diff --git a/CleanedUpNotes_InvoluteGears_July2022.pdf b/CleanedUpNotes_InvoluteGears_July2022.pdf new file mode 100644 index 0000000..47330dd Binary files /dev/null and b/CleanedUpNotes_InvoluteGears_July2022.pdf differ diff --git a/InvoluteGears.png b/InvoluteGears.png new file mode 100644 index 0000000..b67a123 Binary files /dev/null and b/InvoluteGears.png differ diff --git a/LICENSE b/LICENSE index 6dcab5e..6b76146 100644 --- a/LICENSE +++ b/LICENSE @@ -1,3 +1,6 @@ +Copyright 2022, Aaron M. Schinder +Released under the MIT/BSD License + Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. diff --git a/example_output/gear_12_12_v1.scad b/example_output/gear_12_12_v1.scad new file mode 100644 index 0000000..1488705 --- /dev/null +++ b/example_output/gear_12_12_v1.scad @@ -0,0 +1,793 @@ +// openscad + +module gear_12_12() +{ +pts = [ [0.268229,-0.268229], + [0.269895,-0.266553], + [0.27155,-0.264866], + [0.273195,-0.26317], + [0.274829,-0.261463], + [0.276453,-0.259745], + [0.278065,-0.258018], + [0.279667,-0.256281], + [0.281259,-0.254534], + [0.282839,-0.252777], + [0.285718,-0.250399], + [0.28912,-0.248308], + [0.292939,-0.246592], + [0.297066,-0.245335], + [0.301395,-0.244626], + [0.305817,-0.244551], + [0.310225,-0.245197], + [0.314512,-0.246649], + [0.318569,-0.248996], + [0.370186,-0.28934], + [0.371436,-0.290214], + [0.375363,-0.292558], + [0.382196,-0.295937], + [0.392108,-0.299891], + [0.405219,-0.303937], + [0.421588,-0.307582], + [0.441216,-0.310322], + [0.464045,-0.311654], + [0.489927,-0.31106], + [0.492815,-0.306463], + [0.495661,-0.30184], + [0.498462,-0.29719], + [0.501221,-0.292514], + [0.503935,-0.287813], + [0.506605,-0.283086], + [0.509231,-0.278335], + [0.511813,-0.273559], + [0.51438,-0.268775], + [0.501923,-0.246048], + [0.489355,-0.226944], + [0.477167,-0.211315], + [0.465827,-0.198961], + [0.455767,-0.18963], + [0.447387,-0.183023], + [0.441044,-0.178795], + [0.43705,-0.176566], + [0.435669,-0.17592], + [0.374922,-0.151391], + [0.370861,-0.14905], + [0.367459,-0.146065], + [0.364696,-0.14257], + [0.36255,-0.138702], + [0.361,-0.134599], + [0.360024,-0.130397], + [0.359602,-0.126231], + [0.359711,-0.122239], + [0.36033,-0.118557], + [0.361062,-0.11631], + [0.361779,-0.114059], + [0.362483,-0.111803], + [0.363172,-0.109542], + [0.363848,-0.107278], + [0.364509,-0.105009], + [0.365156,-0.102736], + [0.365789,-0.100459], + [0.366408,-0.0981787], + [0.367012,-0.0958942], + [0.367603,-0.0936059], + 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[0.245335,-0.297066], + [0.246592,-0.292939], + [0.248308,-0.28912], + [0.250399,-0.285718], + [0.252777,-0.282839], + [0.254534,-0.281259], + [0.256281,-0.279667], + [0.258018,-0.278065], + [0.259745,-0.276453], + [0.261463,-0.274829], + [0.26317,-0.273195], + [0.264866,-0.27155], + [0.266553,-0.269895], + [0.268229,-0.268229], +]; + +polygon(points=pts,convexity=200); +} + +linear_extrude(height=0.1,convexity=200) +gear_12_12(); + diff --git a/example_output/gear_12_24_v1.scad b/example_output/gear_12_24_v1.scad new file mode 100644 index 0000000..36be411 --- /dev/null +++ b/example_output/gear_12_24_v1.scad @@ -0,0 +1,1573 @@ +// openscad + +module gear_12_24() +{ +pts = [ [0.812398,-0.336506], + [0.813333,-0.33424], + [0.814262,-0.331971], + [0.815184,-0.3297], + [0.8161,-0.327426], + [0.81701,-0.325149], + [0.817913,-0.32287], + [0.81881,-0.320588], + [0.819701,-0.318304], + [0.820585,-0.316018], + [0.82241,-0.312548], + [0.82492,-0.309307], + [0.82801,-0.306387], + 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[0.806656,-0.350048], + [0.807628,-0.347798], + [0.808595,-0.345545], + [0.809555,-0.343289], + [0.810509,-0.341031], + [0.811457,-0.33877], + [0.812398,-0.336506], +]; + +polygon(points=pts,convexity=200); +} + +linear_extrude(height=0.1,convexity=200) +gear_12_24(); + diff --git a/example_output/gear_12_36_v1.scad b/example_output/gear_12_36_v1.scad new file mode 100644 index 0000000..21cbc77 --- /dev/null +++ b/example_output/gear_12_36_v1.scad @@ -0,0 +1,2353 @@ +// openscad + +module gear_12_36() +{ +pts = [ [1.33233,-0.356998], + [1.33283,-0.355135], + [1.33333,-0.353271], + [1.33382,-0.351407], + [1.33431,-0.349542], + [1.3348,-0.347676], + [1.33528,-0.34581], + [1.33576,-0.343943], + [1.33624,-0.342075], + [1.33672,-0.340207], + [1.33813,-0.336475], + [1.34026,-0.332934], + [1.34303,-0.329679], + [1.34632,-0.32681], + [1.35003,-0.324423], + [1.35406,-0.322616], + [1.3583,-0.321487], + [1.36265,-0.321133], + [1.367,-0.321651], + [1.37207,-0.322843], + [1.37426,-0.323274], + 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[1.842,-0.372731], + [1.84231,-0.371208], + [1.84261,-0.369686], + [1.84292,-0.368163], + [1.84322,-0.36664], +]; + +polygon(points=pts,convexity=200); +} + +linear_extrude(height=0.1,convexity=200) +gear_12_48(); + diff --git a/example_output/gear_36_18_v1.scad b/example_output/gear_36_18_v1.scad new file mode 100644 index 0000000..9e637d4 --- /dev/null +++ b/example_output/gear_36_18_v1.scad @@ -0,0 +1,1183 @@ +// openscad + +module gear_36_18() +{ +pts = [ [0.166854,-0.122698], + [0.167453,-0.121879], + [0.168048,-0.121057], + [0.16864,-0.120232], + [0.169227,-0.119404], + [0.16981,-0.118573], + [0.170389,-0.11774], + [0.170964,-0.116903], + [0.171535,-0.116064], + [0.172101,-0.115222], + [0.172946,-0.114242], + [0.173993,-0.113374], + [0.175203,-0.112643], + [0.176537,-0.112074], + [0.177956,-0.111693], + [0.179421,-0.111526], + [0.180893,-0.111597], + [0.182333,-0.111933], + [0.183702,-0.11256], + [0.200311,-0.122737], + [0.200779,-0.122995], + [0.202224,-0.123684], + 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+ [0.160082,-0.132292], + [0.160599,-0.131034], + [0.161282,-0.129935], + [0.161917,-0.129143], + [0.162548,-0.128348], + [0.163175,-0.12755], + [0.163798,-0.126749], + [0.164417,-0.125945], + [0.165032,-0.125137], + [0.165643,-0.124327], + [0.166251,-0.123514], + [0.166854,-0.122698], +]; + +polygon(points=pts,convexity=200); +} + +linear_extrude(height=0.1,convexity=200) +gear_36_18(); + diff --git a/example_output/gear_36_36_v1.scad b/example_output/gear_36_36_v1.scad new file mode 100644 index 0000000..02d352e --- /dev/null +++ b/example_output/gear_36_36_v1.scad @@ -0,0 +1,2353 @@ +// openscad + +module gear_36_36() +{ +pts = [ [0.453862,-0.0544038], + [0.453961,-0.0535729], + [0.454058,-0.0527417], + [0.454154,-0.0519104], + [0.454248,-0.0510789], + [0.454341,-0.0502473], + [0.454432,-0.0494155], + [0.454522,-0.0485835], + [0.45461,-0.0477513], + [0.454697,-0.046919], + [0.454979,-0.0456153], + [0.455513,-0.0443407], + [0.456268,-0.0431319], + [0.457215,-0.0420259], + 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[0.650919,-0.276244], +]; + +polygon(points=pts,convexity=200); +} + +linear_extrude(height=0.1,convexity=200) +gear_36_54(); + diff --git a/example_output/gear_36_72_v1.scad b/example_output/gear_36_72_v1.scad new file mode 100644 index 0000000..412579c --- /dev/null +++ b/example_output/gear_36_72_v1.scad @@ -0,0 +1,4549 @@ +// openscad + +module gear_36_72() +{ +pts = [ [0.953828,0.0792063], + [0.95378,0.0797817], + [0.953732,0.080357], + [0.953683,0.0809324], + [0.953634,0.0815077], + [0.953585,0.082083], + [0.953535,0.0826582], + [0.953485,0.0832334], + [0.953435,0.0838086], + [0.953384,0.0843838], + [0.953422,0.0857035], + [0.953743,0.0869716], + [0.954311,0.0881772], + [0.955094,0.0893097], + [0.956054,0.0903581], + [0.95716,0.0913118], + [0.958374,0.09216], + [0.959664,0.0928919], + [0.960993,0.0934967], + [0.965837,0.0952106], + [0.971072,0.097194], + [0.976688,0.0994652], + [0.982675,0.102042], + [0.989021,0.104941], + [0.995716,0.10818], + [1.00275,0.111776], + 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[1.22433,-0.0505872], + [1.22527,-0.0524712], + [1.22646,-0.0543376], + [1.22789,-0.056132], + [1.22956,-0.0577998], + [1.23146,-0.0592866], + [1.23357,-0.0605378], + [1.23589,-0.061499], + [1.2384,-0.0621157], + [1.24111,-0.0623333], + [1.24599,-0.0623333], + [1.24869,-0.0621157], + [1.25121,-0.061499], + [1.25353,-0.0605378], + [1.25564,-0.0592866], + [1.25753,-0.0577998], + [1.2592,-0.056132], + [1.26064,-0.0543376], + [1.26183,-0.0524712], + [1.26276,-0.0505872], + [1.29052,0.0416667], + [1.309,0.0416667], + [1.309,-0.25], + [0,-0.25], + [0,0.0416667], +]; + +polygon(points=pts,convexity=200); +} + +linear_extrude(height=0.1,convexity=200) +rack24(); + diff --git a/example_output/rack36.scad b/example_output/rack36.scad new file mode 100644 index 0000000..d0dfac4 --- /dev/null +++ b/example_output/rack36.scad @@ -0,0 +1,247 @@ +// openscad + +module rack36() +{ +pts = [ [0,0.0277778], + [0,0.0277778], + [0.0123161,0.0277778], + [0.0310512,-0.0350581], + [0.0316714,-0.0363149], + [0.0324626,-0.0375596], + [0.0334181,-0.0387559], + [0.0345314,-0.0398677], + [0.0357959,-0.0408587], + [0.0372051,-0.0416925], + [0.0387523,-0.042333], + [0.040431,-0.0427439], + [0.0422347,-0.0428889], + [0.0450318,-0.0428889], + [0.0468354,-0.0427439], + [0.0485142,-0.042333], + [0.0500614,-0.0416925], + [0.0514706,-0.0408587], + [0.0527351,-0.0398677], + [0.0538484,-0.0387559], + [0.0548039,-0.0375596], + [0.0555951,-0.0363149], + [0.0562153,-0.0350581], + [0.0749504,0.0277778], + [0.0872665,0.0277778], + [0.0995825,0.0277778], + [0.118318,-0.0350581], + [0.118938,-0.0363149], + [0.119729,-0.0375596], + [0.120685,-0.0387559], + [0.121798,-0.0398677], + [0.123062,-0.0408587], + [0.124472,-0.0416925], + [0.126019,-0.042