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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+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
 
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+
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+
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-This section is intended to make thoroughly clear what is believed to
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-
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+  If the Program specifies that a proxy can decide which future
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-                            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
-FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW.  EXCEPT WHEN
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-PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
-REPAIR OR CORRECTION.
+  15. Disclaimer of Warranty.
 
-  12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
-WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
-REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
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-PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
-POSSIBILITY OF SUCH DAMAGES.
+  THERE IS NO 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.
+
+  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}
-    Copyright (C) {year}  {fullname}
+    <one line to give the program's name and a brief idea of what it does.>
+    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
-    with this program; if not, write to the Free Software Foundation, Inc.,
-    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <https://www.gnu.org/licenses/>.
 
 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
-when it starts in an interactive mode:
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
 
-    Gnomovision version 69, Copyright (C) year name of author
-    Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    <program>  Copyright (C) <year>  <name of author>
+    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
-be called something other than `show w' and `show c'; they could even be
-mouse-clicks or menu items--whatever suits your program.
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
 
-You should also get your employer (if you work as a programmer) or your
-school, if any, to sign a "copyright disclaimer" for the program, if
-necessary.  Here is a sample; alter the names:
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+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
-  `Gnomovision' (which makes passes at compilers) written by James Hacker.
-
-  {signature of Ty Coon}, 1 April 1989
-  Ty Coon, President of Vice
-
-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.
+  The GNU 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.  But first, please read
+<https://www.gnu.org/licenses/why-not-lgpl.html>.

MANIFEST.in

@@ -0,0 +1 @@
+recursive-include freecad/gears/icons *

README.md

@@ -1,14 +1,101 @@
-a gearmodule for freecad
+## A Gear module for FreeCAD
+[![Liberapay](http://img.shields.io/liberapay/patrons/looooo.svg?logo=liberapay)](https://liberapay.com/looooo/donate) 
+
+## Requirements
+FreeCAD > v0.16  
+__python > 3 (for python2 use branch py2)__
+
+
+## Supported gear-types
+
+### Cylindric Involute
+* Shifting
+* Helical
+* Double Helical
+* Undercut  
+
+![involute-gear](examples/involute-double-helical-gear.png)
+
+
+### Involute Rack
+![involute-rack](examples/involute-rack.png)
+
+### Cylindric Cycloid
+* Helical
+* Double Helical
+
+![cycloid-gear](examples/cycloid-gear.png)
+
+### Cycloid Rack
+
+![cycloid-rack](examples/cycloid-rack.png)
+
+### Spherical Involute Bevel-Gear
+* 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)
+
 ---------------------------
 
-* install:
-  * git clone https://github.com/looooo/FCGear.git
-  * link or copy the FCgear/gear into /freecad/Mod (sudo ln -s (path_to_FCGear)/gear (path_to_freecad)/Mod
+## Installation
 
+### 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.
 
-* create a gear:
-  * open freecad
-  * go to the gear workbench
-  * create new document
-  * create a gear (click on gear symbol)
-  * change parameters 
+### pip
+
+`pip install https://github.com/looooo/FCGear/archive/master.tar.gz`
+
+**Important note:** Most systems have multiple versions of python installed. Make sure the `pip` you're using is used by FreeCAD as well.
+
+## Usage
+
+### Create a gear manually
+* Open freecad
+* Switch to the gear workbench
+* Create new document
+* Create a gear (click on a gear symbol in the toolbar)
+* Change the gear parameters
+
+## Scripted gears
+Use the power of python to automate your gear modeling: 
+
+```python
+import FreeCAD as App
+import freecad.gears.commands
+gear = freecad.gears.commands.CreateInvoluteGear.create()
+gear.teeth = 20
+gear.beta = 20
+gear.height = 10
+gear.double_helix = True
+App.ActiveDocument.recompute()
+Gui.SendMsgToActiveView("ViewFit")
+```
+
+## References
+* Elements of Metric Gear Technology ([PDF](http://qtcgears.com/tools/catalogs/PDF_Q420/Tech.pdf))
+
+### FreeCAD Forum threads
+These are forum threads where FreeCAD Gears has been discussed. If you want to give Feedback
+or report a bug please use the below threads. Please make sure that the report hasn't been reported already
+by browsing this repositories [issue queue](https://github.com/looooo/freecad.gears/issues).   
+* "CONTINUED: involute gear generator preview !" ([thread](https://forum.freecadweb.org/viewtopic.php?f=10&t=4829))  
+* "Bevel gear - module/script/tutorial" ([thread](https://forum.freecadweb.org/viewtopic.php?f=3&t=12878))  
+* "Gears in FreeCAD: FC Gear" ([thread](https://forum.freecadweb.org/viewtopic.php?f=24&t=27381))  
+* "FC Gears: Feedback thread" ([thread](https://forum.freecadweb.org/viewtopic.php?f=8&t=27626))  
+
+# License
+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

@@ -0,0 +1,29 @@
+# script for bevel-gear animation
+
+from PySide import QtCore
+import FreeCAD as app
+import FreeCADGui as gui
+import numpy as np
+
+doc = app.ActiveDocument
+g2 = doc.Common
+g1 = doc.Common001
+
+timer = QtCore.QTimer()
+
+def make_pics():
+    n = 30
+    for i in range(n):
+        phi = np.pi * 2 / 30 / n
+        g1.Placement.Rotation.Angle += phi * 2
+        g2.Placement.Rotation.Angle -= phi
+        gui.activeDocument().activeView().saveImage('/home/lo/Schreibtisch/animated_gear/gear_{}.png'.format(i) ,300,300,'Current')
+
+def update(*args):
+    print("time")
+    delta_phi = 0.005
+    g1.Placement.Rotation.Angle += delta_phi * 2
+    g2.Placement.Rotation.Angle -= delta_phi
+
+timer.timeout.connect(update)
+timer.start()

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/gears/__init__.py

@@ -0,0 +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

@@ -0,0 +1,217 @@
+# -*- 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 FreeCAD
+import FreeCADGui as Gui
+
+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):
+    NAME = ""
+    GEAR_FUNCTION = None
+    ICONDIR = os.path.join(os.path.dirname(__file__), "icons")
+
+    def __init__(self):
+        pass
+
+    def IsActive(self):
+        if FreeCAD.ActiveDocument is None:
+            return False
+        else:
+            return True
+
+    def Activated(self):
+        Gui.doCommandGui("import freecad.gears.commands")
+        Gui.doCommandGui(
+            "freecad.gears.commands.{}.create()".format(self.__class__.__name__)
+        )
+        FreeCAD.ActiveDocument.recompute()
+        Gui.SendMsgToActiveView("ViewFit")
+
+    @classmethod
+    def create(cls):
+        if FreeCAD.GuiUp:
+            # borrowed from threaded profiles
+            # 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,
+            "MenuText": self.MenuText,
+            "ToolTip": self.ToolTip,
+        }
+
+
+class CreateInvoluteGear(BaseCommand):
+    NAME = "InvoluteGear"
+    GEAR_FUNCTION = InvoluteGear
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "involutegear.svg")
+    MenuText = "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 = InvoluteGearRack
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "involuterack.svg")
+    MenuText = "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 = CrownGear
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "crowngear.svg")
+    MenuText = "Crown Gear"
+    ToolTip = "Create a Crown gear"
+
+
+class CreateCycloidGear(BaseCommand):
+    NAME = "CycloidGear"
+    GEAR_FUNCTION = CycloidGear
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "cycloidgear.svg")
+    MenuText = "Cycloid Gear"
+    ToolTip = "Create a Cycloid gear"
+
+
+class CreateBevelGear(BaseCommand):
+    NAME = "BevelGear"
+    GEAR_FUNCTION = BevelGear
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "bevelgear.svg")
+    MenuText = "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

