The gear calculation in Gear.ko turned into a function and used to design a couple of gears

gearing.py

"""
examples/gearing.ko

Turned the gear example into a generic function
to produce solid gears. 

See gear.ko for description and notes for the original function.

This function takes 
	R: radius of the gear. 
	z0 and z1: top and bottom elevation to produce the thickness of the gear
	nt: number of teeth of the gear. Defaults to 32
	pressureAngle: defaults to 20, an industry standard.  See tutorial.
	clearance: extra depth to compensate for fillet produce by the tool.
			   1.157 in US, 1.1666 in EU
	
Returns a full 3D shape that can be manipulated just like any other.
To make a hole for the axis, you can just substract a cylinder from it.	

Though the radius doesn't produce any visible feature on the gear,
it is what should be used in calculations about how this gear 
engages other gears.  It is the radius a toothless gear, that is, 
a wheel, would have to roll on another toothless gear.

The involute gear construction is based on the tutorial at
http://www.cartertools.com/involute.html
"""

from math import sqrt, atan2, sin, cos, pi, radians
import operator

from koko.lib.shapes import *


def gear(R, z0, z1, nt = 32, pressureAngle = 20, clearance = 1.16666): 
	P  = nt / R / 2    # diametral pitch

	RB = R*cos(radians(pressureAngle))   # base circle radius
	a = 1/P     # addendum
	d = clearance/P # dedendum
	RO = R+a    # outer radius
	RR = R-d    # root radius


	# MathTree expressions for r and r**2
	r_2 = MathTree.square(X) + MathTree.square(Y)
	r = MathTree.sqrt(r_2)

	# See note (1) for derivation of tooth rotation
	t = sqrt(R**2/RB**2 -1)
	rot = atan2(sin(t)-t*cos(t), cos(t)+t*sin(t)) + pi/2/nt

	# See note (2) for derivation of involute curve
	tooth = (
		MathTree.sqrt(r_2-RB**2) - RB*(MathTree.atan(Y/X) +
		MathTree.acos(RB/r)) - RB*rot
	)

	tooth.shape = True
	tooth &= reflect_y(tooth)

	# If we have an odd number of teeth, then we can't take
	# advantage of bilateral tooth symmetry.
	if nt % 2:
		tooth &= -X
		teeth = reduce(operator.add, [rotate(tooth, i*360./nt)
									  for i in range(nt)])
	else:
		teeth = reduce(operator.add, [rotate(tooth, i*360./nt)
									  for i in range(nt/2)])

	teeth += circle(0, 0, RR)
	teeth &= circle(0, 0, RO)
	teeth.bounds = circle(0, 0, RO).bounds
	teeth = extrusion(teeth, z0, z1)

	return teeth
	
	
# Simple test:

#Number of teeth and radius of first gear
nt1 = 32
r1 = 20.

#Number of teeth and radius of second gear
nt2 = 16
r2 = 10.

#height of both
z0 = -1.
z1 = 1.

#diameter of hole
axld = 1

g1 = gear(r1, z0, z1, nt1)
g1.color = 'blue'
g1 -=cylinder(0, 0, z0, z1, axld)

g2 = gear(r2, z0, z1, nt2)
g2 -= cylinder(0, 0, z0, z1, axld)
g2.color = 'red'

if not nt2 % 2:
	g2 = rotate(g2, 180. / nt2)
g2 = move(g2, r1 + r2, 0, 0)

cad.shapes = g1, g2