.gear.dw / 2
-            fp.Shape=Part.makeCylinder(rw,fp.height.Value)
-
-        fp.dw = fp.gear.dw
-
-    def __getstate__(self):
-        return None
-
-    def __setstate__(self, state):
-        return None
-
-
-class involute_gear_rack(object):
-
-    """FreeCAD gear rack"""
-
-    def __init__(self, obj):
-        self.involute_rack = involute_rack()
-        obj.addProperty("App::PropertyInteger",
-                        "teeth", "gear_parameter", "number of teeth")
-        obj.addProperty(
-            "App::PropertyLength", "module", "gear_parameter", "module")
-        obj.addProperty(
-            "App::PropertyLength", "height", "gear_parameter", "height")
-        obj.addProperty(
-            "App::PropertyLength", "thickness", "gear_parameter", "thickness")
-        obj.addProperty(
-            "App::PropertyAngle", "beta", "gear_parameter", "beta ")
-        obj.addProperty(
-            "App::PropertyAngle", "pressure_angle", "involute_parameter", "pressure angle")
-        obj.addProperty(
-            "App::PropertyBool", "double_helix", "gear_parameter", "double helix")
-        obj.addProperty(
-            "App::PropertyFloat", "head", "gear_parameter", "head_value * modul_value = additional length of head")
-        obj.addProperty("App::PropertyPythonObject", "rack", "test", "test")
-        obj.rack = self.involute_rack
-        obj.teeth = 15
-        obj.module = '1. mm'
-        obj.pressure_angle = '20. deg'
-        obj.height = '5. mm'
-        obj.thickness = '5 mm'
-        obj.beta = '0. deg'
-        self.obj = obj
-        obj.Proxy = self
-
-    def execute(self, fp):
-        fp.rack.m = fp.module.Value
-        fp.rack.z = fp.teeth
-        fp.rack.pressure_angle = fp.pressure_angle.Value * np.pi / 180.
-        fp.rack.thickness = fp.thickness.Value
-        fp.rack.beta = fp.beta.Value * np.pi / 180.
-        fp.rack.head = fp.head
-        fp.rack._update()
-        pts = fp.rack.points()
-        pol = Wire(makePolygon(list(map(fcvec, pts))))
-        if fp.beta.Value == 0:
-            face = Face(Wire(pol))
-            fp.Shape = face.extrude(fcvec([0., 0., fp.height.Value]))
-        elif fp.double_helix:
-            beta = fp.beta.Value * np.pi / 180.
-            pol2 = Part.Wire(pol)
-            pol2.translate(fcvec([0., np.tan(beta) * fp.height.Value / 2, fp.height.Value / 2]))
-            pol3 = Part.Wire(pol)
-            pol3.translate(fcvec([0., 0., fp.height.Value]))
-            fp.Shape = makeLoft([pol, pol2, pol3], True, True)
-        else:
-            beta = fp.beta.Value * np.pi / 180.
-            pol2 = Part.Wire(pol)
-            pol2.translate(fcvec([0., np.tan(beta) * fp.height.Value, fp.height.Value]))
-            fp.Shape = makeLoft([pol, pol2], True)
-
-    def __getstate__(self):
-        return None
-
-    def __setstate__(self, state):
-        return None
-
-
-class crown_gear(object):
-    def __init__(self, obj):
-        obj.addProperty("App::PropertyInteger",
-                        "teeth", "gear_parameter", "number of teeth")
-        obj.addProperty("App::PropertyInteger",
-                        "other_teeth", "gear_parameter", "number of teeth of other gear")
-        obj.addProperty(
-            "App::PropertyLength", "module", "gear_parameter", "module")
-        obj.addProperty(
-            "App::PropertyLength", "height", "gear_parameter", "height")
-        obj.addProperty(
-            "App::PropertyLength", "thickness", "gear_parameter", "thickness")
-        obj.addProperty(
-            "App::PropertyAngle", "pressure_angle", "involute_parameter", "pressure angle")
-        obj.addProperty("App::PropertyInteger",
-                        "num_profiles", "accuracy", "number of profiles used for loft")
-        obj.addProperty("App::PropertyBool",
-                        "construct", "accuracy", "number of profiles used for loft")
-        obj.teeth = 15
-        obj.other_teeth = 15
-        obj.module = '1. mm'
-        obj.pressure_angle = '20. deg'
-        obj.height = '2. mm'
-        obj.thickness = '5 mm'
-        obj.num_profiles = 4
-        obj.construct = True
-        self.obj = obj
-        obj.Proxy = self
-
-
-    def profile(self, m, r, r0, t_c, t_i, alpha_w, y0, y1, y2):
-        r_ew = m * t_i / 2
-
-        # 1: modifizierter Waelzkreisdurchmesser:
-        r_e = r / r0 * r_ew
-
-        # 2: modifizierter Schraegungswinkel:
-        alpha = np.arccos(r0 / r * np.cos(alpha_w))
-
-        # 3: winkel phi bei senkrechter stellung eines zahns:
-        phi = np.pi / t_i / 2 + (alpha - alpha_w) + (np.tan(alpha_w) - np.tan(alpha))
-
-        # 4: Position des Eingriffspunktes:
-        x_c = r_e * np.sin(phi)
-        dy = -r_e * np.cos(phi) + r_ew
-
-        # 5: oberer Punkt:
-        b = y1 - dy
-        a = np.tan(alpha) * b
-        x1 = a + x_c
-
-        # 6: unterer Punkt
-        d = y2 + dy
-        c = np.tan(alpha) * d
-        x2 = x_c - c
-
-        r *= np.cos(phi)
-        pts = [
-            [-x1, r, y0],
-            [-x2, r, y0 - y1 - y2],
-            [x2, r, y0 - y1 - y2],
-            [x1, r, y0]
-        ]
-        pts.append(pts[0])
-        return pts
-
-    def execute(self, fp):
-        inner_diameter = fp.module.Value * fp.teeth
-        outer_diameter = inner_diameter + fp.height.Value * 2
-        inner_circle = Part.Wire(Part.makeCircle(inner_diameter / 2.))
-        outer_circle = Part.Wire(Part.makeCircle(outer_diameter / 2.))
-        inner_circle.reverse()
-        face = Part.Face([outer_circle, inner_circle])
-        solid = face.extrude(App.Vector([0., 0., -fp.thickness.Value]))
-
-        ### cutting obj
-        alpha_w = np.deg2rad(fp.pressure_angle.Value)
-        m = fp.module.Value
-        t = fp.teeth
-        t_c = t
-        t_i = fp.other_teeth
-        rm = inner_diameter / 2
-        y0 = m * 0.5
-        y1 = m + y0
-        y2 = m
-        r0 = inner_diameter / 2 - fp.height.Value * 0.1
-        r1 = outer_diameter / 2 + fp.height.Value * 0.3
-        polies = []
-        for r_i in np.linspace(r0, r1, fp.num_profiles):
-            pts = self.profile(m, r_i, rm, t_c, t_i, alpha_w, y0, y1, y2)
-            poly = Wire(makePolygon(list(map(fcvec, pts))))
-            polies.append(poly)
-        loft = makeLoft(polies, True)
-        rot = App.Matrix()
-        rot.rotateZ(2 * np.pi / t)
-        if fp.construct:
-            cut_shapes = [solid]
-            for _ in range(t):
-                loft = loft.transformGeometry(rot)
-                cut_shapes.append(loft)
-            fp.Shape = Part.Compound(cut_shapes)
-        else:
-            for i in range(t):
-                loft = loft.transformGeometry(rot)
-                solid = solid.cut(loft)
-            fp.Shape = solid
-        
-
-    def __getstate__(self):
-        pass
-
-    def __setstate__(self, state):
-        pass
-
-
-class cycloide_gear(object):
-    """FreeCAD gear"""
-    def __init__(self, obj):
-        self.cycloide_tooth = cycloide_tooth()
-        obj.addProperty("App::PropertyInteger",
-                        "teeth", "gear_parameter", "number of teeth")
-        obj.addProperty(
-            "App::PropertyLength", "module", "gear_parameter", "module")
-        obj.addProperty(
-            "App::PropertyLength", "inner_diameter", "cycloid_parameter", "inner_diameter")
-        obj.addProperty(
-            "App::PropertyLength", "outer_diameter", "cycloid_parameter", "outer_diameter")
-        obj.addProperty(
-            "App::PropertyLength", "height", "gear_parameter", "height")
-        obj.addProperty(
-            "App::PropertyBool", "double_helix", "gear_parameter", "double helix")
-        obj.addProperty(
-            "App::PropertyFloat", "clearance", "gear_parameter", "clearance")
-        obj.addProperty("App::PropertyInteger", "numpoints",
-                        "gear_parameter", "number of points for spline")
-        obj.addProperty("App::PropertyAngle", "beta", "gear_parameter", "beta")
-        obj.addProperty(
-            "App::PropertyLength", "backlash", "gear_parameter", "backlash in mm")
-        obj.addProperty("App::PropertyPythonObject", "gear", "gear_parameter", "the python object")
-        obj.gear = self.cycloide_tooth
-        obj.teeth = 15
-        obj.module = '1. mm'
-        obj.inner_diameter = '5 mm'
-        obj.outer_diameter = '5 mm'
-        obj.beta = '0. deg'
-        obj.height = '5. mm'
-        obj.clearance = 0.25
-        obj.numpoints = 15
-        obj.backlash = '0.00 mm'
-        obj.double_helix = False
-        obj.Proxy = self
-
-    def execute(self, fp):
-        fp.gear.m = fp.module.Value
-        fp.gear.z = fp.teeth
-        fp.gear.z1 = fp.inner_diameter.Value
-        fp.gear.z2 = fp.outer_diameter.Value
-        fp.gear.clearance = fp.clearance
-        fp.gear.backlash = fp.backlash.Value
-        fp.gear._update()
-        pts = fp.gear.points(num=fp.numpoints)
-        rotated_pts = pts
-        rot = rotation(-fp.gear.phipart)
-        for i in range(fp.gear.z - 1):
-            rotated_pts = list(map(rot, rotated_pts))
-            pts.append(np.array([pts[-1][-1], rotated_pts[0][0]]))
-            pts += rotated_pts
-        pts.append(np.array([pts[-1][-1], pts[0][0]]))
-        wi = []
-        for i in pts:
-            out = BSplineCurve()
-            out.interpolate(list(map(fcvec, i)))
-            wi.append(out.toShape())
-        wi = Wire(wi)
-        if fp.beta.Value == 0:
-            sh = Face(wi)
-            fp.Shape = sh.extrude(App.Vector(0, 0, fp.height.Value))
-        else:
-            fp.Shape = helicalextrusion(
-                wi, fp.height.Value, fp.height.Value * np.tan(fp.beta.Value * np.pi / 180) * 2 / fp.gear.d, fp.double_helix)
-
-    def __getstate__(self):
-        return None
-
-    def __setstate__(self, state):
-        return None
-
-
-class bevel_gear(object):
-
-    """parameters:
-        pressure_angle:  pressureangle,   10-30°
-        pitch_angle:  cone angle,      0 < pitch_angle < pi/4
-    """
-
-    def __init__(self, obj):
-        self.bevel_tooth = bevel_tooth()
-        obj.addProperty("App::PropertyInteger",
-                        "teeth", "gear_parameter", "number of teeth")
-        obj.addProperty(
-            "App::PropertyLength", "height", "gear_parameter", "height")
-        obj.addProperty(
-            "App::PropertyAngle", "pitch_angle", "involute_parameter", "pitch_angle")
-        obj.addProperty(
-            "App::PropertyAngle", "pressure_angle", "involute_parameter", "pressure_angle")
-        obj.addProperty("App::PropertyLength", "m", "gear_parameter", "m")
-        obj.addProperty(
-            "App::PropertyFloat", "clearance", "gear_parameter", "clearance")
-        obj.addProperty("App::PropertyInteger", "numpoints",
-                        "gear_parameter", "number of points for spline")
-        obj.addProperty("App::PropertyBool", "reset_origin", "gear_parameter",
-            "if value is true the gears outer face will match the z=0 plane")
-        obj.addProperty(
-            "App::PropertyLength", "backlash", "gear_parameter", "backlash in mm")
-        obj.addProperty("App::PropertyPythonObject", "gear", "gear_paramenter", "test")
-        obj.addProperty("App::PropertyAngle", "beta", "gear_paramenter", "test")
-        obj.gear = self.bevel_tooth
-        obj.m = '1. mm'
-        obj.teeth = 15
-        obj.pressure_angle = '20. deg'
-        obj.pitch_angle = '45. deg'
-        obj.height = '5. mm'
-        obj.numpoints = 6
-        obj.backlash = '0.00 mm'
-        obj.clearance = 0.1
-        obj.beta = '0 deg'
-        obj.reset_origin = True
-        self.obj = obj
-        obj.Proxy = self
-
-    def execute(self, fp):
-        fp.gear.z = fp.teeth
-        fp.gear.module = fp.m.Value
-        fp.gear.pressure_angle = (90 - fp.pressure_angle.Value) * np.pi / 180.
-        fp.gear.pitch_angle = fp.pitch_angle.Value * np.pi / 180
-        fp.gear.backlash = fp.backlash.Value
-        scale = fp.m.Value * fp.gear.z / 2 / np.tan(fp.pitch_angle.Value * np.pi / 180)
-        fp.gear.clearance = fp.clearance / scale
-        fp.gear._update()
-        pts = list(fp.gear.points(num=fp.numpoints))
-        rot = rotation3D(2  * np.pi / fp.teeth)
-        # if fp.beta.Value != 0:
-        #     pts = [np.array([self.spherical_rot(j, fp.beta.Value * np.pi / 180.) for j in i]) for i in pts]
-
-        rotated_pts = pts
-        for i in range(fp.gear.z - 1):
-            rotated_pts = list(map(rot, rotated_pts))
-            pts.append(np.array([pts[-1][-1], rotated_pts[0][0]]))
-            pts += rotated_pts
-        pts.append(np.array([pts[-1][-1], pts[0][0]]))
-        wires = []
-        scale_0 = scale - fp.height.Value / 2
-        scale_1 = scale + fp.height.Value / 2
-        if fp.beta.Value == 0:
-            wires.append(makeBSplineWire([scale_0 * p for p in pts]))
-            wires.append(makeBSplineWire([scale_1 * p for p in pts]))
-        else:
-            for scale_i  in np.linspace(scale_0, scale_1, 20):
-                # beta_i = (scale_i - scale_0) * fp.beta.Value * np.pi / 180
-                # rot = rotation3D(beta_i)
-                # points = [rot(pt) * scale_i for pt in pts]
-                angle =  fp.beta.Value * np.pi / 180. * np.sin(np.pi / 4) / np.sin(fp.pitch_angle.Value * np.pi / 180.)
-                points = [np.array([self.spherical_rot(p, angle) for p in scale_i * pt]) for pt in pts]
-                wires.append(makeBSplineWire(points))
-        shape = makeLoft(wires, True)
-        if fp.reset_origin:
-            mat = App.Matrix()
-            mat.A33 = -1
-            mat.move(fcvec([0, 0, scale_1]))
-            shape = shape.transformGeometry(mat)
-        fp.Shape = shape
-        # fp.Shape = self.create_teeth(pts, pos1, fp.teeth)
-
-
-    def create_tooth(self):
-        w = []
-        scal1 = self.obj.m.Value * self.obj.gear.z / 2 / np.tan(
-            self.obj.pitch_angle.Value * np.pi / 180) - self.obj.height.Value / 2
-        scal2 = self.obj.m.Value * self.obj.gear.z / 2 / np.tan(
-            self.obj.pitch_angle.Value * np.pi / 180) + self.obj.height.Value / 2
-        s = [scal1, scal2]
-        pts = self.obj.gear.points(num=self.obj.numpoints)
-        for j, pos in enumerate(s):
-            w1 = []
-            scale = lambda x: fcvec(x * pos)
-            for i in pts:
-                i_scale = list(map(scale, i))
-                w1.append(i_scale)
-            w.append(w1)
-        surfs = []
-        w_t = zip(*w)
-        for i in w_t:
-            b = BSplineSurface()
-            b.interpolate(i)
-            surfs.append(b)
-        return Shape(surfs)
-
-    def spherical_rot(self, point, phi):
-        new_phi = np.sqrt(np.linalg.norm(point)) * phi
-        return rotation3D(new_phi)(point)
-
-    def create_teeth(self, pts, pos, teeth):
-        w1 = []
-        pts = [pt * pos for pt in pts]
-        rotated_pts = scaled_points
-        rot = rotation3D(- 2 * i * np.pi / teeth)
-        for i in range(teeth - 1):
-            rotated_pts = map(rot, rotated_pts)
-            pts.append(np.array([pts[-1][-1], rotated_pts[0][0]]))
-            pts += rotated_pts
-        s = Wire(Shape(w1).Edges)
-        wi = []
-        for i in range(teeth):
-            rot = App.Matrix()
-            rot.rotateZ(2 * i * np.pi / teeth)
-            tooth_rot = s.transformGeometry(rot)
-            if i != 0:
-                pt_0 = wi[-1].Edges[-1].Vertexes[0].Point
-                pt_1 = tooth_rot.Edges[0].Vertexes[-1].Point
-                wi.append(Wire([Line(pt_0, pt_1).toShape()]))
-            wi.append(tooth_rot)
-        pt_0 = wi[-1].Edges[-1].Vertexes[0].Point
-        pt_1 = wi[0].Edges[0].Vertexes[-1].Point
-        wi.append(Wire([Line(pt_0, pt_1).toShape()]))
-        return(Wire(wi))
-
-    def __getstate__(self):
-        return None
-
-    def __setstate__(self, state):
-        return None
-
-
-def helicalextrusion(wire, height, angle, double_helix = False):
-    direction = bool(angle < 0)
-    if double_helix:
-        first_spine = makeHelix(height * 2. * np.pi / abs(angle), 0.5 * height, 10., 0, direction)
-        first_solid = first_spine.makePipeShell([wire], True, True)
-        second_solid = first_solid.mirror(fcvec([0.,0.,0.]), fcvec([0,0,1]))
-        faces = first_solid.Faces + second_solid.Faces
-        faces = [f for f in faces if not on_mirror_plane(f, 0., fcvec([0., 0., 1.]))]
-        solid = makeSolid(makeShell(faces))
-        mat = App.Matrix()
-        mat.move(fcvec([0, 0, 0.5 * height]))
-        return solid.transformGeometry(mat)
-    else:
-        first_spine = makeHelix(height * 2 * np.pi / abs(angle), height, 10., 0, direction)
-        first_solid = first_spine.makePipeShell([wire], True, True)
-        return first_solid
-
-
-
-def make_face(edge1, edge2):
-    v1, v2 = edge1.Vertexes
-    v3, v4 = edge2.Vertexes
-    e1 = Wire(edge1)
-    e2 = Line(v1.Point, v3.Point).toShape().Edges[0]
-    e3 = edge2
-    e4 = Line(v4.Point, v2.Point).toShape().Edges[0]
-    w = Wire([e3, e4, e1, e2])
-    return(Face(w))
-
-
-def makeBSplineWire(pts):
-    wi = []
-    for i in pts:
-        out = BSplineCurve()
-        out.interpolate(list(map(fcvec, i)))
-        wi.append(out.toShape())
-    return Wire(wi)
-
-def on_mirror_plane(face, z, direction, small_size=0.000001):
-    # the tolerance is very high. Maybe there is a bug in Part.makeHelix.
-    return (face.normalAt(0, 0).cross(direction).Length < small_size and
-            abs(face.CenterOfMass.z - z)  < small_size)