@@ -0,0 +1,33 @@
+# -*- 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/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+
+# this file is only for backwards compatibility
+
+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 .basegear import ViewProviderGear, BaseGear

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

@@ -0,0 +1,159 @@
+# -*- 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 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(
+        "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"""
+
+    MenuText = "Gear"
+    ToolTip = "Gear Workbench"
+    Icon = os.path.join(__dirname__, "icons", "gearworkbench.svg")
+    commands = [
+        "CreateInvoluteGear",
+        "CreateInternalInvoluteGear",
+        "CreateInvoluteRack",
+        "CreateCycloidGear",
+        "CreateCycloidRack",
+        "CreateBevelGear",
+        "CreateCrownGear",
+        "CreateWormGear",
+        "CreateTimingGearT",
+        "CreateTimingGear",
+        "CreateLanternGear",
+        "CreateHypoCycloidGear",
+        "CreateGearConnector",
+    ]
+
+    def GetClassName(self):
+        return "Gui::PythonWorkbench"
+
+    def Initialize(self):
+        from .commands import (
+            CreateCycloidGear,
+            CreateInvoluteGear,
+            CreateInternalInvoluteGear,
+            CreateBevelGear,
+            CreateInvoluteRack,
+            CreateCrownGear,
+            CreateWormGear,
+            CreateTimingGearT,
+            CreateTimingGear,
+            CreateLanternGear,
+            CreateHypoCycloidGear,
+            CreateCycloidRack,
+            CreateGearConnector,
+        )
+
+        self.appendToolbar("Gear", self.commands)
+        self.appendMenu("Gear", self.commands)
+        Gui.addCommand("CreateInvoluteGear", CreateInvoluteGear())
+        Gui.addCommand("CreateInternalInvoluteGear", CreateInternalInvoluteGear())
+        Gui.addCommand("CreateCycloidGear", CreateCycloidGear())
+        Gui.addCommand("CreateCycloidRack", CreateCycloidRack())
+        Gui.addCommand("CreateBevelGear", CreateBevelGear())
+        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())

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

gear/InitGui.py

@@ -1,54 +0,0 @@
-#***************************************************************************
-#*                                                                         *
-#*   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                                                                   *
-#*                                                                         *
-#***************************************************************************
-
-import FreeCADGui as Gui
-import FreeCAD
-import gear_rc
-
-
-class gearWorkbench(Workbench):
-    """glider workbench"""
-    MenuText = "gear"
-    ToolTip = "gear workbench"
-    Icon = "gearworkbench.svg"
-
-    def GetClassName(self):
-        return "Gui::PythonWorkbench"
-
-    def Initialize(self):
-
-        from gearfunc import CreateCycloideGear, CreateInvoluteGear, CreateBevelGear, CreateInvoluteRack
-
-        self.appendToolbar("Gear", ["CreateInvoluteGear", "CreateInvoluteRack", "CreateCycloideGear", "CreateBevelGear"])
-        self.appendMenu("Gear", ["CreateInvoluteGear", "CreateInvoluteRack", "CreateCycloideGear","CreateBevelGear"])
-        Gui.addIconPath(FreeCAD.getHomePath()+"Mod/gear/icons/")
-        Gui.addCommand('CreateInvoluteGear', CreateInvoluteGear())
-        Gui.addCommand('CreateCycloideGear', CreateCycloideGear())
-        Gui.addCommand('CreateBevelGear', CreateBevelGear())
-        Gui.addCommand('CreateInvoluteRack', CreateInvoluteRack())
-
-    def Activated(self):
-        pass
-
-
-    def Deactivated(self):
-        pass
-
-Gui.addWorkbench(gearWorkbench())

gear/Resources/gear.qrc

@@ -1,9 +0,0 @@
-<RCC>
-    <qresource> 
-        <file>icons/gearworkbench.svg</file>
-        <file>icons/involutegear.svg</file>
-        <file>icons/cycloidegear.svg</file>
-        <file>icons/involuterack.svg</file>
-	<file>icons/bevelgear.svg</file>
-    </qresource>
-</RCC> 

gear/Resources/gear.qrc~

@@ -1,7 +0,0 @@
-<RCC>
-    <qresource> 
-        <file>icons/gearworkbench.svg</file>
-        <file>icons/involutegear.svg</file>
-        <file>icons/cycloidegear.svg</file>
-    </qresource>
-</RCC> 

gear/__init__.py

@@ -1,20 +0,0 @@
-#!/usr/lib/python
-
-from gearfunc._involute_tooth import involute_rack, involute_tooth
-from gearfunc._cycloide_tooth import cycloide_tooth
-from gearfunc._bevel_tooth import bevel_tooth
-from gearfunc import CreateInvoluteRack, CreateCycloideGear, CreateInvoluteGear, CreateBevelGear
-
-from tests import bspline_surf
-
-
-__All__ = [
-    "CreateInvoluteRack",
-    "CreateCycloideGear",
-    "CreateInvoluteGear",
-    "CreateBevelGear",
-    "involute_rack",
-    "involute_tooth",
-    "bevel_tooth"
-]
-

