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')

README.md

@@ -1,5 +1,5 @@
 ## A Gear module for FreeCAD
-[![Liberapay](http://img.shields.io/liberapay/patrons/looooo.svg?logo=liberapay)](https://liberapay.com/looooo/donate) [![Total alerts](https://img.shields.io/lgtm/alerts/g/looooo/freecad.gears.svg?logo=lgtm&logoWidth=18)](https://lgtm.com/projects/g/looooo/freecad.gears/alerts/) [![Language grade: Python](https://img.shields.io/lgtm/grade/python/g/looooo/freecad.gears.svg?logo=lgtm&logoWidth=18)](https://lgtm.com/projects/g/looooo/freecad.gears/context:python)  
+[![Liberapay](http://img.shields.io/liberapay/patrons/looooo.svg?logo=liberapay)](https://liberapay.com/looooo/donate) 
 
 ## Requirements
 FreeCAD > v0.16  
@@ -26,6 +26,10 @@ __python > 3 (for python2 use branch py2)__
 
 ![cycloid-gear](examples/cycloid-gear.png)
 
+### Cycloid Rack
+
+![cycloid-rack](examples/cycloid-rack.png)
+
 ### Spherical Involute Bevel-Gear
 * Spiral  
 

TODO.md

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

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

@@ -1,23 +1,21 @@
 # -*- 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 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 Library General Public License for more details.                  *
+# * 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 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                                                                   *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
 # *                                                                         *
 # ***************************************************************************
 
 import pygears
+
 __version__ = pygears.__version__

freecad/gears/basegear.py

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

freecad/gears/bevelgear.py

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

freecad/gears/commands.py

@@ -1,29 +1,44 @@
 # -*- coding: utf-8 -*-
 # ***************************************************************************
 # *                                                                         *
-# *   This program is free software; you can redistribute it and/or modify  *
-# *   it under the terms of the GNU Lesser General Public License (LGPL)    *
-# *   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 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 Library General Public License for more details.                  *
+# * 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 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                                                                   *
+# * 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 .features import ViewProviderGear, InvoluteGear, InvoluteGearRack
-from .features import CycloidGear, BevelGear, CrownGear, WormGear, TimingGear, LanternGear, HypoCycloidGear
+
+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):
@@ -42,8 +57,9 @@ class BaseCommand(object):
 
     def Activated(self):
         Gui.doCommandGui("import freecad.gears.commands")
-        Gui.doCommandGui("freecad.gears.commands.{}.create()".format(
-            self.__class__.__name__))
+        Gui.doCommandGui(
+            "freecad.gears.commands.{}.create()".format(self.__class__.__name__)
+        )
         FreeCAD.ActiveDocument.recompute()
         Gui.SendMsgToActiveView("ViewFit")
 
@@ -56,14 +72,16 @@ class BaseCommand(object):
             part = Gui.ActiveDocument.ActiveView.getActiveObject("part")
 
             if body:
-                obj = FreeCAD.ActiveDocument.addObject("PartDesign::FeaturePython", cls.NAME)
+                obj = FreeCAD.ActiveDocument.addObject(
+                    "PartDesign::FeaturePython", cls.NAME
+                )
             else:
                 obj = FreeCAD.ActiveDocument.addObject("Part::FeaturePython", cls.NAME)
-            ViewProviderGear(obj.ViewObject)
+            ViewProviderGear(obj.ViewObject, cls.Pixmap)
             cls.GEAR_FUNCTION(obj)
 
             if body:
-                body.Group += [obj]
+                body.addObject(obj)
             elif part:
                 part.Group += [obj]
         else:
@@ -72,76 +90,128 @@ class BaseCommand(object):
         return obj
 
     def GetResources(self):
-        return {'Pixmap': self.Pixmap,
-                'MenuText': self.MenuText,
-                'ToolTip': self.ToolTip}
+        return {
+            "Pixmap": self.Pixmap,
+            "MenuText": self.MenuText,
+            "ToolTip": self.ToolTip,
+        }
 
