222 lines
8.6 KiB
Python
222 lines
8.6 KiB
Python
#! /usr/bin/env python
|
|
'''
|
|
Copyright (C) 2013 Matthew Dockrey (gfish @ cyphertext.net)
|
|
|
|
This program is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation; either version 2 of the License, or
|
|
(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, write to the Free Software
|
|
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
|
|
|
|
Based on gears.py by Aaron Spike and Tavmjong Bah
|
|
'''
|
|
|
|
import inkex
|
|
import simplestyle
|
|
import sys
|
|
from math import *
|
|
from fablabchemnitz_svg import *
|
|
|
|
class Sprockets(inkex.Effect):
|
|
def __init__(self):
|
|
inkex.Effect.__init__(self)
|
|
self.OptionParser.add_option("-t", "--teeth",
|
|
action="store", type="int",
|
|
dest="teeth", default=24,
|
|
help="Number of teeth")
|
|
self.OptionParser.add_option("-s", "--size",
|
|
action="store", type="string",
|
|
dest="size", default="ANSI #40",
|
|
help="Chain size (common values ANSI #35, ANSI #40, ANSI #60)")
|
|
|
|
def get_pitch(self, size):
|
|
return self.unittouu({
|
|
'ANSI #25': '6.35mm',
|
|
'ANSI #35': '9.53mm',
|
|
'ANSI #40': '12.70mm',
|
|
'ANSI #41': '12.70mm',
|
|
'ANSI #50': '15.88mm',
|
|
'ANSI #60': '19.05mm',
|
|
'ANSI #80': '25.40mm',
|
|
'ANSI #100': '31.75mm',
|
|
'ANSI #120': '38.10mm',
|
|
'ANSI #140': '44.45mm',
|
|
'ANSI #160': '50.80mm',
|
|
'ANSI #180': '57.15mm',
|
|
'ANSI #200': '63.50mm',
|
|
'ANSI #240': '76.20mm'
|
|
}[size])
|
|
|
|
def get_roller_diameter(self, size):
|
|
return self.unittouu({
|
|
'ANSI #25': '3.30mm',
|
|
'ANSI #35': '5.08mm',
|
|
'ANSI #40': '7.77mm',
|
|
'ANSI #41': '7.92mm',
|
|
'ANSI #50': '10.16mm',
|
|
'ANSI #60': '11.91mm',
|
|
'ANSI #80': '15.88mm',
|
|
'ANSI #100': '19.05mm',
|
|
'ANSI #120': '22.23mm',
|
|
'ANSI #140': '25.40mm',
|
|
'ANSI #160': '28.58mm',
|
|
'ANSI #180': '37.08mm',
|
|
'ANSI #200': '39.67mm',
|
|
'ANSI #240': '47.63mm'
|
|
}[size])
|
|
|
|
def invertX(self, p):
|
|
return (-p[0], p[1])
|
|
|
|
def effect(self):
|
|
size = self.options.size
|
|
|
|
P = self.get_pitch(size)
|
|
N = self.options.teeth
|
|
PD = P / sin(pi / N)
|
|
PR = PD / 2
|
|
|
|
# Equations taken from
|
|
# http://www.gearseds.com/files/design_draw_sprocket_5.pdf
|
|
# Also referenced:
|
|
# http://en.wikipedia.org/wiki/Roller_chain (of course)
|
|
# and
|
|
# Chains for Power Transmission and Material Handling:
|
|
# Design and Applications Handbook
|
|
# American Chain Association, 1982
|
|
|
|
Dr = self.get_roller_diameter(size)
|
|
Ds = 1.0005 * Dr + self.unittouu('0.003in')
|
|
R = Ds / 2 # seating curve radius
|
|
A = radians(35 + 60 / N)
|
|
B = radians(18 - 56 / N)
|
|
ac = 0.8 * Dr
|
|
M = ac * cos(A)
|
|
T = ac * sin(A)
|
|
E = 1.3025 * Dr + self.unittouu('0.0015in') # transition radius
|
|
ab = 1.4 * Dr
|
|
W = ab * cos(pi / N)
|
|
V = ab * sin(pi / N)
|
|
F = Dr * (0.8 * cos(radians(18 - 56 / N)) + 1.4 * cos(radians(17 - 64 / N)) - 1.3025) - self.unittouu('0.0015in') # topping curve radius
|
|
|
|
svg = ""
|
|
|
|
t_inc = 2.0 * pi / float(N)
|
|
thetas = [(x * t_inc) for x in range(N)]
|
|
|
|
for theta in thetas:
|
|
# Seating curve center
|
|
seatC = (0, -PR)
|
|
|
|
# Transitional curve center
|
|
c = (M, -PR - T)
|
|
|
|
# Calculate line cx, angle A from x axis
|
|
# Y = mX + b
|
|
cx_m = -tan(A) # Negative because we're in -Y space
|
|
cx_b = c[1] - cx_m * c[0]
|
|
|
|
# Calculate intersection of cx with circle S to get point x
|
|
# http://math.stackexchange.com/questions/228841/how-do-i-calculate-the-intersections-of-a-straight-line-and-a-circle
|
|
qA = cx_m * cx_m + 1
|
|
qB = 2 * (cx_m * cx_b - cx_m * seatC[1] - seatC[0])
|
|