gear/gearfunc/_Classes.py

@@ -1,445 +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
-import FreeCAD as App
-from _involute_tooth import involute_tooth, involute_rack
-from _cycloide_tooth import cycloide_tooth
-from _bevel_tooth import bevel_tooth
-from Part import BSplineCurve, Shape, Wire, Face, makePolygon, \
-    BRepOffsetAPI, Shell, makeLoft, Solid, Line, BSplineSurface, Compound,\
-     show, makePolygon, makeLoft, makeHelix
-import Part
-from _functions import rotation3D
-from numpy import pi, cos, sin, tan
-
-import numpy
-
-
-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 involute_gear():
-
-    """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", "alpha", "involute_parameter", "alpha")
-        obj.addProperty(
-            "App::PropertyFloat", "clearence", "gear_parameter", "clearence")
-        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", "test", "test")
-        obj.gear = self.involute_tooth
-        obj.simple = False
-        obj.undercut = False
-        obj.teeth = 15
-        obj.module = '1. mm'
-        obj.shift = 0.
-        obj.alpha = '20. deg'
-        obj.beta = '0. deg'
-        obj.height = '5. mm'
-        obj.clearence = 0.25
-        obj.numpoints = 6
-        obj.backlash = '0.00 mm'
-        self.obj = obj
-        obj.Proxy = self
-
-    def execute(self, fp):
-        fp.gear.m_n = fp.module.Value
-        fp.gear.z = fp.teeth
-        fp.gear.undercut = fp.undercut
-        fp.gear.shift = fp.shift
-        fp.gear.alpha = fp.alpha.Value * pi / 180.
-        fp.gear.beta = fp.beta.Value * pi / 180
-        fp.gear.clearence = fp.clearence
-        fp.gear.backlash = fp.backlash.Value
-        fp.gear._update()
-        pts = fp.gear.points(num=fp.numpoints)
-        if not fp.simple:
-            wi = []
-            for i in pts:
-                out = BSplineCurve()
-                out.interpolate(map(fcvec, i))
-                wi.append(out)
-            s = Wire(Shape(wi).Edges)
-            wi = []
-            for i in range(fp.gear.z):
-                rot = App.Matrix()
-                rot.rotateZ(-i * fp.gear.phipart)
-                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()]))
-
-            wi = Wire(wi)
-            fp.Shape = 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 * tan(fp.gear.beta) * 2 / fp.gear.d)
-        else:
-            rw = fp.gear.dw / 2
-            circle = Part.Circle(App.Vector(0, 0, 0), App.Vector(0, 0, 1), rw)
-            wire = Part.Wire(circle.toShape())
-            face = Part.Face(wire)
-            fp.Shape = face.extrude(App.Vector(0, 0, fp.height.Value))
-
-    def __getstate__(self):
-        return None
-
-    def __setstate__(self, state):
-        return None
-
-
-class involute_gear_rack():
-
-    """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", "alpha", "involute_parameter", "alpha")
-        obj.addProperty("App::PropertyPythonObject", "rack", "test", "test")
-        obj.rack = self.involute_rack
-        obj.teeth = 15
-        obj.module = '1. mm'
-        obj.alpha = '20. deg'
-        obj.height = '5. mm'
-        obj.thickness = '5 mm'
-        self.obj = obj
-        obj.Proxy = self
-
-    def execute(self, fp):
-        fp.rack.m = fp.module.Value
-        fp.rack.z = fp.teeth
-        fp.rack.alpha = fp.alpha.Value * pi / 180.
-        fp.rack.thickness = fp.thickness.Value
-        fp.rack._update()
-        pts = fp.rack.points()
-        pol = Wire(makePolygon(map(fcvec, pts)))
-        fp.Shape = Face(Wire(pol)).extrude(fcvec([0., 0., fp.height]))
-
-    def __getstate__(self):
-        return None
-
-    def __setstate__(self, state):
-        return None
-
-
-class cycloide_gear():
-
-    """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::PropertyFloat", "clearence", "gear_parameter", "clearence")
-        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", "test", "test")
-        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.clearence = 0.25
-        obj.numpoints = 15
-        obj.backlash = '0.00 mm'
-        obj.Proxy = self
-
-    def execute(self, fp):
-        pass
-        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.clearence = fp.clearence
-        fp.gear.backlash = fp.backlash.Value
-        fp.gear._update()
-        pts = fp.gear.points(num=fp.numpoints)
-        wi = []
-        for i in pts:
-            out = BSplineCurve()
-            out.interpolate(map(fcvec, i))
-            wi.append(out)
-        s = Wire(Shape(wi).Edges)
-        wi = []
-        for i in range(fp.gear.z):
-            rot = App.Matrix()
-            rot.rotateZ(-i * fp.gear.phipart)
-            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()]))
-        wi = Wire(wi)
-        if fp.beta.Value == 0:
-            sh = Face(wi)
-            fp.Shape = sh.extrude(App.Vector(0, 0, fp.height.Value))
-        else:
-            pass
-            fp.Shape = helicalextrusion(
-                wi, fp.height.Value, fp.height.Value * tan(fp.beta.Value * pi / 180) * 2 / fp.gear.d)
-
-    def __getstate__(self):
-        return None
-
-    def __setstate__(self, state):
-        return None
-
-
-class bevel_gear():
-
-    """parameters:
-        alpha:  pressureangle,   10-30°
-        gamma:  cone angle,      0 < gamma < 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", "gamma", "involute_parameter", "gamma")
-        obj.addProperty(
-            "App::PropertyAngle", "alpha", "involute_parameter", "alpha")
-        obj.addProperty("App::PropertyLength", "m", "gear_parameter", "m")
-        obj.addProperty(
-            "App::PropertyFloat", "clearence", "gear_parameter", "clearence")
-        obj.addProperty("App::PropertyInteger", "numpoints",
-                        "gear_parameter", "number of points for spline")
-        obj.addProperty(
-            "App::PropertyLength", "backlash", "gear_parameter", "backlash in mm")
-        obj.addProperty("App::PropertyPythonObject", "gear", "test", "test")
-        obj.gear = self.bevel_tooth
-        obj.m = '1. mm'
-        obj.teeth = 15
-        obj.alpha = '70. deg'
-        obj.gamma = '45. deg'
-        obj.height = '5. mm'
-        obj.numpoints = 6
-        obj.backlash = '0.00 mm'
-        obj.clearence = 0.1
-        self.obj = obj
-        obj.Proxy = self
-
-    def execute1(self, fp):
-        fp.gear.z = fp.teeth
-        fp.gear.alpha = fp.alpha.Value * pi / 180.
-        fp.gear.gamma = fp.gamma.Value * pi / 180
-        fp.gear.backlash = fp.backlash
-        fp.gear._update()
-        pts = fp.gear.points(num=fp.numpoints)
-        tooth = self.create_tooth()
-        teeth = [tooth]
-        rot = App.Matrix()
-        rot.rotateZ(2  * pi / fp.teeth)
-        top_cap = [i.Edges[0] for i in tooth.Faces]
-        bottom_cap = [i.Edges[3] for i in tooth.Faces]
-        for i in range(fp.teeth - 1): 
-            new_tooth = teeth[-1].transformGeometry(rot)
-            edge1 = new_tooth.Faces[0].Edges[2]
-            edge2 = teeth[-1].Faces[-1].Edges[1]
-            face1 = make_face(edge1, edge2)
-            teeth.append(face1)
-            teeth.append(new_tooth)
-            top_cap.append(face1.Edges[3])
-            bottom_cap.append(face1.Edges[1])
-            top_cap += [i.Edges[0] for i in new_tooth.Faces]
-            bottom_cap += [i.Edges[3] for i in new_tooth.Faces]
-        edge1 = teeth[0].Faces[0].Edges[2]
-        edge2 = teeth[-1].Faces[-1].Edges[1]
-        face1 = make_face(edge1, edge2)
-        teeth.append(face1)
-        top_cap.append(face1.Edges[3])
-        bottom_cap.append(face1.Edges[1])
-        top_cap = Face(Wire(top_cap))
-        bottom_cap = Face(Wire(bottom_cap))
-        fcs = Compound(teeth).Faces
-        top_cap.reverse()
-        fp.Shape = Solid(Shell(fcs + [top_cap, bottom_cap]))
-
-
-    def execute(self, fp):
-        fp.gear.z = fp.teeth
-        fp.gear.module = fp.m.Value
-        fp.gear.alpha = fp.alpha.Value * pi / 180.
-        fp.gear.gamma = fp.gamma.Value * pi / 180
-        fp.gear.backlash = fp.backlash.Value
-        fp.gear.clearence = fp.clearence
-        fp.gear._update()
-        pts = fp.gear.points(num=fp.numpoints)
-        scal1 = fp.m.Value * fp.gear.z / 2 / tan(
-            fp.gamma.Value * pi / 180) - fp.height.Value / 2
-        scal2 = fp.m.Value * fp.gear.z / 2 / tan(
-            fp.gamma.Value * pi / 180) + fp.height.Value / 2
-        fp.Shape = makeLoft([self.createteeths(pts, scal1, fp.teeth), self.createteeths(pts, scal2, fp.teeth)], True)
-        # fp.Shape = self.createteeths(pts, pos1, fp.teeth)
-
-
-    def create_tooth(self):
-        w = []
-        scal1 = self.obj.m.Value * self.obj.gear.z / 2 / tan(
-            self.obj.gamma.Value * pi / 180) - self.obj.height.Value / 2
-        scal2 = self.obj.m.Value * self.obj.gear.z / 2 / tan(
-            self.obj.gamma.Value * 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 = 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 createteeths(self, pts, pos, teeth):
-        w1 = []
-        for i in pts:
-            scale = lambda x: x * pos
-            i_scale = map(scale, i)
-            out = BSplineCurve()
-            out.interpolate(map(fcvec, i_scale))
-            w1.append(out)
-        s = Wire(Shape(w1).Edges)
-        wi = []
-        for i in range(teeth):
-            rot = App.Matrix()
-            rot.rotateZ(2 * i * 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):
-    face_a = Face(wire)
-    face_b = face_a.copy()
-    face_transform = App.Matrix()
-    face_transform.rotateZ(angle)
-    face_transform.move(App.Vector(0, 0, height))
-    face_b . transformShape(face_transform)
-    spine = Wire(Line(fcvec([0., 0, 0]), fcvec([0, 0, height])).toShape())
-    auxspine = makeHelix(height * 2 * pi / angle, height, 1.)
-    faces = [face_a, face_b]
-    pipeshell = BRepOffsetAPI.MakePipeShell(spine)
-    pipeshell.setSpineSupport(spine)
-    pipeshell.add(wire)
-    pipeshell.setAuxiliarySpine(auxspine, True, False)
-    assert(pipeshell.isReady())
-    pipeshell.build()
-    faces.extend(pipeshell.shape().Faces)
-
-    fullshell = Shell(faces)
-    solid = Solid(fullshell)
-    if solid.Volume < 0:
-        solid.reverse()
-    assert(solid.Volume >= 0)
-    return(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))
-