 
 class CreateInvoluteGear(BaseCommand):
-    NAME = "involutegear"
+    NAME = "InvoluteGear"
     GEAR_FUNCTION = InvoluteGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'involutegear.svg')
-    MenuText = 'Involute gear'
-    ToolTip = 'Create an Involute gear'
+    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"
+    NAME = "InvoluteRack"
     GEAR_FUNCTION = InvoluteGearRack
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'involuterack.svg')
-    MenuText = 'Involute rack'
-    ToolTip = 'Create an Involute rack'
+    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"
+    NAME = "CrownGear"
     GEAR_FUNCTION = CrownGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'crowngear.svg')
-    MenuText = 'Crown gear'
-    ToolTip = 'Create a Crown gear'
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "crowngear.svg")
+    MenuText = "Crown Gear"
+    ToolTip = "Create a Crown gear"
 
 
 class CreateCycloidGear(BaseCommand):
-    NAME = "cycloidgear"
+    NAME = "CycloidGear"
     GEAR_FUNCTION = CycloidGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'cycloidgear.svg')
-    MenuText = 'Cycloid gear'
-    ToolTip = 'Create a Cycloid gear'
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "cycloidgear.svg")
+    MenuText = "Cycloid Gear"
+    ToolTip = "Create a Cycloid gear"
 
 
 class CreateBevelGear(BaseCommand):
-    NAME = "bevelgear"
+    NAME = "BevelGear"
     GEAR_FUNCTION = BevelGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'bevelgear.svg')
-    MenuText = 'Bevel gear'
-    ToolTip = 'Create a Bevel gear'
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "bevelgear.svg")
+    MenuText = "Bevel Gear"
+    ToolTip = "Create a Bevel gear"
+
 
 class CreateHypoCycloidGear(BaseCommand):
-    NAME = "hypocycloidgear"
+    NAME = "HypocycloidGear"
     GEAR_FUNCTION = HypoCycloidGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'hypocycloidgear.svg')
-    MenuText = 'HypoCycloid gear'
-    ToolTip = 'Create a HypoCycloid gear with its pins'
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "hypocycloidgear.svg")
+    MenuText = "HypoCycloid Gear"
+    ToolTip = "Create a HypoCycloid gear with its pins"
 
 
 class CreateWormGear(BaseCommand):
-    NAME = "wormgear"
+    NAME = "WormGear"
     GEAR_FUNCTION = WormGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'wormgear.svg')
-    MenuText = 'Worm gear'
-    ToolTip = 'Create a Worm gear'
+    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"
+    NAME = "TimingGear"
     GEAR_FUNCTION = TimingGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'timinggear.svg')
-    MenuText = 'Timing gear'
-    ToolTip = 'Create a Timing gear'
+    Pixmap = os.path.join(BaseCommand.ICONDIR, "timinggear.svg")
+    MenuText = "Timing Gear"
+    ToolTip = "Create a Timing gear"
+
 
 class CreateLanternGear(BaseCommand):
-    NAME = "lanterngear"
+    NAME = "LanternGear"
     GEAR_FUNCTION = LanternGear
-    Pixmap = os.path.join(BaseCommand.ICONDIR, 'lanterngear.svg')
-    MenuText = 'Lantern gear'
-    ToolTip = 'Create a Lantern gear'
+    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/hypocycloidgear.py