qC = seatC[1] * seatC[1] - R * R + seatC[0] * seatC[0] - 2 * cx_b * seatC[1] + cx_b * cx_b
|
|
cx_X = (-qB - sqrt(qB * qB - 4 * qA * qC)) / (2 * qA)
|
|
|
|
# Seating curve/Transitional curve junction
|
|
x = (cx_X, cx_m * cx_X + cx_b)
|
|
|
|
# Calculate line cy, angle B past cx
|
|
cy_m = -tan(A - B)
|
|
cy_b = c[1] - cy_m * c[0]
|
|
|
|
# Calculate point y (E along cy from c)
|
|
# http://www.physicsforums.com/showthread.php?t=419561
|
|
yX = c[0] - E / sqrt(1 + cy_m * cy_m)
|
|
|
|
# Transitional curve/Tangent line junction
|
|
y = (yX, cy_m * yX + cy_b)
|
|
|
|
# Solve for circle T with radius E which passes through x and y
|
|
# http://mathforum.org/library/drmath/view/53027.html
|
|
# http://stackoverflow.com/questions/12264841/determine-circle-center-based-on-two-points-radius-known-with-solve-optim
|
|
z = ((x[0] + y[0]) / 2, (x[1] + y[1]) / 2)
|
|
x_diff = y[0] - x[0]
|
|
y_diff = y[1] - x[1]
|
|
q = sqrt(x_diff * x_diff + y_diff * y_diff)
|
|
tX = z[0] + sqrt(E * E - (q / 2) * (q / 2)) * (x[1] - y[1]) / q
|
|
tY = z[1] + sqrt(E * E - (q / 2) * (q / 2)) * (y[0] - x[0]) / q
|
|
|
|
# Transitional curve center
|
|
tranC = (tX, tY)
|
|
|
|
# Tangent line -- tangent to transitional curve at point y
|
|
tanl_m = -(tranC[0] - y[0]) / (tranC[1] - y[1])
|
|
tanl_b = -y[0] * tanl_m + y[1]
|
|
t_off = (y[0] - 10, tanl_m * (y[0] - 10) + tanl_b)
|
|
|
|
# Topping curve center
|
|
topC = (-W, -PR + V)
|
|
|
|
# Adjust F to force topping curve tangent to tangent line
|
|
F = abs(topC[1] - tanl_m * topC[0] - tanl_b) / sqrt(tanl_m * tanl_m + 1) * 1.0001 # Final fudge needed to overcome numerical instability
|
|
|
|
# Find intersection point between topping curve and tangent line
|
|
ttA = tanl_m * tanl_m + 1
|
|
ttB = 2 * (tanl_m * tanl_b - tanl_m * topC[1] - topC[0])
|
|
ttC = topC[1] * topC[1] - F * F + topC[0] * topC[0] - 2 * tanl_b * topC[1] + tanl_b * tanl_b
|
|
tanl_X = (-ttB - sqrt(ttB * ttB - 4 * ttA * ttC)) / (2 * ttA)
|
|
|
|
# Tagent line/Topping curve junction
|
|
tanl = (tanl_X, tanl_m * tanl_X + tanl_b)
|
|
|
|
# Calculate tip line, angle t_inc/2 from Y axis
|
|
tip_m = -tan(pi / 2 + t_inc / 2) # Negative because we're in -Y space
|
|
tip_b = 0
|
|
|
|
# Calculate intersection of tip line with topping curve
|
|
tA = tip_m * tip_m + 1
|
|
tB = 2 * (tip_m * tip_b - tip_m * topC[1] - topC[0])
|
|
tC = topC[1] * topC[1] - F * F + topC[0] * topC[0] - 2 * tip_b * topC[1] + tip_b * tip_b
|
|
tip_X = (-tB - sqrt(tB * tB - 4 * tA * tC)) / (2 * tA)
|
|
|
|
# Topping curve top
|
|
tip = (tip_X, tip_m * tip_X + tip_b)
|
|
|
|
# Set initial location if needed
|
|
if (theta == 0):
|
|
svg += SVG_move(tip, theta)
|
|
|
|
svg += SVG_circle(tanl, F, 1, theta) # Topping curve left
|
|
svg += SVG_line(y, theta) # Tangent line left
|
|
svg += SVG_circle(x, E, 0, theta) # Transitional curve left
|
|
svg += SVG_circle(self.invertX(x), R, 0, theta) # Seating curve
|
|
svg += SVG_circle(self.invertX(y), E, 0, theta) # Transitionl curve right
|
|
svg += SVG_line(self.invertX(tanl), theta) # Tangent line right
|
|
svg += SVG_circle(self.invertX(tip), F, 1, theta) # Topping curve right
|
|
|
|
svg += SVG_close()
|
|
|
|
# Insert as a new element
|
|
sprocket_style = { 'stroke': '#000000',
|
|
'stroke-width': '0.1',
|
|
'fill': 'none'
|
|
}
|
|
g_attribs = {inkex.addNS('label','inkscape'): 'Sprocket ' + size + "-" + str(N),
|
|
'transform': 'translate(' + str(self.view_center[0]) + ',' + str(self.view_center[1]) + ')',
|
|
'style' : simplestyle.formatStyle(sprocket_style),
|
|
'd' : svg }
|
|
g = inkex.etree.SubElement(self.current_layer, inkex.addNS('path','svg'), g_attribs)
|
|
|
|
if __name__ == '__main__':
|
|
e = Sprockets()
|
|
e.affect()
|