gear/gearfunc/__init__.py

@@ -1,108 +0,0 @@
-#***************************************************************************
-#*                                                                         *
-#*   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                                                                   *
-#*                                                                         *
-#***************************************************************************
-
-
-import FreeCAD
-import FreeCADGui as Gui
-from _Classes import involute_gear, cycloide_gear, bevel_gear, involute_gear_rack
-
-
-class CreateInvoluteGear():
-    """create an involute gear"""
-    def __init__(self):
-        pass
-
-    def GetResources(self):
-        return {'Pixmap': 'involutegear.svg', 'MenuText': 'involute gear', 'ToolTip': 'involute gear'}
-
-    def IsActive(self):
-        if FreeCAD.ActiveDocument is None:
-            return False
-        else:
-            return True
-
-    def Activated(self):
-        a = FreeCAD.ActiveDocument.addObject("Part::FeaturePython", "involute_gear")
-        involute_gear(a)
-        a.ViewObject.Proxy = 0.
-        FreeCAD.ActiveDocument.recompute()
-        Gui.SendMsgToActiveView("ViewFit")
-
-
-class CreateInvoluteRack():
-    def __init__(self):
-        pass
-
-    def GetResources(self):
-        return {'Pixmap': 'involuterack.svg', 'MenuText': 'involute rack', 'ToolTip': 'involute rack'}
-
-    def IsActive(self):
-        if FreeCAD.ActiveDocument is None:
-            return False
-        else:
-            return True
-
-    def Activated(self):
-        a = FreeCAD.ActiveDocument.addObject("Part::FeaturePython", "involute_rack")
-        involute_gear_rack(a)
-        a.ViewObject.Proxy = 0.
-        FreeCAD.ActiveDocument.recompute()
-        Gui.SendMsgToActiveView("ViewFit")
-
-
-class CreateCycloideGear():
-    def __init__(self):
-        pass
-
-    def GetResources(self):
-        return {'Pixmap': 'cycloidegear.svg', 'MenuText': 'cycloide gear', 'ToolTip': 'cycloide gear'}
-
-    def IsActive(self):
-        if FreeCAD.ActiveDocument is None:
-            return False
-        else:
-            return True
-
-    def Activated(self):
-        a = FreeCAD.ActiveDocument.addObject("Part::FeaturePython", "cycloide_gear")
-        cycloide_gear(a)
-        a.ViewObject.Proxy = 0.
-        FreeCAD.ActiveDocument.recompute()
-        Gui.SendMsgToActiveView("ViewFit")
-
-class CreateBevelGear():
-    def __init__(self):
-        pass
-
-    def GetResources(self):
-        return {'Pixmap': 'bevelgear.svg', 'MenuText': 'bevel gear', 'ToolTip': 'bevel gear'}
-
-    def IsActive(self):
-        if FreeCAD.ActiveDocument is None:
-            return False
-        else:
-            return True
-
-    def Activated(self):
-        a = FreeCAD.ActiveDocument.addObject("Part::FeaturePython", "bevel_gear")
-        bevel_gear(a)
-        a.ViewObject.Proxy = 0.
-        FreeCAD.ActiveDocument.recompute()
-        Gui.SendMsgToActiveView("ViewFit")