freecad/gears/hypocycloidgear.py

@@ -0,0 +1,283 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import math
+
+import numpy as np
+import scipy as sp
+
+import FreeCAD as App
+import Part
+
+from pygears.bevel_tooth import BevelTooth
+from pygears._functions import rotation
+
+from .basegear import BaseGear, make_bspline_wire
+
+
+class HypoCycloidGear(BaseGear):
+
+    """parameters:
+    pressure_angle:  pressureangle,   10-30°
+    pitch_angle:  cone angle,      0 < pitch_angle < pi/4
+    """
+
+    def __init__(self, obj):
+        super(HypoCycloidGear, self).__init__(obj)
+        obj.addProperty(
+            "App::PropertyFloat",
+            "pin_circle_radius",
+            "gear_parameter",
+            "Pin ball circle radius(overrides Tooth Pitch",
+        )
+        obj.addProperty(
+            "App::PropertyFloat", "roller_diameter", "gear_parameter", "Roller Diameter"
+        )
+        obj.addProperty(
+            "App::PropertyFloat", "eccentricity", "gear_parameter", "Eccentricity"
+        )
+        obj.addProperty(
+            "App::PropertyAngle",
+            "pressure_angle_lim",
+            "gear_parameter",
+            "Pressure angle limit",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "pressure_angle_offset",
+            "gear_parameter",
+            "Offset in pressure angle",
+        )
+        obj.addProperty(
+            "App::PropertyInteger",
+            "teeth_number",
+            "gear_parameter",
+            "Number of teeth in Cam",
+        )
+        obj.addProperty(
+            "App::PropertyInteger",
+            "segment_count",
+            "gear_parameter",
+            "Number of points used for spline interpolation",
+        )
+        obj.addProperty(
+            "App::PropertyLength",
+            "hole_radius",
+            "gear_parameter",
+            "Center hole's radius",
+        )
+
+        obj.addProperty(
+            "App::PropertyBool", "show_pins", "Pins", "Create pins in place"
+        )
+        obj.addProperty("App::PropertyLength", "pin_height", "Pins", "height")
+        obj.addProperty(
+            "App::PropertyBool",
+            "center_pins",
+            "Pins",
+            "Center pin Z axis to generated disks",
+        )
+
+        obj.addProperty(
+            "App::PropertyBool", "show_disk0", "Disks", "Show main cam disk"
+        )
+        obj.addProperty(
+            "App::PropertyBool",
+            "show_disk1",
+            "Disks",
+            "Show another reversed cam disk on top",
+        )
+        obj.addProperty("App::PropertyLength", "disk_height", "Disks", "height")
+
+        obj.pin_circle_radius = 66
+        obj.roller_diameter = 3
+        obj.eccentricity = 1.5
+        obj.pressure_angle_lim = "50.0 deg"
+        obj.pressure_angle_offset = 0.01
+        obj.teeth_number = 42
+        obj.segment_count = 42
+        obj.hole_radius = "30. mm"
+
+        obj.show_pins = True
+        obj.pin_height = "20. mm"
+        obj.center_pins = True
+
+        obj.show_disk0 = True
+        obj.show_disk1 = True
+        obj.disk_height = "10. mm"
+
+        self.obj = obj
+        obj.Proxy = self
+
+    def to_polar(self, x, y):
+        return (x**2 + y**2) ** 0.5, math.atan2(y, x)
+
+    def to_rect(self, r, a):
+        return r * math.cos(a), r * math.sin(a)
+
+    def calcyp(self, p, a, e, n):
+        return math.atan(math.sin(n * a) / (math.cos(n * a) + (n * p) / (e * (n + 1))))
+
+    def calc_x(self, p, d, e, n, a):
+        return (
+            (n * p) * math.cos(a)
+            + e * math.cos((n + 1) * a)
+            - d / 2 * math.cos(self.calcyp(p, a, e, n) + a)
+        )
+
+    def calc_y(self, p, d, e, n, a):
+        return (
+            (n * p) * math.sin(a)
+            + e * math.sin((n + 1) * a)
+            - d / 2 * math.sin(self.calcyp(p, a, e, n) + a)
+        )
+
+    def calc_pressure_angle(self, p, d, n, a):
+        ex = 2**0.5
+        r3 = p * n
+        rg = r3 / ex
+        pp = rg * (ex**2 + 1 - 2 * ex * math.cos(a)) ** 0.5 - d / 2
+        return math.asin((r3 * math.cos(a) - rg) / (pp + d / 2)) * 180 / math.pi
+
+    def calc_pressure_limit(self, p, d, e, n, a):
+        ex = 2**0.5
+        r3 = p * n
+        rg = r3 / ex
+        q = (r3**2 + rg**2 - 2 * r3 * rg * math.cos(a)) ** 0.5
+        x = rg - e + (q - d / 2) * (r3 * math.cos(a) - rg) / q
+        y = (q - d / 2) * r3 * math.sin(a) / q
+        return (x**2 + y**2) ** 0.5
+
+    def check_limit(self, x, y, maxrad, minrad, offset):
+        r, a = self.to_polar(x, y)
+        if (r > maxrad) or (r < minrad):
+            r = r - offset
+            x, y = self.to_rect(r, a)
+        return x, y
+
+    def generate_gear_shape(self, fp):
+        b = fp.pin_circle_radius
+        d = fp.roller_diameter
+        e = fp.eccentricity
+        n = fp.teeth_number
+        p = b / n
+        s = fp.segment_count
+        ang = fp.pressure_angle_lim
+        c = fp.pressure_angle_offset
+
+        q = 2 * math.pi / float(s)
+
+        # Find the pressure angle limit circles
+        minAngle = -1.0
+        maxAngle = -1.0
+        for i in range(0, 180):
+            x = self.calc_pressure_angle(p, d, n, i * math.pi / 180.0)
+            if (x < ang) and (minAngle < 0):
+                minAngle = float(i)
+            if (x < -ang) and (maxAngle < 0):
+                maxAngle = float(i - 1)
+
+        minRadius = self.calc_pressure_limit(p, d, e, n, minAngle * math.pi / 180.0)
+        maxRadius = self.calc_pressure_limit(p, d, e, n, maxAngle * math.pi / 180.0)
+        # unused
+        # Part.Wire(Part.makeCircle(minRadius,App.Vector(-e, 0, 0)))
+        # Part.Wire(Part.makeCircle(maxRadius,App.Vector(-e, 0, 0)))
+
+        App.Console.PrintMessage("Generating cam disk\r\n")
+        # generate the cam profile - note: shifted in -x by eccentricicy amount
+        i = 0
+        x = self.calc_x(p, d, e, n, q * i / float(n))
+        y = self.calc_y(p, d, e, n, q * i / n)
+        x, y = self.check_limit(x, y, maxRadius, minRadius, c)
+        points = [App.Vector(x - e, y, 0)]
+        for i in range(0, s):
+            x = self.calc_x(p, d, e, n, q * (i + 1) / n)
+            y = self.calc_y(p, d, e, n, q * (i + 1) / n)
+            x, y = self.check_limit(x, y, maxRadius, minRadius, c)
+            points.append([x - e, y, 0])
+
+        wi = make_bspline_wire([points])
+        wires = []
+        mat = App.Matrix()
+        mat.move(App.Vector(e, 0.0, 0.0))
+        mat.rotateZ(2 * np.pi / n)
+        mat.move(App.Vector(-e, 0.0, 0.0))
+        for _ in range(n):
+            wi = wi.transformGeometry(mat)
+            wires.append(wi)
+
+        cam = Part.Face(Part.Wire(wires))
+        # add a circle in the center of the cam
+        if fp.hole_radius.Value:
+            centerCircle = Part.Face(
+                Part.Wire(Part.makeCircle(fp.hole_radius.Value, App.Vector(-e, 0, 0)))
+            )
+            cam = cam.cut(centerCircle)
+
+        to_be_fused = []
+        if fp.show_disk0 == True:
+            if fp.disk_height.Value == 0:
+                to_be_fused.append(cam)
+            else:
+                to_be_fused.append(cam.extrude(App.Vector(0, 0, fp.disk_height.Value)))
+
+        # secondary cam disk
+        if fp.show_disk1 == True:
+            App.Console.PrintMessage("Generating secondary cam disk\r\n")
+            second_cam = cam.copy()
+            mat = App.Matrix()
+            mat.rotateZ(np.pi)
+            mat.move(App.Vector(-e, 0, 0))
+            if n % 2 == 0:
+                mat.rotateZ(np.pi / n)
+            mat.move(App.Vector(e, 0, 0))
+            second_cam = second_cam.transformGeometry(mat)
+            if fp.disk_height.Value == 0:
+                to_be_fused.append(second_cam)
+            else:
+                to_be_fused.append(
+                    second_cam.extrude(App.Vector(0, 0, -fp.disk_height.Value))
+                )
+
+        # pins
+        if fp.show_pins == True:
+            App.Console.PrintMessage("Generating pins\r\n")
+            pins = []
+            for i in range(0, n + 1):
+                x = p * n * math.cos(2 * math.pi / (n + 1) * i)
+                y = p * n * math.sin(2 * math.pi / (n + 1) * i)
+                pins.append(Part.Wire(Part.makeCircle(d / 2, App.Vector(x, y, 0))))
+
+            pins = Part.Face(pins)
+
+            z_offset = -fp.pin_height.Value / 2
+            if fp.center_pins == True:
+                if fp.show_disk0 == True and fp.show_disk1 == False:
+                    z_offset += fp.disk_height.Value / 2
+                elif fp.show_disk0 == False and fp.show_disk1 == True:
+                    z_offset += -fp.disk_height.Value / 2
+            # extrude
+            if z_offset != 0:
+                pins.translate(App.Vector(0, 0, z_offset))
+            if fp.pin_height != 0:
+                pins = pins.extrude(App.Vector(0, 0, fp.pin_height.Value))
+
+            to_be_fused.append(pins)
+
+        if to_be_fused:
+            return Part.makeCompound(to_be_fused)

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freecad/gears/init_gui.py

@@ -1,66 +1,159 @@
-#***************************************************************************
+# -*- coding: utf-8 -*-
-#*                                                                         *
+# ***************************************************************************
-#*   This program is free software; you can redistribute it and/or modify  *
+# *                                                                         *
-#*   it under the terms of the GNU Lesser General Public License (LGPL)    *
+# * This program is free software: you can redistribute it and/or modify    *
-#*   as published by the Free Software Foundation; either version 2 of     *
+# * it under the terms of the GNU General Public License as published by    *
-#*   the License, or (at your option) any later version.                   *
+# * the Free Software Foundation, either version 3 of the License, or       *
-#*   for detail see the LICENCE text file.                                 *
+# * (at your option) any later version.                                     *
-#*                                                                         *
+# *                                                                         *
-#*   This program is distributed in the hope that it will be useful,       *
+# * This program is distributed in the hope that it will be useful,         *
-#*   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
-#*   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
-#*   GNU Library General Public License for more details.                  *
+# * GNU General Public License for more details.                            *
-#*                                                                         *
+# *                                                                         *
-#*   You should have received a copy of the GNU Library General Public     *
+# * You should have received a copy of the GNU General Public License       *
-#*   License along with this program; if not, write to the Free Software   *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
-#*   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  *
+# *                                                                         *
-#*   USA                                                                   *
+# ***************************************************************************
-#*                                                                         *
-#***************************************************************************
 
 import os
+import sys
 import FreeCADGui as Gui
 import FreeCAD as App
+
 __dirname__ = os.path.dirname(__file__)
 
 try:
     from FreeCADGui import Workbench
 except ImportError as e:
-    App.Console.PrintWarning("you are using the GearWorkbench with an old version of FreeCAD (<0.16)")
+    App.Console.PrintWarning(
-    App.Console.PrintWarning("the class Workbench is loaded, although not imported: magic")
+        "you are using the GearWorkbench with an old version of FreeCAD (<0.16)"
+    )
+    App.Console.PrintWarning(
+        "the class Workbench is loaded, although not imported: magic"
+    )
+
+
+if sys.version_info[0] == 3 and sys.version_info[1] >= 11:
+    # only works with 0.21.2 and above
+
+    FC_MAJOR_VER_REQUIRED = 0
+    FC_MINOR_VER_REQUIRED = 21
+    FC_PATCH_VER_REQUIRED = 2
+    FC_COMMIT_REQUIRED = 33772
+
+    # Check FreeCAD version
+    App.Console.PrintLog("Checking FreeCAD version\n")
+    ver = App.Version()
+    major_ver = int(ver[0])
+    minor_vers = ver[1].split(".")
+    minor_ver = int(minor_vers[0])
+    if minor_vers[1:] and minor_vers[1]:
+        patch_ver = int(minor_vers[1])
+    else:
+        patch_ver = 0
+    gitver = ver[2].split()
+    if gitver:
+        gitver = gitver[0]
+    if gitver and gitver != "Unknown":
+        gitver = int(gitver)
+    else:
+        # If we don't have the git version, assume it's OK.
+        gitver = FC_COMMIT_REQUIRED
+
+    if major_ver < FC_MAJOR_VER_REQUIRED or (
+        major_ver == FC_MAJOR_VER_REQUIRED
+        and (
+            minor_ver < FC_MINOR_VER_REQUIRED
+            or (
+                minor_ver == FC_MINOR_VER_REQUIRED
+                and (
+                    patch_ver < FC_PATCH_VER_REQUIRED
+                    or (
+                        patch_ver == FC_PATCH_VER_REQUIRED
+                        and gitver < FC_COMMIT_REQUIRED
+                    )
+                )
+            )
+        )
+    ):
+        App.Console.PrintWarning(
+            "FreeCAD version (currently {}.{}.{} ({})) must be at least {}.{}.{} ({}) in order to work with Python 3.11 and above\n".format(
+                int(ver[0]),
+                minor_ver,
+                patch_ver,
+                gitver,
+                FC_MAJOR_VER_REQUIRED,
+                FC_MINOR_VER_REQUIRED,
+                FC_PATCH_VER_REQUIRED,
+                FC_COMMIT_REQUIRED,
+            )
+        )
+
+
+class GearWorkbench(Workbench):
+    """A freecad workbench aiming at gear design"""
 
