cycloidal.py

   1 #based on a work by genehacker
   2 #copyright 2009 ben lipkowitz
   3 #distributed under the terms of the GNU GPL version 2 or later
   4 #
   5 #cycloidal.py: draws a cycloidal gear
   6
   7 import cairo
   8 from math import *
   9
  10 def frange(start, stop, step): #this ought to come with python :(
  11     r = start
  12     while r < stop:
  13         yield r
  14         r += step
  15
  16 height, width = 500, 500
  17 surf = cairo.SVGSurface('cycloidal.svg', height, width)
  18 cr = cairo.Context(surf)
  19 cr.translate(0.5, 0.5) #align pixels
  20 cr.scale(width, height)
  21 cr.translate(0.5, 0.5) #move gear to center of image
  22
  23 tmp = cr.user_to_device(1,1)
  24 scale = (tmp[0] + tmp[1]) / 2.
  25 cr.set_line_width(1/scale)
  26
  27 def cycloidal(teeth=17, module=0.05, resolution=2):
  28     '''draws a cycloidal gear. arguments: number of teeth, circumference per tooth, degrees per step'''
  29     radius = module*teeth/2 #pitch radius
  30     z = teeth*2
  31     ro = radius/z #rolling circle radius
  32     inout = 1
  33     angle = 2*pi/z #angle of 1 lobe of hypo/epicycloid
  34     for m in range(z+1): #teeth):
  35         #for inout in [1, -1]:
  36             inout *= -1
  37             for theta in frange(angle*m, angle*(m+1), resolution*pi/180):
  38                 x = ((radius + inout * ro) * cos(theta)) - inout * \
  39                         (ro * cos(theta * (radius + inout * ro)/ro))
  40                 y = ((radius + inout * ro) * sin(theta)) - \
  41                         (ro * sin(theta * (radius + inout * ro)/ro))
  42                 if m == 0:
  43                     cr.move_to(x, y)
  44                 else:
  45                     cr.line_to(x,y)
  46     cr.set_source_rgb(1,1,1)
  47     cr.fill_preserve()
  48     cr.set_source_rgb(0,0,0)
  49     cr.stroke()
  50
  51 cycloidal(10)
  52 cycloidal(8)
  53 surf.write_to_png('cycloidal.png')