gear/gearfunc/_bevel_tooth.py

@@ -1,168 +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 __future__ import division
-from numpy import cos, sin, tan, arccos, arctan, pi, array, linspace, transpose, vstack, sqrt
-from _functions import rotation3D, reflection3D
-
-
-
-class bevel_tooth(object):
-    def __init__(self, alpha=70 * pi / 180, gamma=pi / 4, clearence=0.1,
-                 z=21, backlash=0.00, module=0.25):
-        self.alpha = alpha
-        self.gamma = gamma
-        self.z = z
-        self.clearence = clearence
-        self.backlash = backlash
-        self.module = module
-
-        self.involute_end = arccos(
-            1 / sqrt(2) * sqrt((42. + 16.*cos(2.*self.alpha) +
-            6.*cos(4.*self.alpha) + cos(4.*self.alpha - 4.*self.gamma) - 8.*cos(2.*self.alpha - 2.*self.gamma) -
-            4.*cos(4.*self.alpha - 2.*self.gamma) + 24.*cos(2.*self.gamma) - 2.*cos(4.*self.gamma) -
-            8.*cos(2.*(self.alpha + self.gamma)) + cos(4.*(self.alpha + self.gamma)) -
-            4.*cos(4.*self.alpha + 2.*self.gamma) + 24.*cos((4.*sin(self.gamma))/self.z) +
-            4.*cos(2.*self.alpha - (4.*sin(self.gamma))/self.z) + 4.*cos(2.*self.alpha -
-            4.*self.gamma - (4.*sin(self.gamma))/self.z) - 8.*cos(2.*self.alpha - 2.*self.gamma -
-            (4.*sin(self.gamma))/self.z) + 24.*cos(4.*(self.gamma + sin(self.gamma)/self.z)) -
-            8.*cos(2.*(self.alpha + self.gamma + (2.*sin(self.gamma))/self.z)) + 4.*cos(2.*self.alpha +
-            (4.*sin(self.gamma))/self.z) + 16.*cos(2.*self.gamma + (4.*sin(self.gamma))/self.z) +
-            4.*cos(2.*self.alpha + 4.*self.gamma + (4.*sin(self.gamma))/self.z) + 32.*abs(cos(self.gamma +
-            (2.*sin(self.gamma))/self.z))*cos(self.alpha)*sqrt(4.*cos(2.*self.alpha) -
-            2.*(-2. + cos(2.*self.alpha - 2.*self.gamma) - 2.*cos(2.*self.gamma) + cos(2.*(self.alpha + self.gamma)) +
-            4.*cos(2.*self.gamma + (4.*sin(self.gamma))/self.z)))*sin(2.*self.gamma))/(-6. - 2.*cos(2.*self.alpha) +
-            cos(2.*self.alpha - 2.*self.gamma) - 2.*cos(2.*self.gamma) + cos(2.*(self.alpha + self.gamma)))**2))
-
-        self.involute_start = -pi/2. + \
-            arctan(1/tan(self.gamma)*1/cos(self.alpha))
-        self.involute_start_radius = self.getradius(self.involute_start)
-        self.r_f = sin(self.gamma - sin(gamma) * 2 / self.z) - self.clearence * sin(self.gamma)
-        self.z_f = cos(self.gamma - sin(gamma) * 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.alpha) + 6*cos(4*self.alpha) -
-                4*cos(4*self.alpha - 2*self.gamma) - 8*cos(2*(self.alpha - self.gamma)) +
-                cos(4*(self.alpha - self.gamma)) + 24*cos(2*self.gamma) - 2*cos(4*self.gamma) -
-                8*cos(2*(self.alpha + self.gamma)) + cos(4*(self.alpha + self.gamma)) -
-                4*cos(2*(2*self.alpha + self.gamma)) + 24*cos((4*sin(self.gamma))/self.z) +
-                4*cos(2*self.alpha - (4*sin(self.gamma))/self.z) + 16*cos(2*self.gamma -
-                (4*sin(self.gamma))/self.z) + 24*cos(4*self.gamma - (4*sin(self.gamma))/self.z) +
-                4*cos(2*self.alpha + 4*self.gamma - (4*sin(self.gamma))/self.z) -
-                8*cos(2*(self.alpha + self.gamma - (2*sin(self.gamma))/self.z)) +
-                4*cos(2*self.alpha + (4*sin(self.gamma))/self.z) + 4*cos(2*self.alpha -
-                4*self.gamma + (4*sin(self.gamma))/self.z) - 8*cos(2*self.alpha - 2*self.gamma +
-                (4*sin(self.gamma))/self.z) + 32*sqrt(2)*sqrt(-(cos(self.alpha)**2*
-                (-2 - 2*cos(2*self.alpha) + cos(2*(self.alpha - self.gamma)) -
-                2*cos(2*self.gamma) + cos(2*(self.alpha + self.gamma)) +
-                4*cos(2*self.gamma - (4*sin(self.gamma))/self.z))*cos(self.gamma - (2*sin(self.gamma))/self.z)**2*
-                sin(2*self.gamma)**2)))/(-6 - 2*cos(2*self.alpha) + cos(2*(self.alpha - self.gamma)) -
-                2*cos(2*self.gamma) + cos(2*(self.alpha + self.gamma)))**2)/sqrt(2))
-
-    def involute_function_x(self):
-        def func(s):
-            return((
-                -(cos(s*1/sin(self.alpha)*1/sin(self.gamma))*sin(self.alpha)*sin(s)) +
-                (cos(s)*sin(self.gamma) + cos(self.alpha)*cos(self.gamma)*sin(s))*
-                sin(s*1/sin(self.alpha)*1/sin(self.gamma))))
-        return(func)
-
-    def involute_function_y(self):
-        def func(s):
-            return((
-                cos(s*1/sin(self.alpha)*1/sin(self.gamma))*(cos(s)*sin(self.gamma) +
-                cos(self.alpha)*cos(self.gamma)*sin(s)) + sin(self.alpha)*sin(s)*
-                sin(s*1/sin(self.alpha)*1/sin(self.gamma))))
-        return(func)
-
-    def involute_function_z(self):
-        def func(s):
-            return((
-                cos(self.gamma)*cos(s) - cos(self.alpha)*sin(self.gamma)*sin(s)))
-        return(func)
-
-    def getradius(self, s):
-        x = self.involute_function_x()
-        y = self.involute_function_y()
-        rx = x(s)
-        ry = y(s)
-        return(sqrt(rx**2 + ry**2))
-
-    def involute_points(self, num=10):
-        pts = linspace(self.involute_start, self.involute_end, num=num)
-        fx = self.involute_function_x()
-        x = array(map(fx, pts))
-        fy = self.involute_function_y()
-        y = array(map(fy, pts))
-        fz = self.involute_function_z()
-        z = array(map(fz, pts))
-        xyz = transpose(array([x, y,z]))
-        if self.add_foot:
-            p = xyz[0]
-            p1 =map(lambda x: x * (self.r_f / sqrt(p[0]**2 + p[1]**2)), p)
-            p1[2] = self.z_f
-            xyz=vstack([[p1], xyz])
-        xy = [[i[0]/i[2],i[1]/i[2],1.] for i in xyz]
-        backlash_rot = rotation3D(self.backlash / 4)
-        xy = backlash_rot(xy)
-        return(xy)
-
-    def points(self, num=10):
-        pts = self.involute_points(num = num)
-        rot = rotation3D(-pi/self.z/2)
-        pts = rot(pts)
-        ref = reflection3D(pi/2)
-        pts1 = ref(pts)[::-1]
-        rot = rotation3D(2*pi/self.z)
-        pt3 = rot(pts[0])
-        if self.add_foot:
-            return(array([
-                [pts[0],pts[1]],
-                pts[1:],
-                [pts[-1], pts1[0]],
-                pts1[:-1],
-                [pts1[-2], pts1[-1]]
-                ]))
-            return(array([pts,[pts[-1],pts1[0]], pts1]))
-        else:
-            return(array([pts,[pts[-1],pts1[0]], pts1]))
-
-
-    def _update(self):
-        self.__init__(z = self.z, clearence = self.clearence,
-                alpha = self.alpha,  gamma = self.gamma, backlash = self.backlash, module = self.module)
-
-
-if __name__ == "__main__":
-	from matplotlib import pyplot
-	gear = bevel_tooth()
-	x = []
-	y = []
-	for i in gear.points(30):
-		for j in i:
-			x.append(j[0])
-			y.append(j[1])
-	pyplot.plot(x,y)
-	pyplot.show()

gear/gearfunc/_cycloide_tooth.py

@@ -1,118 +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 __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, clearence = 0.12, backlash = 0.00):
-        self.m = m
-        self.z = z
-        self.clearence = clearence
-        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.clearence * 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 = map(outer_x, t_vals_outer)
-        pts_outer_y = map(outer_y, t_vals_outer)
-        pts_inner_x = map(inner_x, t_vals_inner)
-        pts_inner_y = 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,
-                      clearence = self.clearence, 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()