333], + [0.127697,-0.0427439], + [0.129501,-0.0428889], + [0.132298,-0.0428889], + [0.134102,-0.0427439], + [0.135781,-0.042333], + [0.137328,-0.0416925], + [0.138737,-0.0408587], + [0.140002,-0.0398677], + [0.141115,-0.0387559], + [0.14207,-0.0375596], + [0.142862,-0.0363149], + [0.143482,-0.0350581], + [0.162217,0.0277778], + [0.174533,0.0277778], + [0.186849,0.0277778], + [0.205584,-0.0350581], + [0.206204,-0.0363149], + [0.206995,-0.0375596], + [0.207951,-0.0387559], + [0.209064,-0.0398677], + [0.210329,-0.0408587], + [0.211738,-0.0416925], + [0.213285,-0.042333], + [0.214964,-0.0427439], + [0.216768,-0.0428889], + [0.219565,-0.0428889], + [0.221368,-0.0427439], + [0.223047,-0.042333], + [0.224594,-0.0416925], + [0.226003,-0.0408587], + [0.227268,-0.0398677], + [0.228381,-0.0387559], + [0.229337,-0.0375596], + [0.230128,-0.0363149], + [0.230748,-0.0350581], + [0.249483,0.0277778], + [0.261799,0.0277778], + [0.274115,0.0277778], + [0.292851,-0.0350581], + [0.293471,-0.0363149], + [0.294262,-0.0375596], + [0.295217,-0.0387559], + [0.296331,-0.0398677], + [0.297595,-0.0408587], + [0.299004,-0.0416925], + [0.300552,-0.042333], + [0.30223,-0.0427439], + [0.304034,-0.0428889], + [0.306831,-0.0428889], + [0.308635,-0.0427439], + [0.310314,-0.042333], + [0.311861,-0.0416925], + [0.31327,-0.0408587], + [0.314534,-0.0398677], + [0.315648,-0.0387559], + [0.316603,-0.0375596], + [0.317394,-0.0363149], + [0.318015,-0.0350581], + [0.33675,0.0277778], + [0.349066,0.0277778], + [0.361382,0.0277778], + [0.380117,-0.0350581], + [0.380737,-0.0363149], + [0.381528,-0.0375596], + [0.382484,-0.0387559], + [0.383597,-0.0398677], + [0.384862,-0.0408587], + [0.386271,-0.0416925], + [0.387818,-0.042333], + [0.389497,-0.0427439], + [0.391301,-0.0428889], + [0.394098,-0.0428889], + [0.395901,-0.0427439], + [0.39758,-0.042333], + [0.399127,-0.0416925], + [0.400536,-0.0408587], + [0.401801,-0.0398677], + [0.402914,-0.0387559], + [0.40387,-0.0375596], + [0.404661,-0.0363149], + [0.405281,-0.0350581], + [0.424016,0.0277778], + [0.436332,0.0277778], + [0.448648,0.0277778], + [0.467383,-0.0350581], + [0.468004,-0.0363149], + [0.468795,-0.0375596], + [0.46975,-0.0387559], + [0.470864,-0.0398677], + [0.472128,-0.0408587], + [0.473537,-0.0416925], + [0.475085,-0.042333], + [0.476763,-0.0427439], + [0.478567,-0.0428889], + [0.481364,-0.0428889], + [0.483168,-0.0427439], + [0.484846,-0.042333], + [0.486394,-0.0416925], + [0.487803,-0.0408587], + [0.489067,-0.0398677], + [0.490181,-0.0387559], + [0.491136,-0.0375596], + [0.491927,-0.0363149], + [0.492548,-0.0350581], + [0.511283,0.0277778], + [0.523599,0.0277778], + [0.535915,0.0277778], + [0.55465,-0.0350581], + [0.55527,-0.0363149], + [0.556061,-0.0375596], + [0.557017,-0.0387559], + [0.55813,-0.0398677], + [0.559395,-0.0408587], + [0.560804,-0.0416925], + [0.562351,-0.042333], + [0.56403,-0.0427439], + [0.565833,-0.0428889], + [0.568631,-0.0428889], + [0.570434,-0.0427439], + [0.572113,-0.042333], + [0.57366,-0.0416925], + [0.575069,-0.0408587], + [0.576334,-0.0398677], + [0.577447,-0.0387559], + [0.578403,-0.0375596], + [0.579194,-0.0363149], + [0.579814,-0.0350581], + [0.598549