# Source code for boxes.pulley

```"""
// Parametric Pulley with multiple belt profiles
// by droftarts January 2012

// Based on pulleys by:
// https://www.thingiverse.com/thing:11256 by me!
// https://github.com/prusajr/PrusaMendel by Josef Prusa
// https://www.thingiverse.com/thing:3104 by GilesBathgate

// dxf tooth data from http://oem.cadregister.com/asp/PPOW_Entry.asp?company=915217&elementID=07807803/METRIC/URETH/WV0025/F
// pulley diameter checked and modelled from data at https://www.sdp-si.com/D265/HTML/D265T016.html
"""
from math import *

from boxes.vectors import *

[docs]
def tooth_spaceing_curvefit(teeth, b, c, d):
return ((c * teeth ** d) / (b + teeth ** d)) * teeth

[docs]
def tooth_spacing(teeth, tooth_pitch, pitch_line_offset):
return (2 * ((teeth * tooth_pitch) / (3.14159265 * 2) - pitch_line_offset))

[docs]
def mirrorx(points):
return [[-x, y] for x, y in points]

[docs]
class Pulley:

spacing = {
"MXL": (False, 2.032, 0.254),
"40DP": (False, 2.07264, 0.1778),
"XL": (False, 5.08, 0.254),
"H": (False, 9.525, 0.381),
"T2_5": (True, 0.7467, 0.796, 1.026),
"T5": (True, 0.6523, 1.591, 1.064),
"T10": (False, 10, 0.93),
"AT5": (True, 0.6523, 1.591, 1.064),
"HTD_3mm": (False, 3, 0.381),
"HTD_5mm": (False, 5, 0.5715),
"HTD_8mm": (False, 8, 0.6858),
"GT2_2mm": (False, 2, 0.254),
"GT2_3mm": (False, 3, 0.381),
"GT2_5mm": (False, 5, 0.5715),
}

profile_data = {
"MXL": (0.508, 1.321),
"40DP": (0.457, 1.226),
"XL": (1.27, 3.051),
"H": (1.905, 5.359),
"T2_5": (0.7, 1.678),
"T5": (1.19, 3.264),
"T10": (2.5, 6.13),
"AT5": (1.19, 4.268),
"HTD_3mm": (1.289, 2.27),
"HTD_5mm": (2.199, 3.781),
"HTD_8mm": (3.607, 6.603),
"GT2_2mm": (0.764, 1.494),
"GT2_3mm": (1.169, 2.31),
"GT2_5mm": (1.969, 3.952),
}

teeth = { "MXL" : [[-0.660421,-0.5],[-0.660421,0],[-0.621898,0.006033],[-0.587714,0.023037],[-0.560056,0.049424],[-0.541182,0.083609],[-0.417357,0.424392],[-0.398413,0.458752],[-0.370649,0.48514],[-0.336324,0.502074],[-0.297744,0.508035],[0.297744,0.508035],[0.336268,0.502074],[0.370452,0.48514],[0.39811,0.458752],[0.416983,0.424392],[0.540808,0.083609],[0.559752,0.049424],[0.587516,0.023037],[0.621841,0.006033],[0.660421,0],[0.660421,-0.5]],
"40DP" : [[-0.612775,-0.5],[-0.612775,0],[-0.574719,0.010187],[-0.546453,0.0381],[-0.355953,0.3683],[-0.327604,0.405408],[-0.291086,0.433388],[-0.248548,0.451049],[-0.202142,0.4572],[0.202494,0.4572],[0.248653,0.451049],[0.291042,0.433388],[0.327609,0.405408],[0.356306,0.3683],[0.546806,0.0381],[0.574499,0.010187],[0.612775,0],[0.612775,-0.5]],
"XL" : [[-1.525411,-1],[-1.525411,0],[-1.41777,0.015495],[-1.320712,0.059664],[-1.239661,0.129034],[-1.180042,0.220133],[-0.793044,1.050219],[-0.733574,1.141021],[-0.652507,1.210425],[-0.555366,1.254759],[-0.447675,1.270353],[0.447675,1.270353],[0.555366,1.254759],[0.652507,1.210425],[0.733574,1.141021],[0.793044,1.050219],[1.180042,0.220133],[1.239711,0.129034],[1.320844,0.059664],[1.417919,0.015495],[1.525411,0],[1.525411,-1]],