gear/gearfunc/_functions.py

@@ -1,162 +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 sin, cos, dot, array, ndarray, vstack, transpose, sqrt
-from numpy.linalg import solve
-
-
-def reflection(alpha):
-    mat = array(
-        [[cos(2 * alpha), -sin(2 * alpha)], [-sin(2 * alpha), -cos(2 * alpha)]])
-
-    def func(x):
-        return(dot(x, mat))
-    return(func)
-
-
-def reflection3D(alpha):
-    mat = array([[cos(2 * alpha), -sin(2 * alpha), 0.],
-                 [-sin(2 * alpha), -cos(2 * alpha), 0.], [0., 0., 1.]])
-
-    def func(x):
-        return(dot(x, mat))
-    return(func)
-
-
-def rotation(alpha, midpoint=[0, 0]):
-    mat = array([[cos(alpha), -sin(alpha)], [sin(alpha), cos(alpha)]])
-    midpoint = array(midpoint)
-    vec = midpoint - dot(midpoint, mat)
-    trans = translation(vec)
-
-    def func(xx):
-        return(trans(dot(xx, mat)))
-    return(func)
-
-
-def rotation3D(alpha):
-    mat = array(
-        [
-            [cos(alpha), -sin(alpha), 0.],
-            [sin(alpha), cos(alpha), 0.],
-            [0., 0., 1.]])
-
-    def func(xx):
-        return(dot(xx, mat))
-    return(func)
-
-
-def translation(vec):
-    def trans(x):
-        return([x[0] + vec[0], x[1] + vec[1]])
-
-    def func(x):
-        return(array(map(trans, x)))
-    return(func)
-
-
-def trim(p1, p2, p3, p4):
-    a1 = array(p1)
-    a2 = array(p2)
-    a3 = array(p3)
-    a4 = array(p4)
-    if all(a1 == a2) or all(a3 == a4):
-        if all(a1 == a3):
-            return(a1)
-        else:
-            return(False)
-    elif all(a1 == a3):
-        if all(a2 == a4):
-            return((a1 + a2) / 2)
-        else:
-            return(a1)
-    elif all(a1 == a4):
-        if all(a2 == a3):
-            return((a1 + a2) / 2)
-        else:
-            return(a1)
-    elif all(a2 == a3) or all(a2 == a4):
-        return(p2)
-    try:
-        g, h = solve(transpose([-a2 + a1, a4 - a3]), a1 - a3)
-    except:
-        print(Exception)
-        return(False)
-    else:
-        if 0. < g < 1. and 0. < h < 1.:
-            return(a1 + g * (a2 - a1))
-        else:
-            return(False)
-    return(False)
-
-
-def trimfunc(l1, l2):
-    ik = 0
-    i0 = array(l1[0])
-    for i in array(l1[1:]):
-        jk = 0
-        j0 = array(l2[0])
-        for j in array(l2[1:]):
-            s = trim(j0, j, i0, i)
-            if isinstance(s, ndarray):
-                if ik == 0:
-                    l1 = [l1[0]]
-                else:
-                    l1 = l1[:ik]
-                if jk == 0:
-                    l2 == [l2[0]]
-                else:
-                    l2 = l2[jk::-1]
-                return(array([vstack([l1, [s]]), vstack([[s], l2])]))
-            j0 = j
-            jk += 1
-        i0 = i
-        ik += 1
-    return(False)
-
-
-def norm(vec1, vec2):
-    vec = array(vec2) - array(vec1)
-    out = 0
-    for i in vec:
-        out += i ** 2
-    return(sqrt(out))
-
-
-def nearestpts(evolv, underc):
-    ik = 0
-    iout = 0
-    jout = 0
-    outmin = 1000.
-    for i in array(evolv[1:]):
-        jk = 0
-        for j in array(underc[1:]):
-            l = norm(i, j)
-            if l < outmin:
-                re = norm(i, [0, 0])
-                ru = 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:]])

gear/gearfunc/_involute_tooth.py

@@ -1,197 +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 tan, cos, sin, sqrt, arctan, pi, array, linspace, transpose, vstack, ndarray
-from _functions import nearestpts, rotation, reflection, trimfunc, norm, translation
-import numpy as np
-
-class involute_tooth():
-    def __init__(self, m=5, z=15, alpha=20 * pi / 180., clearence=0.12, shift=0.5, beta=0., undercut=False, backlash=0.00):
-        self.alpha = alpha
-        self.beta = beta
-        self.m_n = m
-        self.z = z
-        self.undercut = undercut
-        self.shift = shift
-        self.clearence = clearence
-        self.backlash = backlash
-        self._calc_gear_factors()
-
-    def _calc_gear_factors(self):
-        self.alpha_t = arctan(tan(self.alpha) / cos(self.beta))
-        self.m = self.m_n / cos(self.beta)
-        self.c = self.clearence * self.m_n
-        self.midpoint = [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.m_n
-        self.df = self.dw - 2. * self.m_n - \
-            2 * self.c + 2. * self.shift * self.m_n
-        self.dg = self.d * cos(self.alpha_t)
-        self.phipart = 2 * pi / self.z
-
-        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.c + self.m_n) * tan(self.alpha_t))) / self.df)))
-
-        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(
-            sqrt(-self.dg ** 2 + (self.dw) ** 2) / self.dg)
-        self.involute_rot2 = self.m / \
-            (self.d) * (pi / 2 + 2 * self.shift * tan(self.alpha_t))
-        self.involute_rot2 = 1 / self.z * (pi / 2 + 2 * self.shift * tan(self.alpha_t))
-        self.involute_rot = self.involute_rot1 + self.involute_rot2
-        self.involute_start = 0.
-        if self.dg <= self.df:
-            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)
-        fx = self.undercut_function_x()
-        x = array(map(fx, pts))
-        fy = self.undercut_function_y()
-        y = array(map(fy, pts))
-        xy = transpose([x, y])
-        rotate = rotation(
-            self.undercut_rot + self.phipart / 2 - self.backlash / 4)
-        xy = rotate(xy)
-        return(array(xy))
-
-    def involute_points(self, num=10):
-        pts = linspace(self.involute_start, self.involute_end, num=num)
-        fx = self.involute_function_x()
-        x = array(map(fx, pts))
-        fy = self.involute_function_y()
-        y = array(map(fy, pts))
-        rot = rotation(self.involute_rot - self.backlash / 4)
-        xy = rot(transpose(array([x, y])))
-        return(xy)
-
-    def points(self, num=10):
-        l1 = self.undercut_points(num=num)
-        l2 = self.involute_points(num=num)
-        s = trimfunc(l1, l2[::-1])
-        if self.undercut:
-            if isinstance(s, ndarray):
-                u1, e1 = s
-            else:
-                u1, e1 = nearestpts(l2, l1)
-        else:
-            u1 = False
-            if self.dg > self.df:
-                u1 = vstack(
-                    [[l2[0] * self.df / (norm(l2[0], [0, 0]) * 2)], [l2[0]]])
-                e1 = l2
-            else:
-                e1 = l2
-
-        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)
-
-    def gearfunc(self, x):
-        rot = rotation(2 * x / self.dw, self.midpoint)
-        return(rot)
-
-    def undercut_function_x(self):
-        def func(psi):
-            return(
-               cos(psi - (self.df * tan(psi)) / self.dw) * sqrt(self.df ** 2 / 4 +
-                                                                (self.df ** 2 * tan(psi) ** 2) / 4.))
-        return(func)
-
-    def undercut_function_y(self):
-        def func(psi):
-            return(
-                sin(psi - (self.df * tan(psi)) / self.dw) * sqrt(self.df ** 2 / 4 +
-                                                                (self.df ** 2 * tan(psi) ** 2) / 4.))
-        return(func)
-
-    def involute_function_x(self):
-        def func(phi):
-            return(array(self.dg / 2 * cos(phi) + phi * self.dg / 2 * sin(phi)))
-        return(func)
-
-    def involute_function_y(self):
-        def func(phi):
-            return(self.dg / 2 * sin(phi) - phi * self.dg / 2 * cos(phi))
-        return(func)
-
-    def _update(self):
-        self.__init__(m = self.m_n, z = self.z,
-                alpha = self.alpha, clearence = self.clearence, shift = self.shift,
-                beta = self.beta, undercut = self.undercut, backlash = self.backlash)
-
-
-class involute_rack(object):
-    def __init__(self, m=5, z=15, alpha=20 * pi / 180., thickness=5):
-        self.alpha = alpha
-        self.thickness = thickness
-        self.m = m
-        self.z = z
-
-    def _update(self):
-        self.__init__(m = self.m, z = self.z, alpha = self.alpha, thickness = self.thickness)
-
-    def points(self, num=10):
-        a = 2 * self.m * tan(self.alpha)
-        b = ((self.m * pi) / 2 - a) / 2
-        tooth= [
-            [self.m, -a - b],
-            [-self.m, -b],
-            [-self.m, b],
-            [self.m, a + b]
-            ]
-        teeth = [tooth]
-        trans = translation([0., self.m * pi, 0.])
-        for i in range(self.z):
-            teeth.append(trans(teeth[-1]))
-        teeth = list(np.vstack(teeth))
-        teeth.append(list(teeth[-1]))
-        teeth[-1][0] += self.thickness
-        teeth.append(list(teeth[0]))
-        teeth[-1][0] += self.thickness
-        teeth.append(teeth[0])
-        return(teeth)
-
-
-
-
-
-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()
-