-class gearWorkbench(Workbench):
-    """glider workbench"""
     MenuText = "Gear"
     ToolTip = "Gear Workbench"
-    Icon = os.path.join(__dirname__,  'icons', 'gearworkbench.svg')
+    Icon = os.path.join(__dirname__, "icons", "gearworkbench.svg")
     commands = [
-                "CreateInvoluteGear",
+        "CreateInvoluteGear",
-                "CreateInvoluteRack",
+        "CreateInternalInvoluteGear",
-                "CreateCycloideGear",
+        "CreateInvoluteRack",
-                "CreateBevelGear",
+        "CreateCycloidGear",
-                "CreateCrownGear"]
+        "CreateCycloidRack",
+        "CreateBevelGear",
+        "CreateCrownGear",
+        "CreateWormGear",
+        "CreateTimingGearT",
+        "CreateTimingGear",
+        "CreateLanternGear",
+        "CreateHypoCycloidGear",
+        "CreateGearConnector",
+    ]
 
     def GetClassName(self):
         return "Gui::PythonWorkbench"
 
     def Initialize(self):
-        from .commands import CreateCycloideGear, CreateInvoluteGear
+        from .commands import (
-        from .commands import CreateBevelGear, CreateInvoluteRack, CreateCrownGear
+            CreateCycloidGear,
+            CreateInvoluteGear,
+            CreateInternalInvoluteGear,
+            CreateBevelGear,
+            CreateInvoluteRack,
+            CreateCrownGear,
+            CreateWormGear,
+            CreateTimingGearT,
+            CreateTimingGear,
+            CreateLanternGear,
+            CreateHypoCycloidGear,
+            CreateCycloidRack,
+            CreateGearConnector,
+        )
+
         self.appendToolbar("Gear", self.commands)
         self.appendMenu("Gear", self.commands)
-        Gui.addIconPath(App.getHomePath()+"Mod/gear/icons/")
+        Gui.addCommand("CreateInvoluteGear", CreateInvoluteGear())
-        Gui.addCommand('CreateInvoluteGear', CreateInvoluteGear())
+        Gui.addCommand("CreateInternalInvoluteGear", CreateInternalInvoluteGear())
-        Gui.addCommand('CreateCycloideGear', CreateCycloideGear())
+        Gui.addCommand("CreateCycloidGear", CreateCycloidGear())
-        Gui.addCommand('CreateBevelGear', CreateBevelGear())
+        Gui.addCommand("CreateCycloidRack", CreateCycloidRack())
-        Gui.addCommand('CreateInvoluteRack', CreateInvoluteRack())
+        Gui.addCommand("CreateBevelGear", CreateBevelGear())
-        Gui.addCommand('CreateCrownGear', CreateCrownGear())
+        Gui.addCommand("CreateInvoluteRack", CreateInvoluteRack())
+        Gui.addCommand("CreateCrownGear", CreateCrownGear())
+        Gui.addCommand("CreateWormGear", CreateWormGear())
+        Gui.addCommand("CreateTimingGearT", CreateTimingGearT())
+        Gui.addCommand("CreateTimingGear", CreateTimingGear())
+        Gui.addCommand("CreateLanternGear", CreateLanternGear())
+        Gui.addCommand("CreateHypoCycloidGear", CreateHypoCycloidGear())
+        Gui.addCommand("CreateGearConnector", CreateGearConnector())
 
     def Activated(self):
         pass
 
-
     def Deactivated(self):
         pass
 
-Gui.addWorkbench(gearWorkbench())
+
+Gui.addWorkbench(GearWorkbench())

freecad/gears/internalinvolutegear.py

@@ -0,0 +1,248 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+from pygears.involute_tooth import InvoluteTooth
+from pygears._functions import rotation
+
+from .basegear import (
+    BaseGear,
+    points_to_wire,
+    insert_fillet,
+    helicalextrusion,
+    rotate_tooth,
+)
+
+
+class InternalInvoluteGear(BaseGear):
+    """FreeCAD internal involute gear
+
+    Using the same tooth as the external, just turning it inside-out:
+    addedum becomes dedendum, clearance becomes head, negate the backslash, ...
+    """
+
+    def __init__(self, obj):
+        super(InternalInvoluteGear, self).__init__(obj)
+        self.involute_tooth = InvoluteTooth()
+        obj.addProperty("App::PropertyBool", "simple", "precision", "simple")
+        obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
+        obj.addProperty(
+            "App::PropertyLength",
+            "module",
+            "base",
+            "normal module if properties_from_tool=True, \
+                                                                else it's the transverse module.",
+        )
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+        obj.addProperty("App::PropertyLength", "thickness", "base", "thickness")
+        obj.addProperty(
+            "App::PropertyInteger",
+            "numpoints",
+            "accuracy",
+            "number of points for spline",
+        )
+        obj.addProperty("App::PropertyPythonObject", "gear", "base", "test")
+
+        self.add_involute_properties(obj)
+        self.add_tolerance_properties(obj)
+        self.add_fillet_properties(obj)
+        self.add_computed_properties(obj)
+        self.add_limiting_diameter_properties(obj)
+        self.add_helical_properties(obj)
+
+        obj.gear = self.involute_tooth
+        obj.simple = False
+        obj.teeth = 15
+        obj.module = "1. mm"
+        obj.shift = 0.0
+        obj.pressure_angle = "20. deg"
+        obj.beta = "0. deg"
+        obj.height = "5. mm"
+        obj.thickness = "5 mm"
+        obj.clearance = 0.25
+        obj.head = -0.4  # using head=0 and shift=0.5 may be better, but makes placeing the pinion less intuitive
+        obj.numpoints = 6
+        obj.double_helix = False
+        obj.backlash = "0.00 mm"
+        obj.reversed_backlash = False
+        obj.properties_from_tool = False
+        obj.head_fillet = 0
+        obj.root_fillet = 0
+        self.obj = obj
+        obj.Proxy = self
+
+    def add_limiting_diameter_properties(self, obj):
+        obj.addProperty("App::PropertyLength", "da", "computed", "inside diameter", 1)
+        obj.addProperty("App::PropertyLength", "df", "computed", "root diameter", 1)
+
+    def add_computed_properties(self, obj):
+        obj.addProperty("App::PropertyLength", "dw", "computed", "The pitch diameter.")
+        obj.addProperty(
+            "App::PropertyAngle",
+            "angular_backlash",
+            "computed",
+            "The angle by which this gear can turn without moving the mating gear.",
+        )
+        obj.setExpression(
+            "angular_backlash", "backlash / dw * 360° / pi"
+        )  # calculate via expression to ease usage for placement
+        obj.setEditorMode(
+            "angular_backlash", 1
+        )  # set read-only after setting the expression, else it won't be visible. bug?
+        obj.addProperty(
+            "App::PropertyLength", "transverse_pitch", "computed", "transverse_pitch", 1
+        )
+        obj.addProperty(
+            "App::PropertyLength", "outside_diameter", "computed", "Outside diameter", 1
+        )
+
+    def add_fillet_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head_fillet",
+            "fillets",
+            "a fillet for the tooth-head, radius = head_fillet x module",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "root_fillet",
+            "fillets",
+            "a fillet for the tooth-root, radius = root_fillet x module",
+        )
+
+    def add_tolerance_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyLength",
+            "backlash",
+            "tolerance",
+            "The arc length on the pitch circle by which the tooth thicknes is reduced.",
+        )
+        obj.addProperty(
+            "App::PropertyBool", "reversed_backlash", "tolerance", "backlash direction"
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head",
+            "tolerance",
+            "head_value * modul_value = additional length of head",
+        )
+        obj.addProperty("App::PropertyFloat", "clearance", "tolerance", "clearance")
+
+    def add_involute_properties(self, obj):
+        obj.addProperty("App::PropertyFloat", "shift", "involute", "shift")
+        obj.addProperty(
+            "App::PropertyAngle", "pressure_angle", "involute", "pressure angle"
+        )
+
+    def add_helical_properties(self, obj):
+        obj.addProperty("App::PropertyAngle", "beta", "helical", "beta ")
+        obj.addProperty("App::PropertyBool", "double_helix", "helical", "double helix")
+        obj.addProperty(
+            "App::PropertyBool",
+            "properties_from_tool",
+            "helical",
+            "if beta is given and properties_from_tool is enabled, \
+            gear parameters are internally recomputed for the rotated gear",
+        )
+
+    def generate_gear_shape(self, fp):
+        fp.gear.double_helix = fp.double_helix
+        fp.gear.m_n = fp.module.Value
+        fp.gear.z = fp.teeth
+        fp.gear.undercut = False  # no undercut for internal gears
+        fp.gear.shift = fp.shift
+        fp.gear.pressure_angle = fp.pressure_angle.Value * np.pi / 180.0
+        fp.gear.beta = fp.beta.Value * np.pi / 180
+        fp.gear.clearance = fp.head  # swap head and clearance to become "internal"
+        fp.gear.backlash = (
+            fp.backlash.Value * (fp.reversed_backlash - 0.5) * 2.0
+        )  # negate "reversed_backslash", for "internal"
+        fp.gear.head = fp.clearance  # swap head and clearance to become "internal"
+        fp.gear.properties_from_tool = fp.properties_from_tool
+        fp.gear._update()
+
+        fp.dw = "{}mm".format(fp.gear.dw)
+
+        # computed properties
+        fp.transverse_pitch = "{}mm".format(fp.gear.pitch)
+        fp.outside_diameter = fp.dw + 2 * fp.thickness
+        # checksbackwardcompatibility:
+        if not "da" in fp.PropertiesList:
+            self.add_limiting_diameter_properties(fp)
+        fp.da = "{}mm".format(fp.gear.df)  # swap addednum and dedendum for "internal"
+        fp.df = "{}mm".format(fp.gear.da)  # swap addednum and dedendum for "internal"
+
+        outer_circle = Part.Wire(Part.makeCircle(fp.outside_diameter / 2.0))
+        outer_circle.reverse()
+        if not fp.simple:
+            # head-fillet:
+            pts = fp.gear.points(num=fp.numpoints)
+            rot = rotation(-fp.gear.phipart)
+            rotated_pts = list(map(rot, pts))
+            pts.append([pts[-1][-1], rotated_pts[0][0]])
+            pts += rotated_pts
+            tooth = points_to_wire(pts)
+            r_head = float(fp.root_fillet * fp.module)  # reversing head
+            r_root = float(fp.head_fillet * fp.module)  # and foot
+            edges = tooth.Edges
+            if len(tooth.Edges) == 11:
+                pos_head = [1, 3, 9]
+                pos_root = [6, 8]
+                edge_range = [2, 12]
+            else:
+                pos_head = [0, 2, 6]
+                pos_root = [4, 6]
+                edge_range = [1, 9]
+
+            for pos in pos_head:
+                edges = insert_fillet(edges, pos, r_head)
+
+            for pos in pos_root:
+                try:
+                    edges = insert_fillet(edges, pos, r_root)
+                except RuntimeError:
+                    edges.pop(8)
+                    edges.pop(6)
+                    edge_range = [2, 10]
+                    pos_root = [5, 7]
+                    for pos in pos_root:
+                        edges = insert_fillet(edges, pos, r_root)
+                    break
+            edges = edges[edge_range[0] : edge_range[1]]
+            edges = [e for e in edges if e is not None]
+
+            tooth = Part.Wire(edges)
+            profile = rotate_tooth(tooth, fp.teeth)
+            if fp.height.Value == 0:
+                return Part.makeCompound([outer_circle, profile])
+            base = Part.Face([outer_circle, profile])
+            if fp.beta.Value == 0:
+                return base.extrude(App.Vector(0, 0, fp.height.Value))
+            else:
+                twist_angle = fp.height.Value * np.tan(fp.gear.beta) * 2 / fp.gear.d
+                return helicalextrusion(
+                    base, fp.height.Value, twist_angle, fp.double_helix
+                )
+        else:
+            inner_circle = Part.Wire(Part.makeCircle(fp.dw / 2.0))
+            inner_circle.reverse()
+            base = Part.Face([outer_circle, inner_circle])
+            return base.extrude(App.Vector(0, 0, fp.height.Value))

freecad/gears/involutegear.py

@@ -0,0 +1,264 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+from pygears.involute_tooth import InvoluteTooth
+from pygears._functions import rotation
+
+from .basegear import (
+    BaseGear,
+    points_to_wire,
+    insert_fillet,
+    helicalextrusion,
+    rotate_tooth,
+)
+
+
+class InvoluteGear(BaseGear):
+
+    """FreeCAD gear"""
+
+    def __init__(self, obj):
+        super(InvoluteGear, self).__init__(obj)
+        self.involute_tooth = InvoluteTooth()
+
+        obj.addProperty(
+            "App::PropertyPythonObject", "gear", "base", "python gear object"
+        )
+
+        self.add_gear_properties(obj)
+        self.add_fillet_properties(obj)
+        self.add_helical_properties(obj)
+        self.add_computed_properties(obj)
+        self.add_tolerance_properties(obj)
+        self.add_accuracy_properties(obj)
+
+        obj.gear = self.involute_tooth
+        obj.simple = False
+        obj.undercut = False
+        obj.teeth = 15
+        obj.module = "1. mm"
+        obj.shift = 0.0
+        obj.pressure_angle = "20. deg"
+        obj.beta = "0. deg"
+        obj.height = "5. mm"
+        obj.clearance = 0.25
+        obj.head = 0.0
+        obj.numpoints = 6
+        obj.double_helix = False
+        obj.backlash = "0.00 mm"
+        obj.reversed_backlash = False
+        obj.properties_from_tool = False
+        obj.head_fillet = 0
+        obj.root_fillet = 0
+        self.obj = obj
+        obj.Proxy = self
+        self.compute_traverse_properties(obj)
+
+    def add_gear_properties(self, obj):
+        obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
+        obj.addProperty(
+            "App::PropertyLength",
+            "module",
+            "base",
+            "normal module if properties_from_tool=True, \
+                                                                else it's the transverse module.",
+        )
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+        obj.addProperty(
+            "App::PropertyAngle", "pressure_angle", "involute", "pressure angle"
+        )
+        obj.addProperty("App::PropertyFloat", "shift", "involute", "shift")
+
+    def add_fillet_properties(self, obj):
+        obj.addProperty("App::PropertyBool", "undercut", "fillets", "undercut")
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head_fillet",
+            "fillets",
+            "a fillet for the tooth-head, radius = head_fillet x module",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "root_fillet",
+            "fillets",
+            "a fillet for the tooth-root, radius = root_fillet x module",
+        )
+
+    def add_helical_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyBool",
+            "properties_from_tool",
+            "helical",
+            "if beta is given and properties_from_tool is enabled, \
+                         gear parameters are internally recomputed for the rotated gear",
+        )
+        obj.addProperty("App::PropertyAngle", "beta", "helical", "beta ")
+        obj.addProperty("App::PropertyBool", "double_helix", "helical", "double helix")
+
+    def add_computed_properties(self, obj):
+        obj.addProperty("App::PropertyLength", "da", "computed", "outside diameter", 1)
+        obj.addProperty("App::PropertyLength", "df", "computed", "root diameter", 1)
+        self.add_traverse_module_property(obj)
+        obj.addProperty(
+            "App::PropertyLength", "dw", "computed", "The pitch diameter.", 1
+        )
+        obj.addProperty(
+            "App::PropertyAngle",
+            "angular_backlash",
+            "computed",
+            "The angle by which this gear can turn without moving the mating gear.",
+        )
+        obj.setExpression(
+            "angular_backlash", "backlash / dw * 360° / pi"
+        )  # calculate via expression to ease usage for placement
+        obj.setEditorMode(
+            "angular_backlash", 1
+        )  # set read-only after setting the expression, else it won't be visible. bug?
+        obj.addProperty(
+            "App::PropertyLength", "transverse_pitch", "computed", "transverse_pitch", 1
+        )
+
+    def add_tolerance_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyLength",
+            "backlash",
+            "tolerance",
+            "The arc length on the pitch circle by which the tooth thicknes is reduced.",
+        )
+        obj.addProperty(
+            "App::PropertyBool", "reversed_backlash", "tolerance", "backlash direction"
+        )
+        obj.addProperty("App::PropertyFloat", "clearance", "tolerance", "clearance")
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head",
+            "tolerance",
+            "head_value * modul_value = additional length of head",
+        )
+
+    def add_accuracy_properties(self, obj):
+        obj.addProperty("App::PropertyBool", "simple", "accuracy", "simple")
+        obj.addProperty(
+            "App::PropertyInteger",
+            "numpoints",
+            "accuracy",
+            "number of points for spline",
+        )
+
+    def add_traverse_module_property(self, obj):
+        obj.addProperty(
+            "App::PropertyLength",
+            "traverse_module",
+            "computed",
+            "traverse module of the generated gear",
+            1,
+        )
+
+    def compute_traverse_properties(self, obj):
+        # traverse_module added recently, if old freecad doc is loaded without it, it will not exist when generate_gear_shape() is called
+        if not hasattr(obj, "traverse_module"):
+            self.add_traverse_module_property(obj)
+        if obj.properties_from_tool:
+            obj.traverse_module = obj.module / np.cos(obj.gear.beta)
+        else:
+            obj.traverse_module = obj.module
+
+        obj.transverse_pitch = "{}mm".format(obj.gear.pitch)
+        obj.da = "{}mm".format(obj.gear.da)
+        obj.df = "{}mm".format(obj.gear.df)
+        obj.dw = "{}mm".format(obj.gear.dw)
+
+    def generate_gear_shape(self, obj):
+        obj.gear.double_helix = obj.double_helix
+        obj.gear.m_n = obj.module.Value
+        obj.gear.z = obj.teeth
+        obj.gear.undercut = obj.undercut
+        obj.gear.shift = obj.shift
+        obj.gear.pressure_angle = obj.pressure_angle.Value * np.pi / 180.0
+        obj.gear.beta = obj.beta.Value * np.pi / 180
+        obj.gear.clearance = obj.clearance
+        obj.gear.backlash = obj.backlash.Value * (-obj.reversed_backlash + 0.5) * 2.0
+        obj.gear.head = obj.head
+        obj.gear.properties_from_tool = obj.properties_from_tool
+
+        obj.gear._update()
+        self.compute_traverse_properties(obj)
+
+        if not obj.simple:
+            pts = obj.gear.points(num=obj.numpoints)
+            rot = rotation(-obj.gear.phipart)
+            rotated_pts = list(map(rot, pts))
+            pts.append([pts[-1][-1], rotated_pts[0][0]])
+            pts += rotated_pts
+            tooth = points_to_wire(pts)
+            edges = tooth.Edges
+
+            # head-fillet:
+            r_head = float(obj.head_fillet * obj.module)
+            r_root = float(obj.root_fillet * obj.module)
+            if obj.undercut and r_root != 0.0:
+                r_root = 0.0
+                App.Console.PrintWarning(
+                    "root fillet is not allowed if undercut is computed"
+                )
+            if len(tooth.Edges) == 11:
+                pos_head = [1, 3, 9]
+                pos_root = [6, 8]
+                edge_range = [2, 12]
+            else:
+                pos_head = [0, 2, 6]
+                pos_root = [4, 6]
+                edge_range = [1, 9]
+
+            for pos in pos_head:
+                edges = insert_fillet(edges, pos, r_head)
+
+            for pos in pos_root:
+                try:
+                    edges = insert_fillet(edges, pos, r_root)
+                except RuntimeError:
+                    edges.pop(8)
+                    edges.pop(6)
+                    edge_range = [2, 10]
+                    pos_root = [5, 7]
+                    for pos in pos_root:
+                        edges = insert_fillet(edges, pos, r_root)
+                    break
+            edges = edges[edge_range[0] : edge_range[1]]
+            edges = [e for e in edges if e is not None]
+
+            tooth = Part.Wire(edges)
+            profile = rotate_tooth(tooth, obj.teeth)
+
+            if obj.height.Value == 0:
+                return profile
+            base = Part.Face(profile)
+            if obj.beta.Value == 0:
+                return base.extrude(App.Vector(0, 0, obj.height.Value))
+            else:
+                twist_angle = obj.height.Value * np.tan(obj.gear.beta) * 2 / obj.gear.d
+                return helicalextrusion(
+                    base, obj.height.Value, twist_angle, obj.double_helix
+                )
+        else:
+            rw = obj.gear.dw / 2
+            return Part.makeCylinder(rw, obj.height.Value)

