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mightyscape-1.2/extensions/fablabchemnitz/sprocket/sprocket.py

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#!/usr/bin/env python3
'''
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
from math import *
from lxml import etree
def rotate(p, t):
return (p[0] * cos(t) - p[1] * sin(t), p[0] * sin(t) + p[1] * cos(t))
def SVG_move(p, t):
pp = rotate(p, t)
return 'M ' + str(pp[0]) + ',' + str(pp[1]) + '\n'
def SVG_line(p, t):
pp = rotate(p, t)
return 'L ' + str(pp[0]) + ',' + str(pp[1]) + '\n'
def SVG_circle(p, r, sweep, t):
pp = rotate(p, t)
return 'A ' + str(r) + ',' + str(r) + ' 0 0,' + str(sweep) + ' ' + str(pp[0]) + ',' + str(pp[1]) + '\n'
def SVG_curve(p, c1, c2, t):
pp = rotate(p, t)
c1p = rotate(c1, t)
c2p = rotate(c2, t)
return 'C ' + str(pp[0]) + ',' + str(pp[1]) + ' ' + str(c1p[0]) + ',' + str(c1p[1]) + ' ' + str(c2p[0]) + ',' + str(c2p[1]) + '\n'
def SVG_curve2(p1, c11, c12, p2, c21, c22, t):
p1p = rotate(p1, t)
c11p = rotate(c11, t)
c12p = rotate(c12, t)
p2p = rotate(p2, t)
c21p = rotate(c21, t)
c22p = rotate(c22, t)
return 'C ' + str(p1p[0]) + ',' + str(p1p[1]) + ' ' + str(c11p[0]) + ',' + str(c11p[1]) + ' ' + str(c12p[0]) + ',' + str(c12p[1]) + ' ' + str(p2p[0]) + ',' + str(p2p[1]) + ' ' + str(c21p[0]) + ',' + str(c21p[1]) + ' ' + str(c22p[0]) + ',' + str(c22p[1]) + '\n'
def SVG_close():
return 'Z\n'
class Sprocket(inkex.EffectExtension):
def add_arguments(self, pars):
pars.add_argument("-t", "--teeth", type=int, default=24, help="Number of teeth")
pars.add_argument("-s", "--size", default="ANSI #40", help="Chain size (common values ANSI #35, ANSI #40, ANSI #60)")
def get_pitch(self, size):
return self.svg.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.svg.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.svg.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.svg.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.svg.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': self.svg.unittouu(str(0.1) + "mm"),
'fill': 'none'
}
g_attribs = {inkex.addNS('label','inkscape'): 'Sprocket ' + size + "-" + str(N),
'transform': 'translate(' + str(self.svg.namedview.center[0]) + ',' + str(self.svg.namedview.center[1]) + ')',
'style' : str(inkex.Style(sprocket_style)),
'd' : svg }
g = etree.SubElement(self.svg.get_current_layer(), inkex.addNS('path','svg'), g_attribs)
if __name__ == '__main__':
Sprocket().run()
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