"H" : [[-2.6797,-1],[-2.6797,0],[-2.600907,0.006138],[-2.525342,0.024024],[-2.45412,0.052881],[-2.388351,0.091909],[-2.329145,0.140328],[-2.277614,0.197358],[-2.234875,0.262205],[-2.202032,0.334091],[-1.75224,1.57093],[-1.719538,1.642815],[-1.676883,1.707663],[-1.62542,1.764693],[-1.566256,1.813112],[-1.500512,1.85214],[-1.4293,1.880997],[-1.353742,1.898883],[-1.274949,1.905021],[1.275281,1.905021],[1.354056,1.898883],[1.429576,1.880997],[1.500731,1.85214],[1.566411,1.813112],[1.625508,1.764693],[1.676919,1.707663],[1.719531,1.642815],[1.752233,1.57093],[2.20273,0.334091],[2.235433,0.262205],[2.278045,0.197358],[2.329455,0.140328],[2.388553,0.091909],[2.454233,0.052881],[2.525384,0.024024],[2.600904,0.006138],[2.6797,0],[2.6797,-1]],
"T2_5" : [[-0.839258,-0.5],[-0.839258,0],[-0.770246,0.021652],[-0.726369,0.079022],[-0.529167,0.620889],[-0.485025,0.67826],[-0.416278,0.699911],[0.416278,0.699911],[0.484849,0.67826],[0.528814,0.620889],[0.726369,0.079022],[0.770114,0.021652],[0.839258,0],[0.839258,-0.5]],
"T5" : [[-1.632126,-0.5],[-1.632126,0],[-1.568549,0.004939],[-1.507539,0.019367],[-1.450023,0.042686],[-1.396912,0.074224],[-1.349125,0.113379],[-1.307581,0.159508],[-1.273186,0.211991],[-1.246868,0.270192],[-1.009802,0.920362],[-0.983414,0.978433],[-0.949018,1.030788],[-0.907524,1.076798],[-0.859829,1.115847],[-0.80682,1.147314],[-0.749402,1.170562],[-0.688471,1.184956],[-0.624921,1.189895],[0.624971,1.189895],[0.688622,1.184956],[0.749607,1.170562],[0.807043,1.147314],[0.860055,1.115847],[0.907754,1.076798],[0.949269,1.030788],[0.9837,0.978433],[1.010193,0.920362],[1.246907,0.270192],[1.273295,0.211991],[1.307726,0.159508],[1.349276,0.113379],[1.397039,0.074224],[1.450111,0.042686],[1.507589,0.019367],[1.568563,0.004939],[1.632126,0],[1.632126,-0.5]],
"T10" : [[-3.06511,-1],[-3.06511,0],[-2.971998,0.007239],[-2.882718,0.028344],[-2.79859,0.062396],[-2.720931,0.108479],[-2.651061,0.165675],[-2.590298,0.233065],[-2.539962,0.309732],[-2.501371,0.394759],[-1.879071,2.105025],[-1.840363,2.190052],[-1.789939,2.266719],[-1.729114,2.334109],[-1.659202,2.391304],[-1.581518,2.437387],[-1.497376,2.47144],[-1.408092,2.492545],[-1.314979,2.499784],[1.314979,2.499784],[1.408091,2.492545],[1.497371,2.47144],[1.581499,2.437387],[1.659158,2.391304],[1.729028,2.334109],[1.789791,2.266719],[1.840127,2.190052],[1.878718,2.105025],[2.501018,0.394759],[2.539726,0.309732],[2.59015,0.233065],[2.650975,0.165675],[2.720887,0.108479],[2.798571,0.062396],[2.882713,0.028344],[2.971997,0.007239],[3.06511,0],[3.06511,-1]],
"AT5" : [[-2.134129,-0.75],[-2.134129,0],[-2.058023,0.005488],[-1.984595,0.021547],[-1.914806,0.047569],[-1.849614,0.082947],[-1.789978,0.127073],[-1.736857,0.179338],[-1.691211,0.239136],[-1.653999,0.305859],[-1.349199,0.959203],[-1.286933,1.054635],[-1.201914,1.127346],[-1.099961,1.173664],[-0.986896,1.18992],[0.986543,1.18992],[1.099614,1.173664],[1.201605,1.127346],[1.286729,1.054635],[1.349199,0.959203],[1.653646,0.305859],[1.690859,0.239136],[1.73651,0.179338],[1.789644,0.127073],[1.849305,0.082947],[1.914539,0.047569],[1.984392,0.021547],[2.057906,0.005488],[2.134129,0],[2.134129,-0.75]],