freecad/gears/involutegearrack.py

@@ -0,0 +1,239 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+from pygears.involute_tooth import InvoluteRack
+
+from .basegear import BaseGear, fcvec, points_to_wire, insert_fillet
+
+
+class InvoluteGearRack(BaseGear):
+
+    """FreeCAD gear rack"""
+
+    def __init__(self, obj):
+        super(InvoluteGearRack, self).__init__(obj)
+        self.involute_rack = InvoluteRack()
+        obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+        obj.addProperty("App::PropertyLength", "module", "base", "module")
+        obj.addProperty("App::PropertyLength", "thickness", "base", "thickness")
+        obj.addProperty(
+            "App::PropertyBool",
+            "simplified",
+            "precision",
+            "if enabled the rack is drawn with a constant number of \
+            teeth to avoid topologic renaming.",
+        )
+        obj.addProperty("App::PropertyPythonObject", "rack", "base", "test")
+
+        self.add_helical_properties(obj)
+        self.add_computed_properties(obj)
+        self.add_tolerance_properties(obj)
+        self.add_involute_properties(obj)
+        self.add_fillet_properties(obj)
+        obj.rack = self.involute_rack
+        obj.teeth = 15
+        obj.module = "1. mm"
+        obj.pressure_angle = "20. deg"
+        obj.height = "5. mm"
+        obj.thickness = "5 mm"
+        obj.beta = "0. deg"
+        obj.clearance = 0.25
+        obj.head = 0.0
+        obj.properties_from_tool = False
+        obj.add_endings = True
+        obj.simplified = False
+        self.obj = obj
+        obj.Proxy = self
+
+    def add_helical_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyBool",
+            "properties_from_tool",
+            "helical",
+            "if beta is given and properties_from_tool is enabled, \
+            gear parameters are internally recomputed for the rotated gear",
+        )
+        obj.addProperty("App::PropertyAngle", "beta", "helical", "beta ")
+        obj.addProperty("App::PropertyBool", "double_helix", "helical", "double helix")
+
+    def add_computed_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyLength",
+            "transverse_pitch",
+            "computed",
+            "pitch in the transverse plane",
+            1,
+        )
+        obj.addProperty(
+            "App::PropertyBool",
+            "add_endings",
+            "base",
+            "if enabled the total length of the rack is teeth x pitch, \
+            otherwise the rack starts with a tooth-flank",
+        )
+
+    def add_tolerance_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head",
+            "tolerance",
+            "head * module = additional length of head",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "clearance",
+            "tolerance",
+            "clearance * module = additional length of root",
+        )
+
+    def add_involute_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyAngle", "pressure_angle", "involute", "pressure angle"
+        )
+
+    def add_fillet_properties(self, obj):
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head_fillet",
+            "fillets",
+            "a fillet for the tooth-head, radius = head_fillet x module",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "root_fillet",
+            "fillets",
+            "a fillet for the tooth-root, radius = root_fillet x module",
+        )
+
+    def generate_gear_shape(self, obj):
+        obj.rack.m = obj.module.Value
+        obj.rack.z = obj.teeth
+        obj.rack.pressure_angle = obj.pressure_angle.Value * np.pi / 180.0
+        obj.rack.thickness = obj.thickness.Value
+        obj.rack.beta = obj.beta.Value * np.pi / 180.0
+        obj.rack.head = obj.head
+        # checksbackwardcompatibility:
+        if "clearance" in obj.PropertiesList:
+            obj.rack.clearance = obj.clearance
+        if "properties_from_tool" in obj.PropertiesList:
+            obj.rack.properties_from_tool = obj.properties_from_tool
+        if "add_endings" in obj.PropertiesList:
+            obj.rack.add_endings = obj.add_endings
+        if "simplified" in obj.PropertiesList:
+            obj.rack.simplified = obj.simplified
+        obj.rack._update()
+        m, m_n, pitch, pressure_angle_t = obj.rack.compute_properties()
+        obj.transverse_pitch = "{} mm".format(pitch)
+        t = obj.thickness.Value
+        c = obj.clearance
+        h = obj.head
+        alpha = obj.pressure_angle.Value * np.pi / 180.0
+        head_fillet = obj.head_fillet
+        root_fillet = obj.root_fillet
+        x1 = -m * np.pi / 2
+        y1 = -m * (1 + c)
+        y2 = y1
+        x2 = -m * np.pi / 4 + y2 * np.tan(alpha)
+        y3 = m * (1 + h)
+        x3 = -m * np.pi / 4 + y3 * np.tan(alpha)
+        x4 = -x3
+        x5 = -x2
+        x6 = -x1
+        y4 = y3
+        y5 = y2
+        y6 = y1
+        p1 = np.array([y1, x1])
+        p2 = np.array([y2, x2])
+        p3 = np.array([y3, x3])
+        p4 = np.array([y4, x4])
+        p5 = np.array([y5, x5])
+        p6 = np.array([y6, x6])
+        line1 = [p1, p2]
+        line2 = [p2, p3]
+        line3 = [p3, p4]
+        line4 = [p4, p5]
+        line5 = [p5, p6]
+        tooth = Part.Wire(points_to_wire([line1, line2, line3, line4, line5]))
+
+        edges = tooth.Edges
+        edges = insert_fillet(edges, 0, m * root_fillet)
+        edges = insert_fillet(edges, 2, m * head_fillet)
+        edges = insert_fillet(edges, 4, m * head_fillet)
+        edges = insert_fillet(edges, 6, m * root_fillet)
+
+        tooth_edges = [e for e in edges if e is not None]
+        p_end = np.array(tooth_edges[-2].lastVertex().Point[:-1])
+        p_start = np.array(tooth_edges[1].firstVertex().Point[:-1])
+        p_start += np.array([0, np.pi * m])
+        edge = points_to_wire([[p_end, p_start]]).Edges
+        tooth = Part.Wire(tooth_edges[1:-1] + edge)
+        teeth = [tooth]
+
+        for i in range(obj.teeth - 1):
+            tooth = tooth.copy()
+            tooth.translate(App.Vector(0, np.pi * m, 0))
+            teeth.append(tooth)
+
+        teeth[-1] = Part.Wire(teeth[-1].Edges[:-1])
+
+        if obj.add_endings:
+            teeth = [Part.Wire(tooth_edges[0])] + teeth
+            last_edge = tooth_edges[-1]
+            last_edge.translate(App.Vector(0, np.pi * m * (obj.teeth - 1), 0))
+            teeth = teeth + [Part.Wire(last_edge)]
+
+        p_start = np.array(teeth[0].Edges[0].firstVertex().Point[:-1])
+        p_end = np.array(teeth[-1].Edges[-1].lastVertex().Point[:-1])
+        p_start_1 = p_start - np.array([obj.thickness.Value, 0.0])
+        p_end_1 = p_end - np.array([obj.thickness.Value, 0.0])
+
+        line6 = [p_start, p_start_1]
+        line7 = [p_start_1, p_end_1]
+        line8 = [p_end_1, p_end]
+
+        bottom = points_to_wire([line6, line7, line8])
+
+        pol = Part.Wire([bottom] + teeth)
+
+        if obj.height.Value == 0:
+            return pol
+        elif obj.beta.Value == 0:
+            face = Part.Face(Part.Wire(pol))
+            return face.extrude(fcvec([0.0, 0.0, obj.height.Value]))
+        elif obj.double_helix:
+            beta = obj.beta.Value * np.pi / 180.0
+            pol2 = Part.Wire(pol)
+            pol2.translate(
+                fcvec([0.0, np.tan(beta) * obj.height.Value / 2, obj.height.Value / 2])
+            )
+            pol3 = Part.Wire(pol)
+            pol3.translate(fcvec([0.0, 0.0, obj.height.Value]))
+            return Part.makeLoft([pol, pol2, pol3], True, True)
+        else:
+            beta = obj.beta.Value * np.pi / 180.0
+            pol2 = Part.Wire(pol)
+            pol2.translate(
+                fcvec([0.0, np.tan(beta) * obj.height.Value, obj.height.Value])
+            )
+            return Part.makeLoft([pol, pol2], True)

freecad/gears/lanterngear.py

@@ -0,0 +1,133 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+import scipy as sp
+
+from pygears.bevel_tooth import BevelTooth
+from pygears._functions import rotation
+
+from .basegear import BaseGear, fcvec, part_arc_from_points_and_center
+
+
+class LanternGear(BaseGear):
+    def __init__(self, obj):
+        super(LanternGear, self).__init__(obj)
+        obj.addProperty(
+            "App::PropertyInteger", "teeth", "gear_parameter", "number of teeth"
+        )
+        obj.addProperty("App::PropertyLength", "module", "base", "module")
+        obj.addProperty(
+            "App::PropertyLength",
+            "bolt_radius",
+            "base",
+            "the bolt radius of the rack/chain",
+        )
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+        obj.addProperty(
+            "App::PropertyInteger",
+            "num_profiles",
+            "accuracy",
+            "number of profiles used for loft",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head",
+            "tolerance",
+            "head * module = additional length of head",
+        )
+
+        obj.teeth = 15
+        obj.module = "1. mm"
+        obj.bolt_radius = "1 mm"
+
+        obj.height = "5. mm"
+        obj.num_profiles = 10
+
+        self.obj = obj
+        obj.Proxy = self
+
+    def generate_gear_shape(self, fp):
+        m = fp.module.Value
+        teeth = fp.teeth
+        r_r = fp.bolt_radius.Value
+        r_0 = m * teeth / 2
+        r_max = r_0 + r_r + fp.head * m
+
+        phi_max = (r_r + np.sqrt(r_max**2 - r_0**2)) / r_0
+
+        def find_phi_min(phi_min):
+            return r_0 * (
+                phi_min**2 * r_0
+                - 2 * phi_min * r_0 * np.sin(phi_min)
+                - 2 * phi_min * r_r
+                - 2 * r_0 * np.cos(phi_min)
+                + 2 * r_0
+                + 2 * r_r * np.sin(phi_min)
+            )
+
+        phi_min = sp.optimize.root(find_phi_min, (phi_max + r_r / r_0 * 4) / 5).x[
+            0
+        ]  # , r_r / r_0, phi_max)
+
+        # phi_min = 0 # r_r / r_0
+        phi = np.linspace(phi_min, phi_max, fp.num_profiles)
+        x = r_0 * (np.cos(phi) + phi * np.sin(phi)) - r_r * np.sin(phi)
+        y = r_0 * (np.sin(phi) - phi * np.cos(phi)) + r_r * np.cos(phi)
+        xy1 = np.array([x, y]).T
+        p_1 = xy1[0]
+        p_1_end = xy1[-1]
+        bsp_1 = Part.BSplineCurve()
+        bsp_1.interpolate(list(map(fcvec, xy1)))
+        w_1 = bsp_1.toShape()
+
+        xy2 = xy1 * np.array([1.0, -1.0])
+        p_2 = xy2[0]
+        p_2_end = xy2[-1]
+        bsp_2 = Part.BSplineCurve()
+        bsp_2.interpolate(list(map(fcvec, xy2)))
+        w_2 = bsp_2.toShape()
+
+        p_12 = np.array([r_0 - r_r, 0.0])
+
+        arc = Part.Arc(
+            App.Vector(*p_1, 0.0), App.Vector(*p_12, 0.0), App.Vector(*p_2, 0.0)
+        ).toShape()
+
+        rot = rotation(-np.pi * 2 / teeth)
+        p_3 = rot(np.array([p_2_end]))[0]
+        # l = Part.LineSegment(fcvec(p_1_end), fcvec(p_3)).toShape()
+        l = part_arc_from_points_and_center(
+            p_1_end, p_3, np.array([0.0, 0.0])
+        ).toShape()
+        w = Part.Wire([w_2, arc, w_1, l])
+        wires = [w]
+
+        rot = App.Matrix()
+        for _ in range(teeth - 1):
+            rot.rotateZ(np.pi * 2 / teeth)
+            wires.append(w.transformGeometry(rot))
+
+        wi = Part.Wire(wires)
+        if fp.height.Value == 0:
+            return wi
+        else:
+            return Part.Face(wi).extrude(App.Vector(0, 0, fp.height))