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

@@ -0,0 +1,19 @@
+# -*- 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

@@ -0,0 +1,187 @@
+# -*- 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 sin, cos, dot, array, ndarray, vstack, transpose, sqrt
+from numpy.linalg import solve, norm
+
+
+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 * angle), -sin(2 * angle), 0.0],
+            [-sin(2 * angle), -cos(2 * angle), 0.0],
+            [0.0, 0.0, 1.0],
+        ]
+    )
+
+    def func(x):
+        # why not use mat @ x
+        return dot(x, mat)
+
+    return func
+
+
+def rotation(angle, midpoint=None):
+    midpoint = midpoint or [0.0, 0.0]
+    mat = array([[cos(angle), -sin(angle)], [sin(angle), cos(angle)]])
+    midpoint = array(midpoint)
+    vec = midpoint - dot(midpoint, mat)
+    trans = translation(vec)
+
+    def func(xx):
+        return trans(dot(xx, mat))
+
+    return func
+
+
+def rotation3D(angle):
+    mat = array(
+        [[cos(angle), -sin(angle), 0.0], [sin(angle), cos(angle), 0.0], [0.0, 0.0, 1.0]]
+    )
+
+    def func(xx):
+        return dot(xx, mat)
+
+    return func
+
+
+def translation(vec):
+    def trans(x):
+        return [x[0] + vec[0], x[1] + vec[1]]
+
+    def func(x):
+        return array(list(map(trans, x)))
+
+    return func
+
+
+def trim(p1, p2, p3, p4):
+    a1 = array(p1)
+    a2 = array(p2)
+    a3 = array(p3)
+    a4 = array(p4)
+    if all(a1 == a2) or all(a3 == a4):
+        if all(a1 == a3):
+            return a1
+        else:
+            return False
+    elif all(a1 == a3):
+        if all(a2 == a4):
+            return (a1 + a2) / 2
+        else:
+            return a1
+    elif all(a1 == a4):
+        if all(a2 == a3):
+            return (a1 + a2) / 2
+        else:
+            return a1
+    elif all(a2 == a3) or all(a2 == a4):
+        return p2
+    try:
+        g, h = solve(transpose([-a2 + a1, a4 - a3]), a1 - a3)
+    except Exception as e:
+        print(e)
+        return False
+    else:
+        if 0.0 < g < 1.0 and 0.0 < h < 1.0:
+            return a1 + g * (a2 - a1)
+        else:
+            return False
+
+
+def trimfunc(l1, l2):
+    ik = 0
+    i0 = array(l1[0])
+    for i in array(l1[1:]):
+        jk = 0
+        j0 = array(l2[0])
+        for j in array(l2[1:]):
+            s = trim(j0, j, i0, i)
+            if isinstance(s, ndarray):
+                if ik == 0:
+                    l1 = [l1[0]]
+                else:
+                    l1 = l1[:ik]
+                if jk == 0:
+                    l2 == [l2[0]]
+                else:
+                    l2 = l2[jk::-1]
+                return [vstack([l1, [s]]), vstack([[s], l2])]
+            j0 = j
+            jk += 1
+        i0 = i
+        ik += 1
+    return False
+
+
+def diff_norm(vec1, vec2):
+    vec = array(vec2) - array(vec1)
+    return norm(vec)
+
+
+def nearestpts(evolv, underc):
+    ik = 0
+    iout = 0
+    jout = 0
+    outmin = 1000.0
+    for i in array(evolv[1:]):
+        jk = 0
+        for j in array(underc[1:]):
+            l = diff_norm(i, j)
+            if l < outmin:
+                re = diff_norm(i, [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:]]
+
+
+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
+    midpoint 0,0,0"""
+    d = p2 - p1
+    d /= norm(d)
+    p_half = d.dot(p1)
+    q = p1.dot(p1) - r**2
+    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

@@ -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/>.   *
+# *                                                                         *
+# ***************************************************************************
+
+from __future__ import division
+from __future__ import division
+from numpy import (
+    cos,
+    sin,
+    tan,
+    arccos,
+    arctan,
+    pi,
+    array,
+    linspace,
+    transpose,
+    vstack,
+    sqrt,
+)
+from ._functions import rotation3D, reflection3D, intersection_line_circle
+
+
+class BevelTooth(object):
+    def __init__(
+        self,
+        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(
+                (
+                    42.0
+                    + 16.0 * cos(2.0 * self.pressure_angle)
+                    + 6.0 * cos(4.0 * self.pressure_angle)
+                    + cos(4.0 * self.pressure_angle - 4.0 * self.pitch_angle)
+                    - 8.0 * cos(2.0 * self.pressure_angle - 2.0 * self.pitch_angle)
+                    - 4.0 * cos(4.0 * self.pressure_angle - 2.0 * self.pitch_angle)
+                    + 24.0 * cos(2.0 * self.pitch_angle)
+                    - 2.0 * cos(4.0 * self.pitch_angle)
+                    - 8.0 * cos(2.0 * (self.pressure_angle + self.pitch_angle))
+                    + cos(4.0 * (self.pressure_angle + self.pitch_angle))
+                    - 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 / 2.0 + 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.z_f = cos(self.pitch_angle - sin(pitch_angle) * 2 / self.z)
+        self.add_foot = True
+
+    def involute_function_x(self):
+        def func(s):
+            return -(
+                cos(s * 1 / sin(self.pressure_angle) * 1 / sin(self.pitch_angle))
+                * sin(self.pressure_angle)
+                * sin(s)
+            ) + (
+                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 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) * sin(
+                s * 1 / sin(self.pressure_angle) * 1 / sin(self.pitch_angle)
+            )
+
+        return func
+
+    def involute_function_z(self):
+        def func(s):
+            return cos(self.pitch_angle) * cos(s) - cos(self.pressure_angle) * sin(
+                self.pitch_angle
+            ) * 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)
+
+    def involute_points(self, num=10):
+        pts = linspace(self.involute_start, self.involute_end, num=num)
+        fx = self.involute_function_x()
+        x = array(list(map(fx, pts)))
+        fy = self.involute_function_y()
+        y = array(list(map(fy, pts)))
+        fz = self.involute_function_z()
+        z = array(list(map(fz, pts)))
+        xyz = transpose(array([x, y, z]))
+        # conical projection to z=1
+        xy = [[i[0] / i[2], i[1] / i[2]] for i in xyz]
+        xy = array([[0, 0]] + xy)
+
+        r_cut = self.r_f / self.z_f
+        for i, point in enumerate(xy[1:]):
+            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 :]))
+        xyz = [[p[0], p[1], 1] for p in xy]
+        backlash_rot = rotation3D(self.angular_backlash / 2)
+        xyz = backlash_rot(xyz)
+        return xyz
+
+    def points(self, num=10):
+        pts = self.involute_points(num=num)
+        rot = rotation3D(-pi / self.z / 2)
+        pts = rot(pts)
+        ref = reflection3D(pi / 2)
+        pts1 = ref(pts)[::-1]
+        if self.add_foot:
+            return [
+                array([pts[0], pts[1]]),
+                array(pts[1:]),
+                array([pts[-1], pts1[0]]),
+                array(pts1[:-1]),
+                array([pts1[-2], pts1[-1]]),
+            ]
+        else:
+            return [pts, array([pts[-1], pts1[0]]), pts1]
+
+    def _update(self):
+        self.__init__(
+            z=self.z,
+            clearance=self.clearance,
+            pressure_angle=self.pressure_angle,
+            pitch_angle=self.pitch_angle,
+            backlash=self.backlash,
+            module=self.module,
+        )