"HTD_3mm" : [[-1.135062,-0.5],[-1.135062,0],[-1.048323,0.015484],[-0.974284,0.058517],[-0.919162,0.123974],[-0.889176,0.206728],[-0.81721,0.579614],[-0.800806,0.653232],[-0.778384,0.72416],[-0.750244,0.792137],[-0.716685,0.856903],[-0.678005,0.918199],[-0.634505,0.975764],[-0.586483,1.029338],[-0.534238,1.078662],[-0.47807,1.123476],[-0.418278,1.16352],[-0.355162,1.198533],[-0.289019,1.228257],[-0.22015,1.25243],[-0.148854,1.270793],[-0.07543,1.283087],[-0.000176,1.28905],[0.075081,1.283145],[0.148515,1.270895],[0.219827,1.252561],[0.288716,1.228406],[0.354879,1.19869],[0.418018,1.163675],[0.477831,1.123623],[0.534017,1.078795],[0.586276,1.029452],[0.634307,0.975857],[0.677809,0.91827],[0.716481,0.856953],[0.750022,0.792167],[0.778133,0.724174],[0.800511,0.653236],[0.816857,0.579614],[0.888471,0.206728],[0.919014,0.123974],[0.974328,0.058517],[1.048362,0.015484],[1.135062,0],[1.135062,-0.5]],
"HTD_5mm" : [[-1.89036,-0.75],[-1.89036,0],[-1.741168,0.02669],[-1.61387,0.100806],[-1.518984,0.21342],[-1.467026,0.3556],[-1.427162,0.960967],[-1.398568,1.089602],[-1.359437,1.213531],[-1.310296,1.332296],[-1.251672,1.445441],[-1.184092,1.552509],[-1.108081,1.653042],[-1.024167,1.746585],[-0.932877,1.832681],[-0.834736,1.910872],[-0.730271,1.980701],[-0.62001,2.041713],[-0.504478,2.09345],[-0.384202,2.135455],[-0.259708,2.167271],[-0.131524,2.188443],[-0.000176,2.198511],[0.131296,2.188504],[0.259588,2.167387],[0.384174,2.135616],[0.504527,2.093648],[0.620123,2.04194],[0.730433,1.980949],[0.834934,1.911132],[0.933097,1.832945],[1.024398,1.746846],[1.108311,1.653291],[1.184308,1.552736],[1.251865,1.445639],[1.310455,1.332457],[1.359552,1.213647],[1.39863,1.089664],[1.427162,0.960967],[1.467026,0.3556],[1.518984,0.21342],[1.61387,0.100806],[1.741168,0.02669],[1.89036,0],[1.89036,-0.75]],
"HTD_8mm" : [[-3.301471,-1],[-3.301471,0],[-3.16611,0.012093],[-3.038062,0.047068],[-2.919646,0.10297],[-2.813182,0.177844],[-2.720989,0.269734],[-2.645387,0.376684],[-2.588694,0.496739],[-2.553229,0.627944],[-2.460801,1.470025],[-2.411413,1.691917],[-2.343887,1.905691],[-2.259126,2.110563],[-2.158035,2.30575],[-2.041518,2.490467],[-1.910478,2.66393],[-1.76582,2.825356],[-1.608446,2.973961],[-1.439261,3.10896],[-1.259169,3.22957],[-1.069074,3.335006],[-0.869878,3.424485],[-0.662487,3.497224],[-0.447804,3.552437],[-0.226732,3.589341],[-0.000176,3.607153],[0.226511,3.589461],[0.447712,3.552654],[0.66252,3.497516],[0.870027,3.424833],[1.069329,3.33539],[1.259517,3.229973],[1.439687,3.109367],[1.608931,2.974358],[1.766344,2.825731],[1.911018,2.664271],[2.042047,2.490765],[2.158526,2.305998],[2.259547,2.110755],[2.344204,1.905821],[2.411591,1.691983],[2.460801,1.470025],[2.553229,0.627944],[2.588592,0.496739],[2.645238,0.376684],[2.720834,0.269734],[2.81305,0.177844],[2.919553,0.10297],[3.038012,0.047068],[3.166095,0.012093],[3.301471,0],[3.301471,-1]],
"GT2_2mm" : mirrorx([[0.747183,-0.5],[0.747183,0],[0.647876,0.037218],[0.598311,0.130528],[0.578556,0.238423],[0.547158,0.343077],[0.504649,0.443762],[0.451556,0.53975],[0.358229,0.636924],[0.2484,0.707276],[0.127259,0.750044],[0,0.76447],[-0.127259,0.750044],[-0.2484,0.707276],[-0.358229,0.636924],[-0.451556,0.53975],[-0.504797,0.443762],[-0.547291,0.343077],[-0.578605,0.238423],[-0.598311,0.130528],[-0.648009,0.037218],[-0.747183,0],[-0.747183,-0.5]]),