freecad/gears/timinggear.py

@@ -0,0 +1,285 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+
+from pygears._functions import reflection
+from .basegear import BaseGear, part_arc_from_points_and_center
+
+
+class TimingGear(BaseGear):
+    """FreeCAD gear rack"""
+
+    data = {
+        "gt2": {
+            "pitch": 2.0,
+            "u": 0.254,
+            "h": 0.75,
+            "H": 1.38,
+            "r0": 0.555,
+            "r1": 1.0,
+            "rs": 0.15,
+            "offset": 0.40,
+        },
+        "gt3": {
+            "pitch": 3.0,
+            "u": 0.381,
+            "h": 1.14,
+            "H": 2.40,
+            "r0": 0.85,
+            "r1": 1.52,
+            "rs": 0.25,
+            "offset": 0.61,
+        },
+        "gt5": {
+            "pitch": 5.0,
+            "u": 0.5715,
+            "h": 1.93,
+            "H": 3.81,
+            "r0": 1.44,
+            "r1": 2.57,
+            "rs": 0.416,
+            "offset": 1.03,
+        },
+        "gt8": {
+            "pitch": 8.0,
+            "u": 0.9144,
+            "h": 3.088,
+            "H": 6.096,
+            "r0": 2.304,
+            "r1": 4.112,
+            "rs": 0.6656,
+            "offset": 1.648,
+        },
+        "htd3": {
+            "pitch": 3.0,
+            "u": 0.381,
+            "h": 1.21,
+            "H": 2.40,
+            "r0": 0.89,
+            "r1": 0.89,
+            "rs": 0.26,
+            "offset": 0.0,
+        },
+        "htd5": {
+            "pitch": 5.0,
+            "u": 0.5715,
+            "h": 2.06,
+            "H": 3.80,
+            "r0": 1.49,
+            "r1": 1.49,
+            "rs": 0.43,
+            "offset": 0.0,
+        },
+        "htd8": {
+            "pitch": 8.0,
+            "u": 0.686,
+            "h": 3.45,
+            "H": 6.00,
+            "r0": 2.46,
+            "r1": 2.46,
+            "rs": 0.70,
+            "offset": 0.0,
+        },
+    }
+
+    def __init__(self, obj):
+        super(TimingGear, self).__init__(obj)
+        obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
+        obj.addProperty(
+            "App::PropertyEnumeration", "type", "base", "type of timing-gear"
+        )
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+        obj.addProperty("App::PropertyLength", "pitch", "computed", "pitch of gear", 1)
+        obj.addProperty(
+            "App::PropertyLength", "h", "computed", "radial height of teeth", 1
+        )
+        obj.addProperty(
+            "App::PropertyLength",
+            "u",
+            "computed",
+            "radial difference between pitch diameter and head of gear",
+            1,
+        )
+        obj.addProperty(
+            "App::PropertyLength", "r0", "computed", "radius of first arc", 1
+        )
+        obj.addProperty(
+            "App::PropertyLength", "r1", "computed", "radius of second arc", 1
+        )
+        obj.addProperty(
+            "App::PropertyLength", "rs", "computed", "radius of third arc", 1
+        )
+        obj.addProperty(
+            "App::PropertyLength",
+            "offset",
+            "computed",
+            "x-offset of second arc-midpoint",
+            1,
+        )
+        obj.teeth = 15
+        obj.type = ["gt2", "gt3", "gt5", "gt8", "htd3", "htd5", "htd8"]
+        obj.height = "5. mm"
+
+        self.obj = obj
+        obj.Proxy = self
+
+    def generate_gear_shape(self, fp):
+        # m ... center of arc/circle
+        # r ... radius of arc/circle
+        # x ... end-point of arc
+        # phi ... angle
+        tp = fp.type
+        gt_data = self.data[tp]
+        pitch = fp.pitch = gt_data["pitch"]
+        h = fp.h = gt_data["h"]
+        u = fp.u = gt_data["u"]
+        r_12 = fp.r0 = gt_data["r0"]
+        r_23 = fp.r1 = gt_data["r1"]
+        r_34 = fp.rs = gt_data["rs"]
+        offset = fp.offset = gt_data["offset"]
+
+        arcs = []
+        if offset == 0.0:
+            phi5 = np.pi / fp.teeth
+            ref = reflection(-phi5 - np.pi / 2.0)
+            rp = pitch * fp.teeth / np.pi / 2.0 - u
+
+            m_34 = np.array([-(r_12 + r_34), rp - h + r_12])
+            x2 = np.array([-r_12, m_34[1]])
+            x4 = np.array([m_34[0], m_34[1] + r_34])
+            x6 = ref(x4)
+
+            mir = np.array([-1.0, 1.0])
+            xn2 = mir * x2
+            xn4 = mir * x4
+            mn_34 = mir * m_34
+
+            arcs.append(part_arc_from_points_and_center(xn4, xn2, mn_34).toShape())
+            arcs.append(
+                Part.Arc(
+                    App.Vector(*xn2, 0.0),
+                    App.Vector(0, rp - h, 0.0),
+                    App.Vector(*x2, 0.0),
+                ).toShape()
+            )
+            arcs.append(part_arc_from_points_and_center(x2, x4, m_34).toShape())
+            arcs.append(
+                part_arc_from_points_and_center(x4, x6, np.array([0.0, 0.0])).toShape()
+            )
+
+        else:
+            phi_12 = np.arctan(np.sqrt(1.0 / (((r_12 - r_23) / offset) ** 2 - 1)))
+            rp = pitch * fp.teeth / np.pi / 2.0
+            r4 = r5 = rp - u
+
+            m_12 = np.array([0.0, r5 - h + r_12])
+            m_23 = np.array([offset, offset / np.tan(phi_12) + m_12[1]])
+            m_23y = m_23[1]
+
+            # solving for phi4:
+            # sympy.solve(
+            # ((r5 - r_34) * sin(phi4) + offset) ** 2 + \
+            # ((r5 - r_34) * cos(phi4) - m_23y) ** 2 - \
+            # ((r_34 + r_23) ** 2), phi4)
+
+            phi4 = 2 * np.arctan(
+                (
+                    -2 * offset * r5
+                    + 2 * offset * r_34
+                    + np.sqrt(
+                        -(m_23y**4)
+                        - 2 * m_23y**2 * offset**2
+                        + 2 * m_23y**2 * r5**2
+                        - 4 * m_23y**2 * r5 * r_34
+                        + 2 * m_23y**2 * r_23**2
+                        + 4 * m_23y**2 * r_23 * r_34
+                        + 4 * m_23y**2 * r_34**2
+                        - offset**4
+                        + 2 * offset**2 * r5**2
+                        - 4 * offset**2 * r5 * r_34
+                        + 2 * offset**2 * r_23**2
+                        + 4 * offset**2 * r_23 * r_34
+                        + 4 * offset**2 * r_34**2
+                        - r5**4
+                        + 4 * r5**3 * r_34
+                        + 2 * r5**2 * r_23**2
+                        + 4 * r5**2 * r_23 * r_34
+                        - 4 * r5**2 * r_34**2
+                        - 4 * r5 * r_23**2 * r_34
+                        - 8 * r5 * r_23 * r_34**2
+                        - r_23**4
+                        - 4 * r_23**3 * r_34
+                        - 4 * r_23**2 * r_34**2
+                    )
+                )
+                / (
+                    m_23y**2
+                    + 2 * m_23y * r5
+                    - 2 * m_23y * r_34
+                    + offset**2
+                    + r5**2
+                    - 2 * r5 * r_34
+                    - r_23**2
+                    - 2 * r_23 * r_34
+                )
+            )
+
+            phi5 = np.pi / fp.teeth
+
+            m_34 = (r5 - r_34) * np.array([-np.sin(phi4), np.cos(phi4)])
+
+            x2 = np.array([-r_12 * np.sin(phi_12), m_12[1] - r_12 * np.cos(phi_12)])
+            x3 = m_34 + r_34 / (r_34 + r_23) * (m_23 - m_34)
+            x4 = r4 * np.array([-np.sin(phi4), np.cos(phi4)])
+
+            ref = reflection(-phi5 - np.pi / 2)
+            x6 = ref(x4)
+            mir = np.array([-1.0, 1.0])
+            xn2 = mir * x2
+            xn3 = mir * x3
+            xn4 = mir * x4
+
+            mn_34 = mir * m_34
+            mn_23 = mir * m_23
+
+            arcs.append(part_arc_from_points_and_center(xn4, xn3, mn_34).toShape())
+            arcs.append(part_arc_from_points_and_center(xn3, xn2, mn_23).toShape())
+            arcs.append(part_arc_from_points_and_center(xn2, x2, m_12).toShape())
+            arcs.append(part_arc_from_points_and_center(x2, x3, m_23).toShape())
+            arcs.append(part_arc_from_points_and_center(x3, x4, m_34).toShape())
+            arcs.append(
+                part_arc_from_points_and_center(x4, x6, np.array([0.0, 0.0])).toShape()
+            )
+
+        wire = Part.Wire(arcs)
+        wires = [wire]
+        rot = App.Matrix()
+        rot.rotateZ(np.pi * 2 / fp.teeth)
+        for _ in range(fp.teeth - 1):
+            wire = wire.transformGeometry(rot)
+            wires.append(wire)
+
+        wi = Part.Wire(wires)
+        if fp.height.Value == 0:
+            return wi
+        else:
+            return Part.Face(wi).extrude(App.Vector(0, 0, fp.height))

freecad/gears/timinggear_t.py

@@ -0,0 +1,117 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+
+import numpy as np
+import scipy as sp
+
+import FreeCAD as App
+import Part
+
+from pygears._functions import rotation, reflection
+
+from .basegear import BaseGear, fcvec
+
+
+class TimingGearT(BaseGear):
+    def __init__(self, obj):
+        print("hello gear")
+        obj.addProperty("App::PropertyLength", "pitch", "base", "pitch of gear")
+        obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
+        obj.addProperty(
+            "App::PropertyLength", "tooth_height", "base", "radial height of tooth"
+        )
+        obj.addProperty(
+            "App::PropertyLength",
+            "u",
+            "base",
+            "radial distance from tooth-head to pitch circle",
+        )
+        obj.addProperty("App::PropertyAngle", "alpha", "base", "angle of tooth flanks")
+        obj.addProperty("App::PropertyLength", "height", "base", "extrusion height")
+        obj.pitch = "5. mm"
+        obj.teeth = 15
+        obj.tooth_height = "1.2 mm"
+        obj.u = "0.6 mm"
+        obj.alpha = "40. deg"
+        obj.height = "5 mm"
+        self.obj = obj
+        obj.Proxy = self
+
+    def generate_gear_shape(self, fp):
+        print("generate gear shape")
+        pitch = fp.pitch.Value
+        teeth = fp.teeth
+        u = fp.u.Value
+        tooth_height = fp.tooth_height.Value
+        alpha = fp.alpha.Value / 180.0 * np.pi  # we need radiant
+        height = fp.height.Value
+
+        r_p = pitch * teeth / 2.0 / np.pi
+        gamma_0 = pitch / r_p
+        gamma_1 = gamma_0 / 4
+
+        p_A = np.array([np.cos(-gamma_1), np.sin(-gamma_1)]) * (
+            r_p - u - tooth_height / 2
+        )
+
+        def line(s):
+            p = (
+                p_A
+                + np.array([np.cos(alpha / 2 - gamma_1), np.sin(alpha / 2 - gamma_1)])
+                * s
+            )
+            return p
+
+        def dist_p1(s):
+            return (np.linalg.norm(line(s)) - (r_p - u - tooth_height)) ** 2
+
+        def dist_p2(s):
+            return (np.linalg.norm(line(s)) - (r_p - u)) ** 2
+
+        s1 = sp.optimize.minimize(dist_p1, 0.0).x
+        s2 = sp.optimize.minimize(dist_p2, 0.0).x
+
+        p_1 = line(s1)
+        p_2 = line(s2)
+
+        mirror = reflection(0.0)  # reflect the points at the x-axis
+        p_3, p_4 = mirror(np.array([p_2, p_1]))
+
+        rot = rotation(-gamma_0)  # why is the rotation in wrong direction ???
+        p_5 = rot(np.array([p_1]))[0]  # the rotation expects a list of points
+
+        l1 = Part.LineSegment(fcvec(p_1), fcvec(p_2)).toShape()
+        l2 = Part.LineSegment(fcvec(p_2), fcvec(p_3)).toShape()
+        l3 = Part.LineSegment(fcvec(p_3), fcvec(p_4)).toShape()
+        l4 = Part.LineSegment(fcvec(p_4), fcvec(p_5)).toShape()
+        w = Part.Wire([l1, l2, l3, l4])
+
+        # now using a FreeCAD Matrix (this will turn in the right direction)
+        rot = App.Matrix()
+        rot.rotateZ(gamma_0)
+        wires = []
+        for i in range(teeth):
+            w = w.transformGeometry(rot)
+            wires.append(w.copy())
+        contour = Part.Wire(wires)
+        if height == 0:
+            return contour
+        else:
+            face = Part.Face(Part.Wire(wires))
+            return face.extrude(App.Vector(0.0, 0.0, height))

freecad/gears/wormgear.py

@@ -0,0 +1,151 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+import FreeCAD as App
+import Part
+
+import numpy as np
+from pygears.involute_tooth import InvoluteTooth
+from pygears._functions import rotation
+
+from .basegear import BaseGear, helicalextrusion, fcvec
+
+
+class WormGear(BaseGear):
+
+    """FreeCAD gear rack"""
+
+    def __init__(self, obj):
+        super(WormGear, self).__init__(obj)
+        obj.addProperty("App::PropertyInteger", "teeth", "base", "number of teeth")
+        obj.addProperty("App::PropertyLength", "module", "base", "module")
+        obj.addProperty("App::PropertyLength", "height", "base", "height")
+        obj.addProperty("App::PropertyLength", "diameter", "base", "diameter")
+        obj.addProperty("App::PropertyAngle", "beta", "computed", "beta ", 1)
+        obj.addProperty(
+            "App::PropertyAngle", "pressure_angle", "involute", "pressure angle"
+        )
+        obj.addProperty(
+            "App::PropertyBool", "reverse_pitch", "base", "reverse rotation of helix"
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "head",
+            "tolerance",
+            "head * module = additional length of head",
+        )
+        obj.addProperty(
+            "App::PropertyFloat",
+            "clearance",
+            "tolerance",
+            "clearance * module = additional length of root",
+        )
+        obj.teeth = 3
+        obj.module = "1. mm"
+        obj.pressure_angle = "20. deg"
+        obj.height = "5. mm"
+        obj.diameter = "5. mm"
+        obj.clearance = 0.25
+        obj.head = 0
+        obj.reverse_pitch = False
+
+        self.obj = obj
+        obj.Proxy = self
+
+    def generate_gear_shape(self, fp):
+        m = fp.module.Value
+        d = fp.diameter.Value
+        t = fp.teeth
+        h = fp.height
+
+        clearance = fp.clearance
+        head = fp.head
+        alpha = fp.pressure_angle.Value
+        beta = np.arctan(m * t / d)
+        fp.beta = np.rad2deg(beta)
+        beta = -(fp.reverse_pitch * 2 - 1) * (np.pi / 2 - beta)
+
+        r_1 = (d - (2 + 2 * clearance) * m) / 2
+        r_2 = (d + (2 + 2 * head) * m) / 2
+        z_a = (2 + head + clearance) * m * np.tan(np.deg2rad(alpha))
+        z_b = (m * np.pi - 4 * m * np.tan(np.deg2rad(alpha))) / 2
+        z_0 = clearance * m * np.tan(np.deg2rad(alpha))
+        z_1 = z_b - z_0
+        z_2 = z_1 + z_a
+        z_3 = z_2 + z_b - 2 * head * m * np.tan(np.deg2rad(alpha))
+        z_4 = z_3 + z_a
+
+        def helical_projection(r, z):
+            phi = 2 * z / m / t
+            x = r * np.cos(phi)
+            y = r * np.sin(phi)
+            z = 0 * y
+            return np.array([x, y, z]).T
+
+        # create a circle from phi=0 to phi_1 with r_1
+        phi_0 = 2 * z_0 / m / t
+        phi_1 = 2 * z_1 / m / t
+        c1 = Part.makeCircle(
+            r_1,
+            App.Vector(0, 0, 0),
+            App.Vector(0, 0, 1),
+            np.rad2deg(phi_0),
+            np.rad2deg(phi_1),
+        )
+
+        # create first bspline
+        z_values = np.linspace(z_1, z_2, 10)
+        r_values = np.linspace(r_1, r_2, 10)
+        points = helical_projection(r_values, z_values)
+        bsp1 = Part.BSplineCurve()
+        bsp1.interpolate(list(map(fcvec, points)))
+        bsp1 = bsp1.toShape()
+
+        # create circle from phi_2 to phi_3
+        phi_2 = 2 * z_2 / m / t
+        phi_3 = 2 * z_3 / m / t
+        c2 = Part.makeCircle(
+            r_2,
+            App.Vector(0, 0, 0),
+            App.Vector(0, 0, 1),
+            np.rad2deg(phi_2),
+            np.rad2deg(phi_3),
+        )
+
+        # create second bspline
+        z_values = np.linspace(z_3, z_4, 10)
+        r_values = np.linspace(r_2, r_1, 10)
+        points = helical_projection(r_values, z_values)
+        bsp2 = Part.BSplineCurve()
+        bsp2.interpolate(list(map(fcvec, points)))
+        bsp2 = bsp2.toShape()
+
+        wire = Part.Wire([c1, bsp1, c2, bsp2])
+        w_all = [wire]
+
+        rot = App.Matrix()
+        rot.rotateZ(2 * np.pi / t)
+        for i in range(1, t):
+            w_all.append(w_all[-1].transformGeometry(rot))
+
+        full_wire = Part.Wire(w_all)
+        if h == 0:
+            return full_wire
+        else:
+            shape = helicalextrusion(Part.Face(full_wire), h, h * np.tan(beta) * 2 / d)
+            return shape

package.xml

@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
+<package format="1" xmlns="https://wiki.freecad.org/Package_Metadata">
+  <name>freecad.gears workbench</name>
+  <description>A gear workbench for FreeCAD</description>
+  <version>1.2</version>
+  <date>2022-02-07</date>
+  <maintainer email="sppedflyer@gmail.com">looooo</maintainer>
+  <license file="LICENSE">GPL 3</license>
+  <url type="repository" branch="master">https://github.com/looooo/freecad.gears</url>
+  <url type="bugtracker">https://github.com/looooo/freecad.gears/issues</url>
+  <url type="documentation">https://wiki.freecad.org/FCGear_Workbench</url>
+  <icon>freecad/gears/icons/gearworkbench.svg</icon>
+
+  <content>
+    <workbench>
+      <classname>GearWorkbench</classname>
+      <subdirectory>./</subdirectory>
+      <freecadmin>0.19</freecadmin>
+      <tag>gear</tag>
+      <tag>gears</tag>
+    </workbench>
+  </content>
+
+</package>

pygears/__init__.py

@@ -1 +1,19 @@
-__version__ = "0.01"
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+__version__ = "1.2.0"

pygears/_functions.py

@@ -1,79 +1,85 @@
 # -*- coding: utf-8 -*-
-#***************************************************************************
+# ***************************************************************************
-#*                                                                         *
+# *                                                                         *
-#*   This program is free software; you can redistribute it and/or modify  *
+# * This program is free software: you can redistribute it and/or modify    *
-#*   it under the terms of the GNU Lesser General Public License (LGPL)    *
+# * it under the terms of the GNU General Public License as published by    *
-#*   as published by the Free Software Foundation; either version 2 of     *
+# * the Free Software Foundation, either version 3 of the License, or       *
-#*   the License, or (at your option) any later version.                   *
+# * (at your option) any later version.                                     *
-#*   for detail see the LICENCE text file.                                 *
+# *                                                                         *
-#*                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
-#*   This program is distributed in the hope that it will be useful,       *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
-#*   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
-#*   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
+# * GNU General Public License for more details.                            *
-#*   GNU Library General Public License for more details.                  *
+# *                                                                         *
-#*                                                                         *
+# * You should have received a copy of the GNU General Public License       *
-#*   You should have received a copy of the GNU Library General Public     *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
-#*   License along with this program; if not, write to the Free Software   *
+# *                                                                         *
-#*   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  *
+# ***************************************************************************
-#*   USA                                                                   *
-#*                                                                         *
-#***************************************************************************
 
 from __future__ import division
 from numpy import sin, cos, dot, array, ndarray, vstack, transpose, sqrt
-from numpy.linalg import solve
+from numpy.linalg import solve, norm
-import numpy as np
 