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

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freecad/gears/init_gui.py

@@ -1,75 +1,153 @@
 # -*- 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 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 Library General Public License for more details.                  *
+# * 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 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                                                                   *
+# * 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)")
+        "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")
+        "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):
-    """glider workbench"""
+    """A freecad workbench aiming at gear design"""
+
     MenuText = "Gear"
     ToolTip = "Gear Workbench"
-    Icon = os.path.join(__dirname__,  'icons', 'gearworkbench.svg')
+    Icon = os.path.join(__dirname__, "icons", "gearworkbench.svg")
     commands = [
         "CreateInvoluteGear",
+        "CreateInternalInvoluteGear",
         "CreateInvoluteRack",
         "CreateCycloidGear",
+        "CreateCycloidRack",
         "CreateBevelGear",
         "CreateCrownGear",
         "CreateWormGear",
+        "CreateTimingGearT",
         "CreateTimingGear",
         "CreateLanternGear",
-        "CreateHypoCycloidGear"]
+        "CreateHypoCycloidGear",
+        "CreateGearConnector",
+    ]
 
     def GetClassName(self):
         return "Gui::PythonWorkbench"
 
     def Initialize(self):
-        from .commands import CreateCycloidGear, CreateInvoluteGear
-        from .commands import CreateBevelGear, CreateInvoluteRack, CreateCrownGear
-        from .commands import CreateWormGear, CreateTimingGear, CreateLanternGear
-        from .commands import CreateHypoCycloidGear
+        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.addIconPath(App.getHomePath()+"Mod/gear/icons/")
-        Gui.addCommand('CreateInvoluteGear', CreateInvoluteGear())
-        Gui.addCommand('CreateCycloidGear', CreateCycloidGear())
-        Gui.addCommand('CreateBevelGear', CreateBevelGear())
-        Gui.addCommand('CreateInvoluteRack', CreateInvoluteRack())
-        Gui.addCommand('CreateCrownGear', CreateCrownGear())
-        Gui.addCommand('CreateWormGear', CreateWormGear())
-        Gui.addCommand('CreateTimingGear', CreateTimingGear())
-        Gui.addCommand('CreateLanternGear', CreateLanternGear())
-        Gui.addCommand('CreateHypoCycloidGear', CreateHypoCycloidGear())
+        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

freecad/gears/internalinvolutegear.py

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

freecad/gears/involutegear.py

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

freecad/gears/involutegearrack.py

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

freecad/gears/lanterngear.py

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

freecad/gears/timinggear.py

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

freecad/gears/timinggear_t.py

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

freecad/gears/wormgear.py

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

package.xml

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

pygears/__init__.py

@@ -1,22 +1,19 @@
 # -*- 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 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 Library General Public License for more details.                  *
+# * 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 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                                                                   *
+# * 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__ = "0.0.3"
+__version__ = "1.2.0"

pygears/_functions.py

@@ -1,21 +1,18 @@
 # -*- 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 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 Library General Public License for more details.                  *
+# * 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 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                                                                   *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
 # *                                                                         *
 # ***************************************************************************
 
@@ -25,55 +22,64 @@ from numpy.linalg import solve, norm
 
 
 def reflection(angle):
-    mat = array(
-        [[cos(2 * angle), -sin(2 * angle)], [-sin(2 * angle), -cos(2 * angle)]])
+    mat = array([[cos(2 * angle), -sin(2 * angle)],
+                 [-sin(2 * angle), -cos(2 * angle)]])
 
     def func(x):
-        return(dot(x, mat))
-    return(func)
+        # why not use mat @ x???
+        return dot(x, mat)
+
+    return func
 
 
 def reflection3D(angle):
-    mat = array([[cos(2 * angle), -sin(2 * angle), 0.],
-                 [-sin(2 * angle), -cos(2 * angle), 0.], [0., 0., 1.]])
+    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):
-        return(dot(x, mat))
-    return(func)
+        # why not use mat @ x
+        return dot(x, mat)
+
+    return func
 
 
 def rotation(angle, midpoint=None):
-    midpoint = midpoint or [0., 0.]
-    mat = array([[cos(angle), -sin(angle)],
-                 [sin(angle), cos(angle)]])
+    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)
+        return trans(dot(xx, mat))
+
+    return func
 
 
 def rotation3D(angle):
     mat = array(
-        [
-            [cos(angle), -sin(angle), 0.],
-            [sin(angle), cos(angle), 0.],
-            [0., 0., 1.]])
+        [[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)
+        return dot(xx, mat)
+
+    return func
 