pygears/computation.py

@@ -0,0 +1,65 @@
+# -*- 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
+
+
+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]
+        t1 (int): number of teeth of gear1
+        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]
+    """
+
+    def inv(x):
+        return np.tan(x) - x
+
+    inv_alpha_w = inv(alpha) + 2 * np.tan(alpha) * (x1 + x2) / (t1 + t2)
+
+    def root_inv(x):
+        return inv(x) - inv_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/involute_tooth.py

@@ -0,0 +1,301 @@
+# -*- 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 (
+    tan,
+    cos,
+    sin,
+    sqrt,
+    arctan,
+    pi,
+    array,
+    linspace,
+    transpose,
+    vstack,
+    ndarray,
+)
+from ._functions import (
+    nearestpts,
+    rotation,
+    reflection,
+    trimfunc,
+    diff_norm,
+    translation,
+)
+
+
+class InvoluteTooth:
+    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
+        self.z = z
+        self.undercut = undercut
+        self.shift = shift
+        self.clearance = clearance
+        self.backlash = backlash
+        self.head = head  # factor, rename!!!
+        self.properties_from_tool = properties_from_tool
+        self._calc_gear_factors()
+
+    def _calc_gear_factors(self):
+        if self.properties_from_tool:
+            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, 0.0]
+        self.d = self.z * self.m
+        self.dw = self.m * self.z
+        self.da = self.dw + 2.0 * self.m_n + 2.0 * (self.shift + self.head) * self.m_n
+        self.df = self.dw - 2.0 * self.m_n - 2 * self.c + 2.0 * 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_rot = (
+            -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_rot1 = sqrt(-(self.dg**2) + (self.dw) ** 2) / self.dg - arctan(
+            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 = (
+            1 / self.z * (pi / 2 + 2 * self.shift * tan(self.pressure_angle_t))
+        )
+        self.involute_rot = self.involute_rot1 + self.involute_rot2
+        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
+
+    def undercut_points(self, num=10):
+        pts = linspace(0, self.undercut_end, num=num)
+        fx = self.undercut_function_x()
+        x = array(list(map(fx, pts)))
+        fy = self.undercut_function_y()
+        y = array(list(map(fy, pts)))
+        xy = transpose([x, y])
+        rotate = rotation(
+            self.undercut_rot + self.phipart / 2 - self.angular_backlash / 2
+        )
+        xy = rotate(xy)
+        return array(xy)
+
+    def involute_points(self, num=10):
+        pts = linspace(self.involute_start, self.involute_end, num=num)
+        fx = self.involute_function_x()
+        x = array(list(map(fx, pts)))
+        fy = self.involute_function_y()
+        y = array(list(map(fy, pts)))
+        rot = rotation(self.involute_rot - self.angular_backlash / 2)
+        xy = rot(transpose(array([x, y])))
+        return xy
+
+    def points(self, num=10):
+        l1 = self.undercut_points(num=num)
+        l2 = self.involute_points(num=num)
+        s = trimfunc(l1, l2[::-1])
+        if self.undercut:
+            if isinstance(s, ndarray):
+                u1, e1 = s
+            else:
+                u1, e1 = nearestpts(l2, l1)
+        else:
+            u1 = False
+            if self.dg > self.df:
+                u1 = vstack(
+                    [[l2[0] * self.df / (diff_norm(l2[0], [0, 0]) * 2)], [l2[0]]]
+                )
+                e1 = l2
+            else:
+                e1 = l2
+
+        reflect = reflection(0)
+        e2 = reflect(e1)[::-1]
+        if isinstance(u1, bool):
+            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
+
+    def gearfunc(self, x):
+        rot = rotation(2 * x / self.dw, self.midpoint)
+        return rot
+
+    def undercut_function_x(self):
+        def func(psi):
+            return cos(psi - (self.df * tan(psi)) / self.dw) * sqrt(
+                self.df**2 / 4 + (self.df**2 * tan(psi) ** 2) / 4.0
+            )
+
+        return func
+
+    def undercut_function_y(self):
+        def func(psi):
+            return sin(psi - (self.df * tan(psi)) / self.dw) * sqrt(
+                self.df**2 / 4 + (self.df**2 * tan(psi) ** 2) / 4.0
+            )
+
+        return func
+
+    def involute_function_x(self):
+        def func(phi):
+            return self.dg / 2 * cos(phi) + phi * self.dg / 2 * sin(phi)
+
+        return func
+
+    def involute_function_y(self):
+        def func(phi):
+            return self.dg / 2 * sin(phi) - phi * self.dg / 2 * cos(phi)
+
+        return func
+
+    def _update(self):
+        if not hasattr(self, "properties_from_tool"):
+            self.properties_from_tool = True
+        self._calc_gear_factors()
+
+
+class InvoluteRack(object):
+    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):
+        if not hasattr(self, "add_endings"):
+            self.add_endings = True
+        if not hasattr(self, "simplified"):
+            self.simplified = False
+
+    def points(self, num=10):
+        m, m_n, pitch, pressure_angle_t = self.compute_properties()
+
+        a = (2 + self.head + self.clearance) * m_n * tan(pressure_angle_t)
+        b = pitch / 4 - (1 + self.head) * m_n * tan(pressure_angle_t)
+        tooth = [
+            [-m_n * (1 + self.clearance), -a - b],
+            [m_n * (1 + self.head), -b],
+            [m_n * (1 + self.head), b],
+            [-m_n * (1 + self.clearance), a + b],
+        ]
+        teeth = [tooth]
+        trans = translation([0.0, pitch, 0.0])
+        for i in range(self.z - 1):
+            if self.simplified and i > 3 and i < (self.z - 6):
+                tooth = trans(tooth).tolist()
+            else:
+                tooth = trans(tooth).tolist()
+                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 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

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

@@ -0,0 +1,14 @@
+from setuptools import setup
+from pygears import __version__
+
+setup(
+    name="freecad.gears",
+    version=str(__version__),
+    packages=["freecad", "freecad.gears", "pygears"],
+    maintainer="looooo",
+    maintainer_email="sppedflyer@gmail.com",
+    url="https://github.com/looooo/FCGear",
+    description="gears for FreeCAD",
+    install_requires=["numpy", "scipy"],
+    include_package_data=True,
+)