 
-def reflection(pressure_angle):
+def reflection(angle):
+    mat = array([[cos(2 * angle), -sin(2 * angle)],
+                 [-sin(2 * angle), -cos(2 * angle)]])
+
+    def func(x):
+        # why not use mat @ x???
+        return dot(x, mat)
+
+    return func
+
+
+def reflection3D(angle):
     mat = array(
-        [[cos(2 * pressure_angle), -sin(2 * pressure_angle)], [-sin(2 * pressure_angle), -cos(2 * pressure_angle)]])
+        [
+            [cos(2 * angle), -sin(2 * angle), 0.0],
+            [-sin(2 * angle), -cos(2 * angle), 0.0],
+            [0.0, 0.0, 1.0],
+        ]
+    )
 
     def func(x):
-        return(dot(x, mat))
+        # why not use mat @ x
-    return(func)
+        return dot(x, mat)
+
+    return func
 
 
-def reflection3D(pressure_angle):
+def rotation(angle, midpoint=None):
-    mat = array([[cos(2 * pressure_angle), -sin(2 * pressure_angle), 0.],
+    midpoint = midpoint or [0.0, 0.0]
-                 [-sin(2 * pressure_angle), -cos(2 * pressure_angle), 0.], [0., 0., 1.]])
+    mat = array([[cos(angle), -sin(angle)], [sin(angle), cos(angle)]])
-
-    def func(x):
-        return(dot(x, mat))
-    return(func)
-
-
-def rotation(pressure_angle, midpoint=None):
-    midpoint = midpoint or [0., 0.]
-    mat = array([[cos(pressure_angle), -sin(pressure_angle)], [sin(pressure_angle), cos(pressure_angle)]])
     midpoint = array(midpoint)
     vec = midpoint - dot(midpoint, mat)
     trans = translation(vec)
 
     def func(xx):
-        return(trans(dot(xx, mat)))
+        return trans(dot(xx, mat))
-    return(func)
+
+    return func
 
 
-def rotation3D(pressure_angle):
+def rotation3D(angle):
     mat = array(
-        [
+        [[cos(angle), -sin(angle), 0.0], [sin(angle), cos(angle), 0.0], [0.0, 0.0, 1.0]]
-            [cos(pressure_angle), -sin(pressure_angle), 0.],
+    )
-            [sin(pressure_angle), cos(pressure_angle), 0.],
-            [0., 0., 1.]])
 
     def func(xx):
-        return(dot(xx, mat))
+        return dot(xx, mat)
-    return(func)
+
+    return func
 
 
 def translation(vec):
     def trans(x):
-        return([x[0] + vec[0], x[1] + vec[1]])
+        return [x[0] + vec[0], x[1] + vec[1]]
 
     def func(x):
-        return(array(list(map(trans, x))))
+        return array(list(map(trans, x)))
-    return(func)
+
+    return func
 
 
 def trim(p1, p2, p3, p4):
@@ -83,32 +89,31 @@ def trim(p1, p2, p3, p4):
     a4 = array(p4)
     if all(a1 == a2) or all(a3 == a4):
         if all(a1 == a3):
-            return(a1)
+            return a1
         else:
-            return(False)
+            return False
     elif all(a1 == a3):
         if all(a2 == a4):
-            return((a1 + a2) / 2)
+            return (a1 + a2) / 2
         else:
-            return(a1)
+            return a1
     elif all(a1 == a4):
         if all(a2 == a3):
-            return((a1 + a2) / 2)
+            return (a1 + a2) / 2
         else:
-            return(a1)
+            return a1
     elif all(a2 == a3) or all(a2 == a4):
-        return(p2)
+        return p2
     try:
         g, h = solve(transpose([-a2 + a1, a4 - a3]), a1 - a3)
     except Exception as e:
         print(e)
-        return(False)
+        return False
     else:
-        if 0. < g < 1. and 0. < h < 1.:
+        if 0.0 < g < 1.0 and 0.0 < h < 1.0:
-            return(a1 + g * (a2 - a1))
+            return a1 + g * (a2 - a1)
         else:
-            return(False)
+            return False
-    return(False)
 
 
 def trimfunc(l1, l2):
@@ -128,46 +133,55 @@ def trimfunc(l1, l2):
                     l2 == [l2[0]]
                 else:
                     l2 = l2[jk::-1]
-                return(array([vstack([l1, [s]]), vstack([[s], l2])]))
+                return [vstack([l1, [s]]), vstack([[s], l2])]
             j0 = j
             jk += 1
         i0 = i
         ik += 1
-    return(False)
+    return False
 
 
-def norm(vec1, vec2):
+def diff_norm(vec1, vec2):
     vec = array(vec2) - array(vec1)
-    return np.linalg.norm(vec)
+    return norm(vec)
 
 
 def nearestpts(evolv, underc):
     ik = 0
     iout = 0
     jout = 0
-    outmin = 1000.
+    outmin = 1000.0
     for i in array(evolv[1:]):
         jk = 0
         for j in array(underc[1:]):
-            l = norm(i, j)
+            l = diff_norm(i, j)
             if l < outmin:
-                re = norm(i, [0, 0])
+                re = diff_norm(i, [0, 0])
-                ru = norm(j, [0, 0])
+                ru = diff_norm(j, [0, 0])
                 if re > ru:
                     outmin = l
                     iout, jout = [ik, jk]
             jk += 1
         ik += 1
-    return([vstack([underc[:jout], evolv[iout]]), evolv[iout:]])
+    return [vstack([underc[:jout], evolv[iout]]), evolv[iout:]]
-
 
 
 def intersection_line_circle(p1, p2, r):
-    """return the intersection point of a line from p1 to p2 and a sphere of radius 1 and 
+    """return the intersection point of a line from p1 to p2 and a sphere of radius 1 and
     midpoint 0,0,0"""
     d = p2 - p1
-    d /= np.linalg.norm(d)
+    d /= norm(d)
     p_half = d.dot(p1)
-    q = p1.dot(p1) - r ** 2
+    q = p1.dot(p1) - r**2
-    t = -p_half + sqrt(p_half ** 2 - q)
+    t = -p_half + sqrt(p_half**2 - q)
     return p1 + d * t
+
+
+def arc_from_points_and_center(p_1, p_2, m):
+    """return 3 points (x1, x12, x2) which can be used to create the arc"""
+    r = (norm(p_1 - m) + norm(p_2 - m)) / 2
+    p_12l = (p_1 + p_2) / 2
+    v = p_12l - m
+    v /= norm(v)
+    p_12 = m + v * r
+    return (p_1, p_12, p_2)

pygears/bevel_tooth.py

@@ -1,114 +1,198 @@
 # -*- coding: utf-8 -*-
-#***************************************************************************
+# ***************************************************************************
-#*                                                                         *
+# *                                                                         *
-#*   This program is free software; you can redistribute it and/or modify  *
+# * This program is free software: you can redistribute it and/or modify    *
-#*   it under the terms of the GNU Lesser General Public License (LGPL)    *
+# * it under the terms of the GNU General Public License as published by    *
-#*   as published by the Free Software Foundation; either version 2 of     *
+# * the Free Software Foundation, either version 3 of the License, or       *
-#*   the License, or (at your option) any later version.                   *
+# * (at your option) any later version.                                     *
-#*   for detail see the LICENCE text file.                                 *
+# *                                                                         *
-#*                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
-#*   This program is distributed in the hope that it will be useful,       *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
-#*   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
-#*   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
+# * GNU General Public License for more details.                            *
-#*   GNU Library General Public License for more details.                  *
+# *                                                                         *
-#*                                                                         *
+# * You should have received a copy of the GNU General Public License       *
-#*   You should have received a copy of the GNU Library General Public     *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
-#*   License along with this program; if not, write to the Free Software   *
+# *                                                                         *
-#*   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  *
+# ***************************************************************************
-#*   USA                                                                   *
-#*                                                                         *
-#***************************************************************************
 
 from __future__ import division
 from __future__ import division
-from numpy import cos, sin, tan, arccos, arctan, pi, array, linspace, transpose, vstack, sqrt
+from numpy import (
-import numpy as np
+    cos,
+    sin,
+    tan,
+    arccos,
+    arctan,
+    pi,
+    array,
+    linspace,
+    transpose,
+    vstack,
+    sqrt,
+)
 from ._functions import rotation3D, reflection3D, intersection_line_circle
 
 
-
+class BevelTooth(object):
-class bevel_tooth(object):
+    def __init__(
-    def __init__(self, pressure_angle=70 * pi / 180, pitch_angle=pi / 4, clearance=0.1,
+        self,
-                 z=21, backlash=0.00, module=0.25):
+        pressure_angle=70 * pi / 180,
+        pitch_angle=pi / 4,
+        clearance=0.1,
+        z=21,
+        backlash=0.00,
+        module=0.25,
+    ):
         self.pressure_angle = pressure_angle
         self.pitch_angle = pitch_angle
         self.z = z
         self.clearance = clearance
         self.backlash = backlash
+        self.angular_backlash = backlash / (z * module / 2)
         self.module = module
 
         self.involute_end = arccos(
-            1 / sqrt(2) * sqrt((42. + 16.*cos(2.*self.pressure_angle) +
+            1
-            6.*cos(4.*self.pressure_angle) + cos(4.*self.pressure_angle - 4.*self.pitch_angle) - 8.*cos(2.*self.pressure_angle - 2.*self.pitch_angle) -
+            / sqrt(2)
-            4.*cos(4.*self.pressure_angle - 2.*self.pitch_angle) + 24.*cos(2.*self.pitch_angle) - 2.*cos(4.*self.pitch_angle) -
+            * sqrt(
-            8.*cos(2.*(self.pressure_angle + self.pitch_angle)) + cos(4.*(self.pressure_angle + self.pitch_angle)) -
+                (
-            4.*cos(4.*self.pressure_angle + 2.*self.pitch_angle) + 24.*cos((4.*sin(self.pitch_angle))/self.z) +
+                    42.0
-            4.*cos(2.*self.pressure_angle - (4.*sin(self.pitch_angle))/self.z) + 4.*cos(2.*self.pressure_angle -
+                    + 16.0 * cos(2.0 * self.pressure_angle)
-            4.*self.pitch_angle - (4.*sin(self.pitch_angle))/self.z) - 8.*cos(2.*self.pressure_angle - 2.*self.pitch_angle -
+                    + 6.0 * cos(4.0 * self.pressure_angle)
-            (4.*sin(self.pitch_angle))/self.z) + 24.*cos(4.*(self.pitch_angle + sin(self.pitch_angle)/self.z)) -
+                    + cos(4.0 * self.pressure_angle - 4.0 * self.pitch_angle)
-            8.*cos(2.*(self.pressure_angle + self.pitch_angle + (2.*sin(self.pitch_angle))/self.z)) + 4.*cos(2.*self.pressure_angle +
+                    - 8.0 * cos(2.0 * self.pressure_angle - 2.0 * self.pitch_angle)
-            (4.*sin(self.pitch_angle))/self.z) + 16.*cos(2.*self.pitch_angle + (4.*sin(self.pitch_angle))/self.z) +
+                    - 4.0 * cos(4.0 * self.pressure_angle - 2.0 * self.pitch_angle)
-            4.*cos(2.*self.pressure_angle + 4.*self.pitch_angle + (4.*sin(self.pitch_angle))/self.z) + 32.*abs(cos(self.pitch_angle +
+                    + 24.0 * cos(2.0 * self.pitch_angle)
-            (2.*sin(self.pitch_angle))/self.z))*cos(self.pressure_angle)*sqrt(4.*cos(2.*self.pressure_angle) -
+                    - 2.0 * cos(4.0 * self.pitch_angle)
-            2.*(-2. + cos(2.*self.pressure_angle - 2.*self.pitch_angle) - 2.*cos(2.*self.pitch_angle) + cos(2.*(self.pressure_angle + self.pitch_angle)) +
+                    - 8.0 * cos(2.0 * (self.pressure_angle + self.pitch_angle))
-            4.*cos(2.*self.pitch_angle + (4.*sin(self.pitch_angle))/self.z)))*sin(2.*self.pitch_angle))/(-6. - 2.*cos(2.*self.pressure_angle) +
+                    + cos(4.0 * (self.pressure_angle + self.pitch_angle))
-            cos(2.*self.pressure_angle - 2.*self.pitch_angle) - 2.*cos(2.*self.pitch_angle) + cos(2.*(self.pressure_angle + self.pitch_angle)))**2))
+                    - 4.0 * cos(4.0 * self.pressure_angle + 2.0 * self.pitch_angle)
+                    + 24.0 * cos((4.0 * sin(self.pitch_angle)) / self.z)
+                    + 4.0
+                    * cos(
+                        2.0 * self.pressure_angle
+                        - (4.0 * sin(self.pitch_angle)) / self.z
+                    )
+                    + 4.0
+                    * cos(
+                        2.0 * self.pressure_angle
+                        - 4.0 * self.pitch_angle
+                        - (4.0 * sin(self.pitch_angle)) / self.z
+                    )
+                    - 8.0
+                    * cos(
+                        2.0 * self.pressure_angle
+                        - 2.0 * self.pitch_angle
+                        - (4.0 * sin(self.pitch_angle)) / self.z
+                    )
+                    + 24.0
+                    * cos(4.0 * (self.pitch_angle + sin(self.pitch_angle) / self.z))
+                    - 8.0
+                    * cos(
+                        2.0
+                        * (
+                            self.pressure_angle
+                            + self.pitch_angle
+                            + (2.0 * sin(self.pitch_angle)) / self.z
+                        )
+                    )
+                    + 4.0
+                    * cos(
+                        2.0 * self.pressure_angle
+                        + (4.0 * sin(self.pitch_angle)) / self.z
+                    )
+                    + 16.0
+                    * cos(
+                        2.0 * self.pitch_angle + (4.0 * sin(self.pitch_angle)) / self.z
+                    )
+                    + 4.0
+                    * cos(
+                        2.0 * self.pressure_angle
+                        + 4.0 * self.pitch_angle
+                        + (4.0 * sin(self.pitch_angle)) / self.z
+                    )
+                    + 32.0
+                    * abs(
+                        cos(self.pitch_angle + (2.0 * sin(self.pitch_angle)) / self.z)
+                    )
+                    * cos(self.pressure_angle)
+                    * sqrt(
+                        4.0 * cos(2.0 * self.pressure_angle)
+                        - 2.0
+                        * (
+                            -2.0
+                            + cos(2.0 * self.pressure_angle - 2.0 * self.pitch_angle)
+                            - 2.0 * cos(2.0 * self.pitch_angle)
+                            + cos(2.0 * (self.pressure_angle + self.pitch_angle))
+                            + 4.0
+                            * cos(
+                                2.0 * self.pitch_angle
+                                + (4.0 * sin(self.pitch_angle)) / self.z
+                            )
+                        )
+                    )
+                    * sin(2.0 * self.pitch_angle)
+                )
+                / (
+                    -6.0
+                    - 2.0 * cos(2.0 * self.pressure_angle)
+                    + cos(2.0 * self.pressure_angle - 2.0 * self.pitch_angle)
+                    - 2.0 * cos(2.0 * self.pitch_angle)
+                    + cos(2.0 * (self.pressure_angle + self.pitch_angle))
+                )
+                ** 2
+            )
+        )
 
-        self.involute_start = -pi/2. + arctan(1/tan(self.pitch_angle)*1/cos(self.pressure_angle))
+        self.involute_start = -pi / 2.0 + arctan(
+            1 / tan(self.pitch_angle) * 1 / cos(self.pressure_angle)
+        )
         self.involute_start_radius = self.get_radius(self.involute_start)
-        self.r_f = sin(self.pitch_angle - sin(pitch_angle) * 2 / self.z) - self.clearance * sin(self.pitch_angle)
+        self.r_f = sin(
+            self.pitch_angle - sin(pitch_angle) * 2 / self.z
+        ) - self.clearance * sin(self.pitch_angle)
         self.z_f = cos(self.pitch_angle - sin(pitch_angle) * 2 / self.z)
         self.add_foot = True
 