 
 def translation(vec):
     def trans(x):
-        return([x[0] + vec[0], x[1] + vec[1]])
+        return [x[0] + vec[0], x[1] + vec[1]]
 
     def func(x):
-        return(array(list(map(trans, x))))
-    return(func)
+        return array(list(map(trans, x)))
+
+    return func
 
 
 def trim(p1, p2, p3, p4):
@@ -83,31 +89,31 @@ def trim(p1, p2, p3, p4):
     a4 = array(p4)
     if all(a1 == a2) or all(a3 == a4):
         if all(a1 == a3):
-            return(a1)
+            return a1
         else:
-            return(False)
+            return False
     elif all(a1 == a3):
         if all(a2 == a4):
-            return((a1 + a2) / 2)
+            return (a1 + a2) / 2
         else:
-            return(a1)
+            return a1
     elif all(a1 == a4):
         if all(a2 == a3):
-            return((a1 + a2) / 2)
+            return (a1 + a2) / 2
         else:
-            return(a1)
+            return a1
     elif all(a2 == a3) or all(a2 == a4):
-        return(p2)
+        return p2
     try:
         g, h = solve(transpose([-a2 + a1, a4 - a3]), a1 - a3)
     except Exception as e:
         print(e)
-        return(False)
+        return False
     else:
-        if 0. < g < 1. and 0. < h < 1.:
-            return(a1 + g * (a2 - a1))
+        if 0.0 < g < 1.0 and 0.0 < h < 1.0:
+            return a1 + g * (a2 - a1)
         else:
-            return(False)
+            return False
 
 
 def trimfunc(l1, l2):
@@ -127,12 +133,12 @@ def trimfunc(l1, l2):
                     l2 == [l2[0]]
                 else:
                     l2 = l2[jk::-1]
-                return([vstack([l1, [s]]), vstack([[s], l2])])
+                return [vstack([l1, [s]]), vstack([[s], l2])]
             j0 = j
             jk += 1
         i0 = i
         ik += 1
-    return(False)
+    return False
 
 
 def diff_norm(vec1, vec2):
@@ -144,7 +150,7 @@ def nearestpts(evolv, underc):
     ik = 0
     iout = 0
     jout = 0
-    outmin = 1000.
+    outmin = 1000.0
     for i in array(evolv[1:]):
         jk = 0
         for j in array(underc[1:]):
@@ -157,17 +163,17 @@ def nearestpts(evolv, underc):
                     iout, jout = [ik, jk]
             jk += 1
         ik += 1
-    return([vstack([underc[:jout], evolv[iout]]), evolv[iout:]])
+    return [vstack([underc[:jout], evolv[iout]]), evolv[iout:]]
 
 
 def intersection_line_circle(p1, p2, r):
-    """return the intersection point of a line from p1 to p2 and a sphere of radius 1 and 
+    """return the intersection point of a line from p1 to p2 and a sphere of radius 1 and
     midpoint 0,0,0"""
     d = p2 - p1
     d /= norm(d)
     p_half = d.dot(p1)
-    q = p1.dot(p1) - r ** 2
-    t = -p_half + sqrt(p_half ** 2 - q)
+    q = p1.dot(p1) - r**2
+    t = -p_half + sqrt(p_half**2 - q)
     return p1 + d * t
 
 
@@ -179,5 +185,3 @@ def arc_from_points_and_center(p_1, p_2, m):
     v /= norm(v)
     p_12 = m + v * r
     return (p_1, p_12, p_2)
-
-    

