Merge pull request #13 from CadQuery/gear

Add another involute gear example

Author: adam-urbanczyk

README.md

@@ -57,6 +57,10 @@ A place to share CadQuery scripts, modules, tutorials and projects
 
 * [3D_Printer_Extruder_Support.py](examples/3D_Printer_Extruder_Support.py) - Designed for mounting hotend to an i3 X-carriage inspired by the P3steel Toolson
 
+* [Involute_Gear.py](examples/Involute_Gear.py) - Fast involute gear generator.
+
+    <img src="examples/images/Involute_Gear.png" width="600"/>
+
 ### Tutorials
 
 * [Ex000 Start Here.ipynb](tutorials/Ex000%20Start%20Here.ipynb) - iPython notebook that is the entry point for a set of CadQuery tutorials

examples/Involute_Gear.py

@@ -0,0 +1,81 @@
+from cadquery import Workplane, Edge, Wire, Vector
+from math import *
+
+
+def involute_gear(m, z, alpha=20, shift=0, N=20):
+    '''
+    See https://khkgears.net/new/gear_knowledge/gear_technical_reference/involute_gear_profile.html
+    for math
+    '''
+    
+    alpha = radians(alpha)
+
+    # radii
+    r_ref = m*z/2
+    r_top = r_ref + m*(1+shift)
+    r_base = r_ref*cos(alpha)
+    r_d = r_ref - 1.25*m
+    
+    inv = lambda a: tan(a) - a
+    
+    # angles of interest
+    alpha_inv = inv(alpha)
+    alpha_tip = acos(r_base/r_top)
+    alpha_tip_inv = inv(alpha_tip)
+    
+    a = 90/z+degrees(alpha_inv)
+    a2 = 90/z++degrees(alpha_inv)-degrees(alpha_tip_inv)
+    a3 = 360/z-a
+    
+    # involute curve (radius based parametrization)
+    def involute_curve(r_b,sign=1):
+        
+        def f(r):
+            alpha = sign*acos(r_b/r)
+            x = r*cos(tan(alpha) - alpha) 
+            y = r*sin(tan(alpha) - alpha)
+        
+            return x,y
+        
+        return f
+    
+    # construct all the profiles
+    right = (
+        Workplane()
+        .transformed(rotate=(0,0,a))
+        .parametricCurve(involute_curve(r_base,-1), start=r_base, stop = r_top, makeWire=False, N=N)
+        .val()
+    )
+    
+    left = (
+        Workplane()
+        .transformed(rotate=(0,0,-a))
+        .parametricCurve(involute_curve(r_base), start=r_base, stop = r_top, makeWire=False, N=N)
+        .val()
+    )
+
+    top = Edge.makeCircle(r_top,angle1=-a2, angle2=a2)
+    bottom = Edge.makeCircle(r_d, angle1=-a3, angle2=-a)
+    
+    side = Edge.makeLine( cq.Vector(r_d,0), cq.Vector(r_base,0))
+    side1 = side.rotate(cq.Vector(0, 0, 0), cq.Vector(0, 0, 1), -a)
+    side2 = side.rotate(cq.Vector(0, 0, 0), cq.Vector(0, 0, 1), -a3)
+    
+    # single tooth profile
+    profile = Wire.assembleEdges([left,top,right,side1,bottom,side2])
+    profile = profile.chamfer2D(m/4, profile.Vertices()[-3:-1])
+
+    # complete gear
+    res = (
+        Workplane()
+        .polarArray(0,0,360,z)
+        .each(lambda loc: profile.located(loc))
+        .consolidateWires()
+    )
+
+    return res.val()
+
+
+show_object(
+    Workplane(obj=involute_gear(1, 20)).toPending().twistExtrude(20, 30)
+)