-        # if self.involute_start_radius < self.r_f:
-        #     self.add_foot = False
-        #     self.involute_start = -arccos(
-        #         sqrt((42 + 16*cos(2*self.pressure_angle) + 6*cos(4*self.pressure_angle) -
-        #         4*cos(4*self.pressure_angle - 2*self.pitch_angle) - 8*cos(2*(self.pressure_angle - self.pitch_angle)) +
-        #         cos(4*(self.pressure_angle - self.pitch_angle)) + 24*cos(2*self.pitch_angle) - 2*cos(4*self.pitch_angle) -
-        #         8*cos(2*(self.pressure_angle + self.pitch_angle)) + cos(4*(self.pressure_angle + self.pitch_angle)) -
-        #         4*cos(2*(2*self.pressure_angle + self.pitch_angle)) + 24*cos((4*sin(self.pitch_angle))/self.z) +
-        #         4*cos(2*self.pressure_angle - (4*sin(self.pitch_angle))/self.z) + 16*cos(2*self.pitch_angle -
-        #         (4*sin(self.pitch_angle))/self.z) + 24*cos(4*self.pitch_angle - (4*sin(self.pitch_angle))/self.z) +
-        #         4*cos(2*self.pressure_angle + 4*self.pitch_angle - (4*sin(self.pitch_angle))/self.z) -
-        #         8*cos(2*(self.pressure_angle + self.pitch_angle - (2*sin(self.pitch_angle))/self.z)) +
-        #         4*cos(2*self.pressure_angle + (4*sin(self.pitch_angle))/self.z) + 4*cos(2*self.pressure_angle -
-        #         4*self.pitch_angle + (4*sin(self.pitch_angle))/self.z) - 8*cos(2*self.pressure_angle - 2*self.pitch_angle +
-        #         (4*sin(self.pitch_angle))/self.z) + 32*sqrt(2)*sqrt(-(cos(self.pressure_angle)**2*
-        #         (-2 - 2*cos(2*self.pressure_angle) + cos(2*(self.pressure_angle - self.pitch_angle)) -
-        #         2*cos(2*self.pitch_angle) + cos(2*(self.pressure_angle + self.pitch_angle)) +
-        #         4*cos(2*self.pitch_angle - (4*sin(self.pitch_angle))/self.z))*cos(self.pitch_angle - (2*sin(self.pitch_angle))/self.z)**2*
-        #         sin(2*self.pitch_angle)**2)))/(-6 - 2*cos(2*self.pressure_angle) + cos(2*(self.pressure_angle - self.pitch_angle)) -
-        #         2*cos(2*self.pitch_angle) + cos(2*(self.pressure_angle + self.pitch_angle)))**2)/sqrt(2))
-
     def involute_function_x(self):
         def func(s):
-            return((
+            return -(
-                -(cos(s*1/sin(self.pressure_angle)*1/sin(self.pitch_angle))*sin(self.pressure_angle)*sin(s)) +
+                cos(s * 1 / sin(self.pressure_angle) * 1 / sin(self.pitch_angle))
-                (cos(s)*sin(self.pitch_angle) + cos(self.pressure_angle)*cos(self.pitch_angle)*sin(s))*
+                * sin(self.pressure_angle)
-                sin(s*1/sin(self.pressure_angle)*1/sin(self.pitch_angle))))
+                * sin(s)
-        return(func)
+            ) + (
+                cos(s) * sin(self.pitch_angle)
+                + cos(self.pressure_angle) * cos(self.pitch_angle) * sin(s)
+            ) * sin(s * 1 / sin(self.pressure_angle) * 1 / sin(self.pitch_angle))
+
+        return func
 
     def involute_function_y(self):
         def func(s):
-            return((
+            return cos(s * 1 / sin(self.pressure_angle) * 1 / sin(self.pitch_angle)) * (
-                cos(s*1/sin(self.pressure_angle)*1/sin(self.pitch_angle))*(cos(s)*sin(self.pitch_angle) +
+                cos(s) * sin(self.pitch_angle)
-                cos(self.pressure_angle)*cos(self.pitch_angle)*sin(s)) + sin(self.pressure_angle)*sin(s)*
+                + cos(self.pressure_angle) * cos(self.pitch_angle) * sin(s)
-                sin(s*1/sin(self.pressure_angle)*1/sin(self.pitch_angle))))
+            ) + sin(self.pressure_angle) * sin(s) * sin(
-        return(func)
+                s * 1 / sin(self.pressure_angle) * 1 / sin(self.pitch_angle)
+            )
+
+        return func
 
     def involute_function_z(self):
         def func(s):
-            return((
+            return cos(self.pitch_angle) * cos(s) - cos(self.pressure_angle) * sin(
-                cos(self.pitch_angle)*cos(s) - cos(self.pressure_angle)*sin(self.pitch_angle)*sin(s)))
+                self.pitch_angle
-        return(func)
+            ) * sin(s)
+
+        return func
 
     def get_radius(self, s):
         x = self.involute_function_x()
         y = self.involute_function_y()
         rx = x(s)
         ry = y(s)
-        return(sqrt(rx**2 + ry**2))
+        return sqrt(rx**2 + ry**2)
 
     def involute_points(self, num=10):
         pts = linspace(self.involute_start, self.involute_end, num=num)
@@ -125,45 +209,40 @@ class bevel_tooth(object):
 
         r_cut = self.r_f / self.z_f
         for i, point in enumerate(xy[1:]):
-            if point.dot(point) >= r_cut ** 2:
+            if point.dot(point) >= r_cut**2:
                 break
         if i > 0:
             self.add_foot = False
         intersection_point = intersection_line_circle(xy[i], point, r_cut)
-        xy = array([intersection_point] + list(xy[i+1:]))
+        xy = array([intersection_point] + list(xy[i + 1 :]))
         xyz = [[p[0], p[1], 1] for p in xy]
-        backlash_rot = rotation3D(self.backlash / 4)
+        backlash_rot = rotation3D(self.angular_backlash / 2)
         xyz = backlash_rot(xyz)
-        return(xyz)
+        return xyz
 
     def points(self, num=10):
         pts = self.involute_points(num=num)
-        rot = rotation3D(-pi/self.z/2)
+        rot = rotation3D(-pi / self.z / 2)
         pts = rot(pts)
-        ref = reflection3D(pi/2)
+        ref = reflection3D(pi / 2)
         pts1 = ref(pts)[::-1]
-        rot = rotation3D(2*pi/self.z)
         if self.add_foot:
-            return(array([
+            return [
                 array([pts[0], pts[1]]),
-                pts[1:],
+                array(pts[1:]),
                 array([pts[-1], pts1[0]]),
-                pts1[:-1],
+                array(pts1[:-1]),
-                array([pts1[-2], pts1[-1]])
+                array([pts1[-2], pts1[-1]]),
-                ]))
+            ]
         else:
-            return(array([pts, array([pts[-1], pts1[0]]), pts1]))
+            return [pts, array([pts[-1], pts1[0]]), pts1]
 
     def _update(self):
-        self.__init__(z=self.z, clearance=self.clearance,
+        self.__init__(
-                      pressure_angle=self.pressure_angle,
+            z=self.z,
-                      pitch_angle=self.pitch_angle,
+            clearance=self.clearance,
-                      backlash=self.backlash, module=self.module)
+            pressure_angle=self.pressure_angle,
-
+            pitch_angle=self.pitch_angle,
-
+            backlash=self.backlash,
-if __name__ == "__main__":
+            module=self.module,
-    from matplotlib import pyplot
+        )
-    gear = bevel_tooth(z=60, clearance=0.0, pitch_angle=np.deg2rad(45))
-    x, y, z = gear.involute_points().T
-    pyplot.plot(x, y)
-    pyplot.show()

pygears/computation.py

@@ -1,9 +1,27 @@
-import numpy as np
+# -*- coding: utf-8 -*-
-from scipy import optimize as opt
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
 
-def computeShiftedGears(m, alpha, t1, t2, x1, x2):
+import numpy as np
+
+
+def compute_shifted_gears(m, alpha, t1, t2, x1, x2):
     """Summary
-    
+
     Args:
         m (float): common module of both gears [length]
         alpha (float): pressure-angle [rad]
@@ -11,13 +29,37 @@ def computeShiftedGears(m, alpha, t1, t2, x1, x2):
         t2 (int): number of teeth of gear2
         x1 (float): relative profile-shift of gear1
         x2 (float): relative profile-shift of gear2
-    
+
     Returns:
         (float, float): distance between gears [length], pressure angle of the assembly [rad]
     """
-    inv = lambda x: np.tan(x) - x
+
+    def inv(x):
+        return np.tan(x) - x
+
     inv_alpha_w = inv(alpha) + 2 * np.tan(alpha) * (x1 + x2) / (t1 + t2)
-    root_inv = lambda x: inv(x) - inv_alpha_w
+
-    alpha_w = opt.fsolve(root_inv, 0.)
+    def root_inv(x):
-    dist = m * (t1+ t2) / 2 * np.cos(alpha) / np.cos(alpha_w)
+        return inv(x) - inv_alpha_w
-    return dist, alpha_w
+
+    def d_root_inv(x):
+        return 1.0 / np.cos(x) - 1
+
+    alpha_w = find_root(alpha, root_inv, d_root_inv)
+    dist = m * (t1 + t2) / 2 * np.cos(alpha) / np.cos(alpha_w)
+    return dist, alpha_w
+
+
+def find_root(x0, f, df, epsilon=2e-10, max_iter=100):
+    x_n = x0
+    for i in range(max_iter):
+        f_xn = f(x_n)
+        if abs(f_xn) < epsilon:
+            return x_n
+        else:
+            df_xn = df(x_n)
+            if df_xn == 0:
+                return None
+            else:
+                x_n = x_n - f_xn / df_xn / 2  # adding (/ 2) to avoid oscillation
+    return None

pygears/cycloid_tooth.py

@@ -0,0 +1,130 @@
+# -*- coding: utf-8 -*-
+# ***************************************************************************
+# *                                                                         *
+# * This program is free software: you can redistribute it and/or modify    *
+# * it under the terms of the GNU General Public License as published by    *
+# * the Free Software Foundation, either version 3 of the License, or       *
+# * (at your option) any later version.                                     *
+# *                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
+# * GNU General Public License for more details.                            *
+# *                                                                         *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+from __future__ import division
+from numpy import cos, sin, arccos, pi, array, linspace, transpose, vstack
+from ._functions import rotation, reflection
+
+
+class CycloidTooth:
+    def __init__(self, z1=5, z2=5, z=14, m=5, clearance=0.25, backlash=0.00, head=0.0):
+        self.m = m
+        self.z = z
+        self.clearance = clearance
+        self.backlash = backlash
+        self.z1 = z1
+        self.z2 = z2
+        self.head = head
+        self._calc_gear_factors()
+
+    def _calc_gear_factors(self):
+        self.d1 = self.z1 * self.m
+        self.d2 = self.z2 * self.m
+        self.phi = self.m * pi
+        self.d = self.z * self.m
+        self.da = self.d + 2 * (1 + self.head) * self.m
+        self.di = self.d - 2 * (1 + self.clearance) * self.m
+        self.phipart = 2 * pi / self.z
+        self.angular_backlash = self.backlash / (self.d / 2)
+
+    def epicycloid_x(self):
+        def func(t):
+            return ((self.d2 + self.d) * cos(t)) / 2.0 - (
+                self.d2 * cos((1 + self.d / self.d2) * t)
+            ) / 2.0
+
+        return func
+
+    def epicycloid_y(self):
+        def func(t):
+            return ((self.d2 + self.d) * sin(t)) / 2.0 - (
+                self.d2 * sin((1 + self.d / self.d2) * t)
+            ) / 2.0
+
+        return func
+
+    def hypocycloid_x(self):
+        def func(t):
+            return (self.d - self.d1) * cos(t) / 2 + self.d1 / 2 * cos(
+                (self.d / self.d1 - 1) * t
+            )
+
+        return func
+
+    def hypocycloid_y(self):
+        def func(t):
+            return (self.d - self.d1) * sin(t) / 2 - self.d1 / 2 * sin(
+                (self.d / self.d1 - 1) * t
+            )
+
+        return func
+
+    def inner_end(self):
+        return -(
+            (
+                self.d1
+                * arccos(
+                    (2 * self.d1**2 - self.di**2 - 2 * self.d1 * self.d + self.d**2)
+                    / (2.0 * self.d1 * (self.d1 - self.d))
+                )
+            )
+            / self.d
+        )
+
+    def outer_end(self):
+        return (
+            self.d2
+            * arccos(
+                (2 * self.d2**2 - self.da**2 + 2 * self.d2 * self.d + self.d**2)
+                / (2.0 * self.d2 * (self.d2 + self.d))
+            )
+        ) / self.d
+
+    def points(self, num=10):
+        inner_x = self.hypocycloid_x()
+        inner_y = self.hypocycloid_y()
+        outer_x = self.epicycloid_x()
+        outer_y = self.epicycloid_y()
+        t_inner_end = self.inner_end()
+        t_outer_end = self.outer_end()
+        t_vals_outer = linspace(0, t_outer_end, num)
+        t_vals_inner = linspace(t_inner_end, 0, num)
+        pts_outer_x = list(map(outer_x, t_vals_outer))
+        pts_outer_y = list(map(outer_y, t_vals_outer))
+        pts_inner_x = list(map(inner_x, t_vals_inner))
+        pts_inner_y = list(map(inner_y, t_vals_inner))
+        pts_outer = transpose([pts_outer_x, pts_outer_y])
+        pts_inner = transpose([pts_inner_x, pts_inner_y])
+        pts1 = vstack([pts_inner[:-2], pts_outer])
+        rot = rotation(self.phipart / 4 - self.angular_backlash / 2)
+        pts1 = rot(pts1)
+        ref = reflection(0.0)
+        pts2 = ref(pts1)[::-1]
+        one_tooth = [pts1, array([pts1[-1], pts2[0]]), pts2]
+        return one_tooth
+
+    def _update(self):
+        self.__init__(
+            m=self.m,
+            z=self.z,
+            z1=self.z1,
+            z2=self.z2,
+            clearance=self.clearance,
+            backlash=self.backlash,
+            head=self.head,
+        )

pygears/cycloide_tooth.py

@@ -1,117 +0,0 @@
-# -*- coding: utf-8 -*-
-#***************************************************************************
-#*                                                                         *
-#*   This program is free software; you can redistribute it and/or modify  *
-#*   it under the terms of the GNU Lesser General Public License (LGPL)    *
-#*   as published by the Free Software Foundation; either version 2 of     *
-#*   the License, or (at your option) any later version.                   *
-#*   for detail see the LICENCE text file.                                 *
-#*                                                                         *
-#*   This program is distributed in the hope that it will be useful,       *
-#*   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
-#*   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
-#*   GNU Library General Public License for more details.                  *
-#*                                                                         *
-#*   You should have received a copy of the GNU Library General Public     *
-#*   License along with this program; if not, write to the Free Software   *
-#*   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  *
-#*   USA                                                                   *
-#*                                                                         *
-#***************************************************************************
-
-from __future__ import division
-from numpy import cos, sin, arccos, pi, array, linspace, transpose, vstack
-from ._functions import rotation, reflection
-
-class cycloide_tooth():
-    def __init__(self, z1 = 5, z2 = 5, z = 14, m = 5, clearance = 0.12, backlash = 0.00):
-        self.m = m
-        self.z = z
-        self.clearance = clearance
-        self.backlash = backlash
-        self.z1 = z1
-        self.z2 = z2
-        self._calc_gear_factors()
-
-    def _calc_gear_factors(self):
-        self.d1 = self.z1 * self.m
-        self.d2 = self.z2 * self.m
-        self.phi = self.m * pi
-        self.d = self.z * self.m
-        self.da = self.d + 2*self.m
-        self.di = self.d - 2*self.m - self.clearance * self.m
-        self.phipart = 2 * pi / self.z
-
-    def epicycloide_x(self):
-        def func(t):
-            return(((self.d2 + self.d) * cos(t))/2. - (self.d2 * cos((1 + self.d / self.d2) * t))/2.)
-        return(func)
-
-    def epicycloide_y(self):
-        def func(t):
-            return(((self.d2 + self.d) * sin(t))/2. - (self.d2 * sin((1 + self.d / self.d2) * t))/2.)
-        return(func)
-
-    def hypocycloide_x(self):
-        def func(t):
-            return((self.d - self.d1)*cos(t)/2 + self.d1/2 * cos((self.d / self.d1 - 1) * t))
-        return(func)
-
-    def hypocycloide_y(self):
-        def func(t):
-            return((self.d - self.d1)*sin(t)/2 - self.d1/2 *sin((self.d/self.d1 - 1)*t))
-        return(func)
-
-    def inner_end(self):
-        return(
-            -((self.d1*arccos((2*self.d1**2 - self.di**2 -
-                2*self.d1*self.d + self.d**2)/(2.*self.d1*
-                (self.d1 - self.d))))/self.d)
-            )
-
-    def outer_end(self):
-        return(
-            (self.d2*arccos((2*self.d2**2 - self.da**2 +
-                2*self.d2*self.d + self.d**2)/
-                (2.*self.d2*(self.d2 + self.d))))/self.d
-            )
-
-    def points(self, num = 10):
-
-        inner_x = self.hypocycloide_x()
-        inner_y = self.hypocycloide_y()
-        outer_x = self.epicycloide_x()
-        outer_y = self.epicycloide_y()
-        t_inner_end = self.inner_end()
-        t_outer_end = self.outer_end()
-        t_vals_outer = linspace(0, t_outer_end, num)
-        t_vals_inner = linspace(t_inner_end,0,num)
-        pts_outer_x = list(map(outer_x, t_vals_outer))
-        pts_outer_y = list(map(outer_y, t_vals_outer))
-        pts_inner_x = list(map(inner_x, t_vals_inner))
-        pts_inner_y = list(map(inner_y, t_vals_inner))
-        pts_outer = transpose([pts_outer_x, pts_outer_y])
-        pts_inner = transpose([pts_inner_x, pts_inner_y])
-        pts1 = vstack([pts_inner[:-2],pts_outer])
-        rot =rotation(self.phipart / 4 - self.backlash)
-        pts1 = rot(pts1)
-        ref = reflection(0.)
-        pts2 = ref(pts1)[::-1]
-        one_tooth = [pts1,array([pts1[-1],pts2[0]]), pts2]
-        return(one_tooth)
-
-    def _update(self):
-        self.__init__(m = self.m, z = self.z, z1 = self.z1, z2 = self.z2,
-                      clearance = self.clearance, backlash = self.backlash)
-
-if __name__ == "__main__":
-	from matplotlib import pyplot
-	gear = cycloide_tooth()
-	x = []
-	y = []
-	for i in gear.points(30):
-		for j in i:
-			x.append(j[0])
-			y.append(j[1])
-	pyplot.plot(x[-60:],y[-60:])
-	pyplot.show()

pygears/involute_tooth.py

@@ -1,32 +1,59 @@
 # -*- coding: utf-8 -*-
-#***************************************************************************
+# ***************************************************************************
-#*                                                                         *
+# *                                                                         *
-#*   This program is free software; you can redistribute it and/or modify  *
+# * This program is free software: you can redistribute it and/or modify    *
-#*   it under the terms of the GNU Lesser General Public License (LGPL)    *
+# * it under the terms of the GNU General Public License as published by    *
-#*   as published by the Free Software Foundation; either version 2 of     *
+# * the Free Software Foundation, either version 3 of the License, or       *
-#*   the License, or (at your option) any later version.                   *
+# * (at your option) any later version.                                     *
-#*   for detail see the LICENCE text file.                                 *
+# *                                                                         *
-#*                                                                         *
+# * This program is distributed in the hope that it will be useful,         *
-#*   This program is distributed in the hope that it will be useful,       *
+# * but WITHOUT ANY WARRANTY; without even the implied warranty of          *
-#*   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
+# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the           *
-#*   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
+# * GNU General Public License for more details.                            *
-#*   GNU Library General Public License for more details.                  *
+# *                                                                         *
-#*                                                                         *
+# * You should have received a copy of the GNU General Public License       *
-#*   You should have received a copy of the GNU Library General Public     *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
-#*   License along with this program; if not, write to the Free Software   *
+# *                                                                         *
-#*   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  *
+# ***************************************************************************
-#*   USA                                                                   *
-#*                                                                         *
-#***************************************************************************
 
 from __future__ import division
-from numpy import tan, cos, sin, sqrt, arctan, pi, array, linspace, transpose, vstack, ndarray
+from numpy import (
-from ._functions import nearestpts, rotation, reflection, trimfunc, norm, translation
+    tan,
-import numpy as np
+    cos,
+    sin,
+    sqrt,
+    arctan,
+    pi,
+    array,
+    linspace,
+    transpose,
+    vstack,
+    ndarray,
+)
+from ._functions import (
+    nearestpts,
+    rotation,
+    reflection,
+    trimfunc,
+    diff_norm,
+    translation,
+)
 