pygears/bevel_tooth.py

@@ -1,93 +1,198 @@
 # -*- 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 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 Library General Public License for more details.                  *
+# * 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 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                                                                   *
+# * 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 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):
+    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. + 16.*cos(2.*self.pressure_angle) +
-                                6.*cos(4.*self.pressure_angle) + cos(4.*self.pressure_angle - 4.*self.pitch_angle) - 8.*cos(2.*self.pressure_angle - 2.*self.pitch_angle) -
-                                4.*cos(4.*self.pressure_angle - 2.*self.pitch_angle) + 24.*cos(2.*self.pitch_angle) - 2.*cos(4.*self.pitch_angle) -
-                                8.*cos(2.*(self.pressure_angle + self.pitch_angle)) + cos(4.*(self.pressure_angle + self.pitch_angle)) -
-                                4.*cos(4.*self.pressure_angle + 2.*self.pitch_angle) + 24.*cos((4.*sin(self.pitch_angle))/self.z) +
-                                4.*cos(2.*self.pressure_angle - (4.*sin(self.pitch_angle))/self.z) + 4.*cos(2.*self.pressure_angle -
-                                                                                                            4.*self.pitch_angle - (4.*sin(self.pitch_angle))/self.z) - 8.*cos(2.*self.pressure_angle - 2.*self.pitch_angle -
-                                                                                                                                                                              (4.*sin(self.pitch_angle))/self.z) + 24.*cos(4.*(self.pitch_angle + sin(self.pitch_angle)/self.z)) -
-                                8.*cos(2.*(self.pressure_angle + self.pitch_angle + (2.*sin(self.pitch_angle))/self.z)) + 4.*cos(2.*self.pressure_angle +
-                                                                                                                                 (4.*sin(self.pitch_angle))/self.z) + 16.*cos(2.*self.pitch_angle + (4.*sin(self.pitch_angle))/self.z) +
-                                4.*cos(2.*self.pressure_angle + 4.*self.pitch_angle + (4.*sin(self.pitch_angle))/self.z) + 32.*abs(cos(self.pitch_angle +
-                                                                                                                                       (2.*sin(self.pitch_angle))/self.z))*cos(self.pressure_angle)*sqrt(4.*cos(2.*self.pressure_angle) -
-                                                                                                                                                                                                         2.*(-2. + cos(2.*self.pressure_angle - 2.*self.pitch_angle) - 2.*cos(2.*self.pitch_angle) + cos(2.*(self.pressure_angle + self.pitch_angle)) +
-                                                                                                                                                                                                             4.*cos(2.*self.pitch_angle + (4.*sin(self.pitch_angle))/self.z)))*sin(2.*self.pitch_angle))/(-6. - 2.*cos(2.*self.pressure_angle) +
-                                                                                                                                                                                                                                                                                                          cos(2.*self.pressure_angle - 2.*self.pitch_angle) - 2.*cos(2.*self.pitch_angle) + cos(2.*(self.pressure_angle + self.pitch_angle)))**2))
+            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. + \
-            arctan(1/tan(self.pitch_angle)*1/cos(self.pressure_angle))
+        self.involute_start = -pi / 2.0 + arctan(
+            1 / tan(self.pitch_angle) * 1 / cos(self.pressure_angle)
+        )
         self.involute_start_radius = self.get_radius(self.involute_start)
-        self.r_f = sin(self.pitch_angle - sin(pitch_angle) * 2 /
-                       self.z) - self.clearance * sin(self.pitch_angle)
+        self.r_f = sin(
+            self.pitch_angle - sin(pitch_angle) * 2 / self.z
+        ) - self.clearance * sin(self.pitch_angle)
         self.z_f = cos(self.pitch_angle - sin(pitch_angle) * 2 / self.z)
         self.add_foot = True
 