"GT2_3mm" : [[-1.155171,-0.5],[-1.155171,0],[-1.065317,0.016448],[-0.989057,0.062001],[-0.93297,0.130969],[-0.90364,0.217664],[-0.863705,0.408181],[-0.800056,0.591388],[-0.713587,0.765004],[-0.60519,0.926747],[-0.469751,1.032548],[-0.320719,1.108119],[-0.162625,1.153462],[0,1.168577],[0.162625,1.153462],[0.320719,1.108119],[0.469751,1.032548],[0.60519,0.926747],[0.713587,0.765004],[0.800056,0.591388],[0.863705,0.408181],[0.90364,0.217664],[0.932921,0.130969],[0.988924,0.062001],[1.065168,0.016448],[1.155171,0],[1.155171,-0.5]],
"GT2_5mm" : [[-1.975908,-0.75],[-1.975908,0],[-1.797959,0.03212],[-1.646634,0.121224],[-1.534534,0.256431],[-1.474258,0.426861],[-1.446911,0.570808],[-1.411774,0.712722],[-1.368964,0.852287],[-1.318597,0.989189],[-1.260788,1.123115],[-1.195654,1.25375],[-1.12331,1.380781],[-1.043869,1.503892],[-0.935264,1.612278],[-0.817959,1.706414],[-0.693181,1.786237],[-0.562151,1.851687],[-0.426095,1.9027],[-0.286235,1.939214],[-0.143795,1.961168],[0,1.9685],[0.143796,1.961168],[0.286235,1.939214],[0.426095,1.9027],[0.562151,1.851687],[0.693181,1.786237],[0.817959,1.706414],[0.935263,1.612278],[1.043869,1.503892],[1.123207,1.380781],[1.195509,1.25375],[1.26065,1.123115],[1.318507,0.989189],[1.368956,0.852287],[1.411872,0.712722],[1.447132,0.570808],[1.474611,0.426861],[1.534583,0.256431],[1.646678,0.121223],[1.798064,0.03212],[1.975908,0],[1.975908,-0.75]],
}

def __init__(self, boxes) -> None:
self.boxes = boxes

[docs]
@classmethod
def getProfiles(cls):
return list(sorted(cls.teeth.keys()))

[docs]
def diameter(self, teeth, profile):
if self.spacing[profile][0]:

def __call__(self, teeth, profile, insideout=False, r_axle=None,
callback=None, move=""):

# ********************************
# ** Scaling tooth for good fit **
# ********************************
# To improve fit of belt to pulley, set the following constant. Decrease or increase by 0.1mm at a time. We are modelling the *BELT* tooth here, not the tooth on the pulley. Increasing the number will *decrease* the pulley tooth size. Increasing the tooth width will also scale proportionately the tooth depth, to maintain the shape of the tooth, and increase how far into the pulley the tooth is indented. Can be negative

# If you need more tooth depth than this provides, adjust the following constant. However, this will cause the shape of the tooth to change.

pulley_OD = self.diameter(teeth, profile)

tooth_depth, tooth_width = self.profile_data[profile]
tooth_distance_from_centre = ((pulley_OD / 2) ** 2 - ((tooth_width + additional_tooth_width) / 2) ** 2) ** 0.5
tooth_width_scale = (tooth_width + additional_tooth_width) / tooth_width
tooth_depth_scale = ((tooth_depth + additional_tooth_depth) / tooth_depth)

if insideout:
pulley_OD += 2*tooth_depth * tooth_depth_scale
tooth_depth_scale *= -1

total_width = max(pulley_OD, 2*(r_axle or 0.0))

if self.boxes.move(total_width, total_width, move, before=True):
return

self.boxes.moveTo(total_width / 2, total_width / 2)
self.boxes.cc(callback, None, 0.0, 0.0)

if r_axle:
if insideout:
self.boxes.circle(0, 0, r_axle)
else:
self.boxes.hole(0, 0, r_axle)

points = []
for i in range(teeth):
m = [[tooth_width_scale, 0, 0],
[0, tooth_depth_scale, -tooth_distance_from_centre]]
m = mmul(m, rotm(i * 2 * pi / teeth))
points.extend(vtransl(pt, m) for pt in self.teeth[profile][1:-1])

self.boxes.drawPoints(points, kerfdir=-1 if insideout else 1)
self.boxes.move(total_width, total_width, move)

```