-class involute_tooth():
+
-    def __init__(self, m=5, z=15, pressure_angle=20 * pi / 180., clearance=0.12, shift=0.5, beta=0.,
+class InvoluteTooth:
-                       undercut=False, backlash=0.00, head=0.00):
+    def __init__(
+        self,
+        m=5,
+        z=15,
+        pressure_angle=20 * pi / 180.0,
+        clearance=0.12,
+        shift=0.5,
+        beta=0.0,
+        undercut=False,
+        backlash=0.00,
+        head=0.00,
+        properties_from_tool=False,
+    ):
         self.pressure_angle = pressure_angle
         self.beta = beta
         self.m_n = m
@@ -35,37 +62,61 @@ class involute_tooth():
         self.shift = shift
         self.clearance = clearance
         self.backlash = backlash
-        self.head = head        # factor, rename!!!
+        self.head = head  # factor, rename!!!
+        self.properties_from_tool = properties_from_tool
         self._calc_gear_factors()
 
     def _calc_gear_factors(self):
-        self.pressure_angle_t = arctan(tan(self.pressure_angle) / cos(self.beta))
+        if self.properties_from_tool:
-        self.m = self.m_n / cos(self.beta)
+            self.pressure_angle_t = arctan(tan(self.pressure_angle) / cos(self.beta))
+            self.m = self.m_n / cos(self.beta)
+        else:
+            self.pressure_angle_t = self.pressure_angle
+            self.m = self.m_n
+
+        self.pitch = self.m * pi
         self.c = self.clearance * self.m_n
-        self.midpoint = [0., 0.]
+        self.midpoint = [0.0, 0.0]
         self.d = self.z * self.m
         self.dw = self.m * self.z
-        self.da = self.dw + 2. * self.m_n + 2. * (self.shift + self.head) * self.m_n
+        self.da = self.dw + 2.0 * self.m_n + 2.0 * (self.shift + self.head) * self.m_n
-        self.df = self.dw - 2. * self.m_n - \
+        self.df = self.dw - 2.0 * self.m_n - 2 * self.c + 2.0 * self.shift * self.m_n
-            2 * self.c + 2. * self.shift * self.m_n
         self.dg = self.d * cos(self.pressure_angle_t)
         self.phipart = 2 * pi / self.z
 
-        self.undercut_end = sqrt(-self.df ** 2 + self.da ** 2) / self.da
+        self.undercut_end = sqrt(-(self.df**2) + self.da**2) / self.da
-        self.undercut_rot = (-self.df / self.dw * tan(arctan((2 * ((self.m * pi) / 4. -
+        self.undercut_rot = (
-                            (self.c + self.m_n) * tan(self.pressure_angle_t))) / self.df)))
+            -self.df
+            / self.dw
+            * tan(
+                arctan(
+                    (
+                        2
+                        * (
+                            (self.m * pi) / 4.0
+                            - (self.c + self.m_n) * tan(self.pressure_angle_t)
+                        )
+                    )
+                    / self.df
+                )
+            )
+        )
 
-        self.involute_end = sqrt(self.da ** 2 - self.dg ** 2) / self.dg
+        self.involute_end = sqrt(self.da**2 - self.dg**2) / self.dg
-        self.involute_rot1 = sqrt(-self.dg ** 2 + (self.dw) ** 2) / self.dg - arctan(
+        self.involute_rot1 = sqrt(-(self.dg**2) + (self.dw) ** 2) / self.dg - arctan(
-            sqrt(-self.dg ** 2 + (self.dw) ** 2) / self.dg)
+            sqrt(-(self.dg**2) + (self.dw) ** 2) / self.dg
-        self.involute_rot2 = self.m / \
+        )
-            (self.d) * (pi / 2 + 2 * self.shift * tan(self.pressure_angle_t))
+        self.involute_rot2 = (
-        self.involute_rot2 = 1 / self.z * (pi / 2 + 2 * self.shift * tan(self.pressure_angle_t))
+            self.m / (self.d) * (pi / 2 + 2 * self.shift * tan(self.pressure_angle_t))
+        )
+        self.involute_rot2 = (
+            1 / self.z * (pi / 2 + 2 * self.shift * tan(self.pressure_angle_t))
+        )
         self.involute_rot = self.involute_rot1 + self.involute_rot2
-        self.involute_start = 0.
+        self.angular_backlash = self.backlash / (self.d / 2)
+        self.involute_start = 0.0
         if self.dg <= self.df:
-            self.involute_start = sqrt(self.df ** 2 - self.dg ** 2) / self.dg
+            self.involute_start = sqrt(self.df**2 - self.dg**2) / self.dg
-
 
     def undercut_points(self, num=10):
         pts = linspace(0, self.undercut_end, num=num)
@@ -75,9 +126,10 @@ class involute_tooth():
         y = array(list(map(fy, pts)))
         xy = transpose([x, y])
         rotate = rotation(
-            self.undercut_rot + self.phipart / 2 - self.backlash / 4)
+            self.undercut_rot + self.phipart / 2 - self.angular_backlash / 2
+        )
         xy = rotate(xy)
-        return(array(xy))
+        return array(xy)
 
     def involute_points(self, num=10):
         pts = linspace(self.involute_start, self.involute_end, num=num)
@@ -85,9 +137,9 @@ class involute_tooth():
         x = array(list(map(fx, pts)))
         fy = self.involute_function_y()
         y = array(list(map(fy, pts)))
-        rot = rotation(self.involute_rot - self.backlash / 4)
+        rot = rotation(self.involute_rot - self.angular_backlash / 2)
         xy = rot(transpose(array([x, y])))
-        return(xy)
+        return xy
 
     def points(self, num=10):
         l1 = self.undercut_points(num=num)
@@ -102,7 +154,8 @@ class involute_tooth():
             u1 = False
             if self.dg > self.df:
                 u1 = vstack(
-                    [[l2[0] * self.df / (norm(l2[0], [0, 0]) * 2)], [l2[0]]])
+                    [[l2[0] * self.df / (diff_norm(l2[0], [0, 0]) * 2)], [l2[0]]]
+                )
                 e1 = l2
             else:
                 e1 = l2
@@ -110,96 +163,139 @@ class involute_tooth():
         reflect = reflection(0)
         e2 = reflect(e1)[::-1]
         if isinstance(u1, bool):
-            u2 = False
             one_tooth = [e1, [e1[-1], e2[0]], e2]
         else:
             u2 = reflect(u1)[::-1]
             one_tooth = [u1, e1, [e1[-1], e2[0]], e2, u2]
-        return(one_tooth)
+        return one_tooth
 
     def gearfunc(self, x):
         rot = rotation(2 * x / self.dw, self.midpoint)
-        return(rot)
+        return rot
 
     def undercut_function_x(self):
         def func(psi):
-            return(
+            return cos(psi - (self.df * tan(psi)) / self.dw) * sqrt(
-               cos(psi - (self.df * tan(psi)) / self.dw) * sqrt(self.df ** 2 / 4 +
+                self.df**2 / 4 + (self.df**2 * tan(psi) ** 2) / 4.0
-                                                                (self.df ** 2 * tan(psi) ** 2) / 4.))
+            )
-        return(func)
+
+        return func
 
     def undercut_function_y(self):
         def func(psi):
-            return(
+            return sin(psi - (self.df * tan(psi)) / self.dw) * sqrt(
-                sin(psi - (self.df * tan(psi)) / self.dw) * sqrt(self.df ** 2 / 4 +
+                self.df**2 / 4 + (self.df**2 * tan(psi) ** 2) / 4.0
-                                                                (self.df ** 2 * tan(psi) ** 2) / 4.))
+            )
-        return(func)
+
+        return func
 
     def involute_function_x(self):
         def func(phi):
-            return(array(self.dg / 2 * cos(phi) + phi * self.dg / 2 * sin(phi)))
+            return self.dg / 2 * cos(phi) + phi * self.dg / 2 * sin(phi)
-        return(func)
+
+        return func
 
     def involute_function_y(self):
         def func(phi):
-            return(self.dg / 2 * sin(phi) - phi * self.dg / 2 * cos(phi))
+            return self.dg / 2 * sin(phi) - phi * self.dg / 2 * cos(phi)
-        return(func)
+
+        return func
 
     def _update(self):
-        self.__init__(m = self.m_n, z = self.z,
+        if not hasattr(self, "properties_from_tool"):
-                pressure_angle = self.pressure_angle, clearance = self.clearance, shift = self.shift,
+            self.properties_from_tool = True
-                beta = self.beta, undercut = self.undercut, backlash = self.backlash, head = self.head)
+        self._calc_gear_factors()
 
 
-class involute_rack(object):
+class InvoluteRack(object):
-    def __init__(self, m=5, z=15, pressure_angle=20 * pi / 180., thickness=5, beta=0, head=0):
+    def __init__(
+        self,
+        m=5,
+        z=15,
+        pressure_angle=20 * pi / 180.0,
+        thickness=5,
+        beta=0,
+        head=0,
+        clearance=0.25,
+        properties_from_tool=False,
+        add_endings=False,
+        simplified=False,
+    ):
         self.pressure_angle = pressure_angle
         self.thickness = thickness
         self.m = m
         self.z = z
         self.beta = beta
         self.head = head
+        self.clearance = clearance
+        self.properties_from_tool = properties_from_tool
+        self.add_endings = add_endings
+        self.simplified = simplified
 
+    # this is not good. Find better way to stay backward compatible -> versions
     def _update(self):
-        self.__init__(m = self.m, z = self.z, pressure_angle = self.pressure_angle,
+        if not hasattr(self, "add_endings"):
-                      thickness=self.thickness, beta=self.beta, head=self.head)
+            self.add_endings = True
+        if not hasattr(self, "simplified"):
+            self.simplified = False
 
     def points(self, num=10):
-        pressure_angle_t = arctan(tan(self.pressure_angle) / cos(self.beta))
+        m, m_n, pitch, pressure_angle_t = self.compute_properties()
-        m = self.m / cos(self.beta)
 
-        a = (2 + self.head) * m * tan(pressure_angle_t)
+        a = (2 + self.head + self.clearance) * m_n * tan(pressure_angle_t)
-        b = (m * pi) / 4 - (1 + self.head) * m * tan(pressure_angle_t)
+        b = pitch / 4 - (1 + self.head) * m_n * tan(pressure_angle_t)
-        tooth= [
+        tooth = [
-            [-self.m, -a - b],
+            [-m_n * (1 + self.clearance), -a - b],
-            [self.m * (1 + self.head), -b],
+            [m_n * (1 + self.head), -b],
-            [self.m * (1 + self.head), b],
+            [m_n * (1 + self.head), b],
-            [-self.m, a + b]
+            [-m_n * (1 + self.clearance), a + b],
-            ]
+        ]
         teeth = [tooth]
-        trans = translation([0., m * pi, 0.])
+        trans = translation([0.0, pitch, 0.0])
         for i in range(self.z - 1):
-            teeth.append(trans(teeth[-1]))
+            if self.simplified and i > 3 and i < (self.z - 6):
-        teeth = list(np.vstack(teeth))
+                tooth = trans(tooth).tolist()
-        teeth.append(list(teeth[-1]))
+            else:
-        teeth[-1][0] -= self.thickness
+                tooth = trans(tooth).tolist()
-        teeth.append(list(teeth[0]))
+                teeth.append(tooth.copy())
+                if self.simplified and (i == 3):
+                    teeth[-1].pop()
+                    teeth[-1].pop()
+                    teeth[-1][-1][0] = 0
+                    teeth[-1][-1][1] -= a / 2
+                if self.simplified and (i == self.z - 6):
+                    teeth[-1].pop(0)
+                    teeth[-1].pop(0)
+                    teeth[-1][0][0] = 0
+                    teeth[-1][0][1] += a / 2
+
+        teeth = array([v for t in teeth for v in t])  # flattening
+        if self.add_endings:
+            ext1 = teeth[0] + array([0.0, a + b - pitch / 2])
+            ext2 = teeth[-1] - array([0.0, a + b - pitch / 2])
+            teeth = (
+                [ext1.tolist(), ext1.tolist()]
+                + teeth.tolist()
+                + [ext2.tolist(), ext2.tolist()]
+            )
+        else:
+            teeth = [teeth[0].tolist()] + teeth.tolist() + [teeth[-1].tolist()]
+        # teeth.append(list(teeth[-1]))
+        teeth[0][0] -= self.thickness
+        # teeth.append(list(teeth[0]))
         teeth[-1][0] -= self.thickness
         teeth.append(teeth[0])
-        return(teeth)
+        return array(teeth)
 
+    def compute_properties(self):
+        if self.properties_from_tool:
+            pressure_angle_t = arctan(tan(self.pressure_angle) / cos(self.beta))
+            m = self.m / cos(self.beta)
+            m_n = self.m
+        else:
+            pressure_angle_t = self.pressure_angle
+            m = self.m
+            m_n = self.m
 
-
+        pitch = m * pi
-
+        return m, m_n, pitch, pressure_angle_t
-
-if __name__ == "__main__":
-    from matplotlib import pyplot
-    gear = involute_rack()
-    x = []
-    y = []
-    for i in gear.points(30):
-        x.append(i[0])
-        y.append(i[1])
-    pyplot.plot(x, y)
-    pyplot.show()
-

pygears/profile.py

@@ -0,0 +1,40 @@
+import numpy as np
+from .involute_tooth import InvoluteTooth, InvoluteRack
+from .bevel_tooth import BevelTooth
+from .cycloid_tooth import CycloidTooth
+from ._functions import rotation, rotation3D
+
+
+class _GearProfile(object):
+    rot3D = False
+
+    def profile(self, num=10):
+        tooth = self.points(num=num)
+        tooth = [list(point) for wire in tooth for point in wire]
+        if self.rot3D:
+            rot = rotation3D(np.pi * 2 / self.z)
+        else:
+            rot = rotation(-np.pi * 2 / self.z)
+        profile = tooth
+        for i in range(self.z - 1):
+            tooth = rot(tooth).tolist()
+            profile = profile + tooth
+        profile.append(profile[0])
+        return np.array(profile)
+
+
+class InvoluteProfile(InvoluteTooth, _GearProfile):
+    pass
+
+
+class CycloidProfile(CycloidTooth, _GearProfile):
+    pass
+
+
+class BevelProfile(BevelTooth, _GearProfile):
+    rot3D = True
+
+
+class InvoluteRackProfile(InvoluteRack):
+    def profile(self):
+        return self.points()

setup.py

@@ -1,14 +1,14 @@
 from setuptools import setup
 from pygears import __version__
 
-setup(name='freecad.gears',
+setup(
-      version=str(__version__),
+    name="freecad.gears",
-      packages=['freecad',
+    version=str(__version__),
-                'freecad.gears',
+    packages=["freecad", "freecad.gears", "pygears"],
-        		'pygears'],
+    maintainer="looooo",
-      maintainer="looooo",
+    maintainer_email="sppedflyer@gmail.com",
-      maintainer_email="sppedflyer@gmail.com",
+    url="https://github.com/looooo/FCGear",
-      url="https://github.com/looooo/FCGear",
+    description="gears for FreeCAD",
-      description="gears for FreeCAD",
+    install_requires=["numpy", "scipy"],
-      install_requires=['numpy'],
+    include_package_data=True,
-include_package_data=True)
+)