     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)
+            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)
+            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)
+            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))
+        return sqrt(rx**2 + ry**2)
 
     def involute_points(self, num=10):
         pts = linspace(self.involute_start, self.involute_end, num=num)
@@ -104,36 +209,40 @@ class BevelTooth(object):
 
         r_cut = self.r_f / self.z_f
         for i, point in enumerate(xy[1:]):
-            if point.dot(point) >= r_cut ** 2:
+            if point.dot(point) >= r_cut**2:
                 break
         if i > 0:
             self.add_foot = False
         intersection_point = intersection_line_circle(xy[i], point, r_cut)
-        xy = array([intersection_point] + list(xy[i+1:]))
+        xy = array([intersection_point] + list(xy[i + 1 :]))
         xyz = [[p[0], p[1], 1] for p in xy]
-        backlash_rot = rotation3D(self.backlash / 4)
+        backlash_rot = rotation3D(self.angular_backlash / 2)
         xyz = backlash_rot(xyz)
-        return(xyz)
+        return xyz
 
     def points(self, num=10):
         pts = self.involute_points(num=num)
-        rot = rotation3D(-pi/self.z/2)
+        rot = rotation3D(-pi / self.z / 2)
         pts = rot(pts)
-        ref = reflection3D(pi/2)
+        ref = reflection3D(pi / 2)
         pts1 = ref(pts)[::-1]
         if self.add_foot:
-            return([
+            return [
                 array([pts[0], pts[1]]),
                 array(pts[1:]),
                 array([pts[-1], pts1[0]]),
                 array(pts1[:-1]),
-                array([pts1[-2], pts1[-1]])
-            ])
+                array([pts1[-2], pts1[-1]]),
+            ]
         else:
-            return([pts, array([pts[-1], pts1[0]]), pts1])
+            return [pts, array([pts[-1], pts1[0]]), pts1]
 
     def _update(self):
-        self.__init__(z=self.z, clearance=self.clearance,
-                      pressure_angle=self.pressure_angle,
-                      pitch_angle=self.pitch_angle,
-                      backlash=self.backlash, module=self.module)
+        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

@@ -1,26 +1,22 @@
 # -*- 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 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 Library General Public License for more details.                  *
+# * 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 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                                                                   *
+# * 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
-from scipy import optimize as opt
 
 
 def compute_shifted_gears(m, alpha, t1, t2, x1, x2):
@@ -37,10 +33,33 @@ def compute_shifted_gears(m, alpha, t1, t2, x1, x2):
     Returns:
         (float, float): distance between gears [length], pressure angle of the assembly [rad]
     """
-    def inv(x): return np.tan(x) - x
+
+    def inv(x):
+        return np.tan(x) - x
+
     inv_alpha_w = inv(alpha) + 2 * np.tan(alpha) * (x1 + x2) / (t1 + t2)
 
-    def root_inv(x): return inv(x) - inv_alpha_w
-    alpha_w = opt.fsolve(root_inv, 0.)
+    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

@@ -1,21 +1,18 @@
 # -*- 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 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 Library General Public License for more details.                  *
+# * 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 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                                                                   *
+# * You should have received a copy of the GNU General Public License       *
+# * along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
 # *                                                                         *
 # ***************************************************************************
 
@@ -24,14 +21,15 @@ 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=0.12, backlash=0.00):
+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):
@@ -39,46 +37,65 @@ class CycloidTooth():
         self.d2 = self.z2 * self.m
         self.phi = self.m * pi
         self.d = self.z * self.m
-        self.da = self.d + 2*self.m
-        self.di = self.d - 2*self.m - self.clearance * self.m
+        self.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. - (self.d2 * cos((1 + self.d / self.d2) * t))/2.)
-        return(func)
+            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. - (self.d2 * sin((1 + self.d / self.d2) * t))/2.)
-        return(func)
+            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)
+            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)
+            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)
+        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.*self.d2*(self.d2 + self.d))))/self.d
-        )
+        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()
@@ -94,14 +111,20 @@ class CycloidTooth():
         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)
+        rot = rotation(self.phipart / 4 - self.angular_backlash / 2)
         pts1 = rot(pts1)
-        ref = reflection(0.)
+        ref = reflection(0.0)
         pts2 = ref(pts1)[::-1]
         one_tooth = [pts1, array([pts1[-1], pts2[0]]), pts2]
-        return(one_tooth)
+        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)
-
+        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

@@ -1,32 +1,59 @@
 # -*- 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 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 Library General Public License for more details.                  *
+# * 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 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                                                                   *
+# * 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
+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., clearance=0.12, shift=0.5, beta=0.,
-                 undercut=False, backlash=0.00, head=0.00, properties_from_tool=False):
+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
@@ -35,14 +62,13 @@ class InvoluteTooth():
         self.shift = shift
         self.clearance = clearance
         self.backlash = backlash
-        self.head = head        # factor, rename!!!
+        self.head = head  # factor, rename!!!
         self.properties_from_tool = properties_from_tool
         self._calc_gear_factors()
 
     def _calc_gear_factors(self):
         if self.properties_from_tool:
-            self.pressure_angle_t = arctan(
-                tan(self.pressure_angle) / cos(self.beta))
+            self.pressure_angle_t = arctan(tan(self.pressure_angle) / cos(self.beta))
             self.m = self.m_n / cos(self.beta)
         else:
             self.pressure_angle_t = self.pressure_angle
@@ -50,31 +76,47 @@ class InvoluteTooth():
 
         self.pitch = self.m * pi
         self.c = self.clearance * self.m_n
-        self.midpoint = [0., 0.]
+        self.midpoint = [0.0, 0.0]
         self.d = self.z * self.m
         self.dw = self.m * self.z
-        self.da = self.dw + 2. * self.m_n + 2. * \
-            (self.shift + self.head) * self.m_n
-        self.df = self.dw - 2. * self.m_n - \
-            2 * self.c + 2. * self.shift * self.m_n
+        self.da = self.dw + 2.0 * self.m_n + 2.0 * (self.shift + self.head) * self.m_n
+        self.df = self.dw - 2.0 * 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. -
-                                                                   (self.c + self.m_n) * tan(self.pressure_angle_t))) / self.df)))
+        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_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.involute_start = 0.
+        self.angular_backlash = self.backlash / (self.d / 2)
+        self.involute_start = 0.0
         if self.dg <= self.df:
-            self.involute_start = sqrt(self.df ** 2 - self.dg ** 2) / self.dg
+            self.involute_start = sqrt(self.df**2 - self.dg**2) / self.dg
 
     def undercut_points(self, num=10):
         pts = linspace(0, self.undercut_end, num=num)
@@ -84,9 +126,10 @@ class InvoluteTooth():
         y = array(list(map(fy, pts)))
         xy = transpose([x, y])
         rotate = rotation(
-            self.undercut_rot + self.phipart / 2 - self.backlash / 4)
+            self.undercut_rot + self.phipart / 2 - self.angular_backlash / 2
+        )
         xy = rotate(xy)
-        return(array(xy))
+        return array(xy)
 
     def involute_points(self, num=10):
         pts = linspace(self.involute_start, self.involute_end, num=num)
@@ -94,9 +137,9 @@ class InvoluteTooth():
         x = array(list(map(fx, pts)))
         fy = self.involute_function_y()
         y = array(list(map(fy, pts)))
-        rot = rotation(self.involute_rot - self.backlash / 4)
+        rot = rotation(self.involute_rot - self.angular_backlash / 2)
         xy = rot(transpose(array([x, y])))
-        return(xy)
+        return xy
 
     def points(self, num=10):
         l1 = self.undercut_points(num=num)
@@ -111,7 +154,8 @@ class InvoluteTooth():
             u1 = False
             if self.dg > self.df:
                 u1 = vstack(
-                    [[l2[0] * self.df / (diff_norm(l2[0], [0, 0]) * 2)], [l2[0]]])
+                    [[l2[0] * self.df / (diff_norm(l2[0], [0, 0]) * 2)], [l2[0]]]
+                )
                 e1 = l2
             else:
                 e1 = l2
@@ -123,35 +167,39 @@ class InvoluteTooth():
         else:
             u2 = reflect(u1)[::-1]
             one_tooth = [u1, e1, [e1[-1], e2[0]], e2, u2]
-        return(one_tooth)
+        return one_tooth
 
     def gearfunc(self, x):
         rot = rotation(2 * x / self.dw, self.midpoint)
-        return(rot)
+        return rot
 
     def undercut_function_x(self):
         def func(psi):
-            return(
-                cos(psi - (self.df * tan(psi)) / self.dw) * sqrt(self.df ** 2 / 4 +
-                                                                 (self.df ** 2 * tan(psi) ** 2) / 4.))
-        return(func)
+            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.))
-        return(func)
+            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)
+            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)
+            return self.dg / 2 * sin(phi) - phi * self.dg / 2 * cos(phi)
+
+        return func
 
     def _update(self):
         if not hasattr(self, "properties_from_tool"):
@@ -160,8 +208,19 @@ class InvoluteTooth():
 
 
 class InvoluteRack(object):
-    def __init__(self, m=5, z=15, pressure_angle=20 * pi / 180., thickness=5, beta=0, head=0, clearance=0.25, 
-                 properties_from_tool=False, add_endings=False, simplified=False):
+    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
@@ -173,8 +232,7 @@ class InvoluteRack(object):
         self.add_endings = add_endings
         self.simplified = simplified
 
-
-# this is not good. Find better way to stay backward compatible -> versions
+    # 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
@@ -182,7 +240,6 @@ class InvoluteRack(object):
             self.simplified = False
 
     def points(self, num=10):
-        import copy
         m, m_n, pitch, pressure_angle_t = self.compute_properties()
 
         a = (2 + self.head + self.clearance) * m_n * tan(pressure_angle_t)
@@ -191,21 +248,21 @@ class InvoluteRack(object):
             [-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]
+            [-m_n * (1 + self.clearance), a + b],
         ]
         teeth = [tooth]
-        trans = translation([0., pitch, 0.])
+        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(copy.deepcopy(tooth))
+                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 
+                    teeth[-1][-1][1] -= a / 2
                 if self.simplified and (i == self.z - 6):
                     teeth[-1].pop(0)
                     teeth[-1].pop(0)
@@ -214,14 +271,18 @@ class InvoluteRack(object):
 
         teeth = array([v for t in teeth for v in t])  # flattening
         if self.add_endings:
-            ext1 = teeth[0] + array([0., a + b - pitch / 2])
-            ext2 = teeth[-1] - array([0., a + b - pitch / 2])
-            teeth = [ext1.tolist(), ext1.tolist()] + teeth.tolist() + [ext2.tolist(), ext2.tolist()]
+            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.append(list(teeth[-1]))
         teeth[0][0] -= self.thickness
-        #teeth.append(list(teeth[0]))
+        # teeth.append(list(teeth[0]))
         teeth[-1][0] -= self.thickness
         teeth.append(teeth[0])
         return array(teeth)
@@ -234,7 +295,7 @@ class InvoluteRack(object):
         else:
             pressure_angle_t = self.pressure_angle
             m = self.m
-            m_n  = self.m
+            m_n = self.m
 
         pitch = m * pi
         return m, m_n, pitch, pressure_angle_t

pygears/profile.py

@@ -7,13 +7,14 @@ 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)
+            rot = rotation3D(np.pi * 2 / self.z)
         else:
-            rot = rotation(- np.pi * 2 / self.z)
+            rot = rotation(-np.pi * 2 / self.z)
         profile = tooth
         for i in range(self.z - 1):
             tooth = rot(tooth).tolist()
@@ -21,19 +22,19 @@ class _GearProfile(object):
         profile.append(profile[0])
         return np.array(profile)
 
+
 class InvoluteProfile(InvoluteTooth, _GearProfile):
     pass
 
+
 class CycloidProfile(CycloidTooth, _GearProfile):
     pass
 
+
 class BevelProfile(BevelTooth, _GearProfile):
     rot3D = True
 
+
 class InvoluteRackProfile(InvoluteRack):
     def profile(self):
         return self.points()
-
-
-
-

setup.py

@@ -1,15 +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'],
-	  include_package_data=True
+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,
 )