,0.0277778], + [0.610865,0.0277778], + [0.623181,0.0277778], + [0.641916,-0.0350581], + [0.642537,-0.0363149], + [0.643328,-0.0375596], + [0.644283,-0.0387559], + [0.645397,-0.0398677], + [0.646661,-0.0408587], + [0.64807,-0.0416925], + [0.649618,-0.042333], + [0.651296,-0.0427439], + [0.6531,-0.0428889], + [0.655897,-0.0428889], + [0.657701,-0.0427439], + [0.659379,-0.042333], + [0.660927,-0.0416925], + [0.662336,-0.0408587], + [0.6636,-0.0398677], + [0.664714,-0.0387559], + [0.665669,-0.0375596], + [0.66646,-0.0363149], + [0.667081,-0.0350581], + [0.685816,0.0277778], + [0.698132,0.0277778], + [0.710448,0.0277778], + [0.729183,-0.0350581], + [0.729803,-0.0363149], + [0.730594,-0.0375596], + [0.73155,-0.0387559], + [0.732663,-0.0398677], + [0.733928,-0.0408587], + [0.735337,-0.0416925], + [0.736884,-0.042333], + [0.738563,-0.0427439], + [0.740366,-0.0428889], + [0.743164,-0.0428889], + [0.744967,-0.0427439], + [0.746646,-0.042333], + [0.748193,-0.0416925], + [0.749602,-0.0408587], + [0.750867,-0.0398677], + [0.75198,-0.0387559], + [0.752936,-0.0375596], + [0.753727,-0.0363149], + [0.754347,-0.0350581], + [0.773082,0.0277778], + [0.785398,0.0277778], + [0.797714,0.0277778], + [0.816449,-0.0350581], + [0.81707,-0.0363149], + [0.817861,-0.0375596], + [0.818816,-0.0387559], + [0.81993,-0.0398677], + [0.821194,-0.0408587], + [0.822603,-0.0416925], + [0.82415,-0.042333], + [0.825829,-0.0427439], + [0.827633,-0.0428889], + [0.83043,-0.0428889], + [0.832234,-0.0427439], + [0.833912,-0.042333], + [0.83546,-0.0416925], + [0.836869,-0.0408587], + [0.838133,-0.0398677], + [0.839247,-0.0387559], + [0.840202,-0.0375596], + [0.840993,-0.0363149], + [0.841613,-0.0350581], + [0.860349,0.0277778], + [0.872665,0.0277778], + [0.872665,-0.25], + [0,-0.25], + [0,0.0277778], +]; + +polygon(points=pts,convexity=200); +} + +linear_extrude(height=0.1,convexity=200) +rack36(); + diff --git a/gearscript.py b/gearscript.py new file mode 100644 index 0000000..bd605cd --- /dev/null +++ b/gearscript.py @@ -0,0 +1,1107 @@ +#!/usr/bin/python3 + +import os,sys,math +import numpy as np +import matplotlib.pyplot as plt + +cos = np.cos +sin = np.sin +pi = np.pi +sqrt = np.sqrt +exp = np.exp +linspace = np.linspace + +## Gear Profile Generation Scripts +## July 2022 +## Copyright Aaron M. Schinder +## Released under the MIT/BSD License +## Do whatever the heck you want with this code. + + +################################### +## Newton's Method Scalar Solver ## +################################### + +def mergedefaults(kwargs,defs): + + merged = dict() + + for k in defs: + if(k in kwargs): + merged[k] = kwargs[k] + else: + merged[k] = defs[k] + + return merged + +def newtonsolve_defaults(): + + defs = dict(); + + defs["maxiter"] = 1000 + defs["dx"] = 1E-5 + defs["tol"] = 1E-5 + defs["alpha"] = 0.5 + defs["randstep"] = 0.5 + defs["use_maxstep"] = False + defs["maxstep"] = 1.0 + + return defs + +#Scalar Newton Solver +#Takes a function of the form y = fptr(x,fpars) and returns a solution x where fptr(x,fpars)=0 +#Use: newtonsolve(fptr,x0,fpars,**kwargs) +#Optional Arguments +# +# +def newtonsolve(fptr,x0,fpars,**kwargs): + + x0 = np.float64(x0) + + flag = -1 + + defs = newtonsolve_defaults() + defs = mergedefaults(kwargs,defs) + maxiter = np.int32(defs["maxiter"]) + dx = np.float64(defs["dx"]) + tol = np.float64(defs["tol"]) + alpha = np.float64(defs["alpha"]) + randstep = np.float64(defs["randstep"]) + use_maxstep = defs["use_maxstep"] + maxstep = defs["maxstep"] + + I = 0 + x = x0 + while(Imaxstep): + deltax = deltax/(np.abs(deltax))*maxstep + else: + deltax = (2.0*np.random.randint(0,2)-1.0)*randstep + + x = x + deltax + + I = I + 1 + + return [x,flag] + +def test_newtonsolve_fn(x,fpars): + + y = np.sin(x*x)+fpars + + return y + +def test_newtonsolve(): + + fpars = 0.75 + fpnt = test_newtonsolve_fn + + for I in range(0,10): + x0 = np.random.rand()*10.0 + [x,flag] = newtonsolve(fpnt,x0,fpars) + y = fpnt(x,fpars) + print("I:{}: x:{:1.3f} y:{:1.4f} flg:{}".format(I,x,y,flag)) + + + return + +#################### +## Basic Geometry ## +#################### + +#Vector norm +def vnorm(v): + n = np.sqrt(np.sum(v*v)) + return n + +#Normalize vector +def vnormalize(v): + n = vnorm(v) + if(n>0.0): + v = v/n + else: + v = np.zeros(v.shape) + return v + +#2d Vector Hodge Dual +def vdual2d(v): + v2 = np.zeros((2),dtype=np.float64) + v2[0] = -v[1] + v2[1] = v[0] + return v2 + +#2d vector cross product +def vcross2d(v1,v2): + c = v1[0]*v2[1] - v1[1]*v2[0] + return c + +def geom_arg(xy): + return np.arctan2(xy[1],xy[0]) + +def involute(phi): + + x = cos(phi)+phi*sin(phi) + y = sin(phi)-phi*cos(phi) + ri = np.sqrt(x*x+y*y) + theta = np.arctan2(y,x) + + return [x,y,ri,theta] + +def involute_r_fn(phi,fpars): + + [x,y,ri,theta] = involute(phi) + + deltar = ri*fpars[0] - fpars[1] + + return deltar + +def involute_r( + r: np.float64, + rbase: np.float64 = 1.0 + ): + + r = np.float64(r) + rbase = np.float64(rbase) + + if(r<=rbase): + theta = np.float64(0.0) + phi = np.float64(0.0) + ri = r + else: + fpnt = involute_r_fn + fpars = [rbase,r] + phi0 = pi/4.0 + [phi,flag] = newtonsolve(fpnt,phi0,fpars,dx=1E-4*rbase,tol=1E-4*rbase,alpha=0.5,maxiter=1000) + [x,y,ri,theta] = involute(phi) + x = x*rbase; y=y*rbase; ri=ri*rbase + + return [phi,theta,ri] + +def involute_theta_fn(phi,fpars): + + [x,y,ri,theta] = involute(phi) + + deltatheta = theta - fpars + + return deltatheta + +def involute_theta( + theta: np.float64, + rbase: np.float64 = 1.0 + ): + + theta = np.float64(theta) + rbase = np.float64(rbase) + + fpnt = involute_theta_fn + fpars = theta + phi0 = pi/4.0 + [phi,flag] = newtonsolve(fpnt,phi0,fpars,dx=1E-4,tol=1E-4,alpha=0.5,maxiter=1000) + [x,y,ri,thetai] = involute(phi) + x = x*rbase; y=y*rbase; ri=ri*rbase + + return [phi,thetai,ri] + + +def test_involute_r(): + + phi = linspace(0,pi/2,500) + rbase = 1.75 + r = 3.0 + + theta = linspace(0,2*pi,500) + xc0 = cos(theta)*r; yc0 = sin(theta)*r; + xc1 = cos(theta)*rbase; yc1 = sin(theta)*rbase; + + [xi,yi,ri,theta] = involute(phi) + xi = xi*rbase; yi=yi*rbase; ri=ri*rbase; + + [phi,theta0,ri0] = involute_r(r,rbase) + + [phi2,theta2,ri2] = involute_theta(pi/4,rbase) + + plt.figure(1) + plt.plot(xc0,yc0,'r') + plt.plot(xc1,yc1,'k') + plt.plot(xi,yi,'b') + plt.plot(cos(theta0)*ri0,sin(theta0)*ri0,'ro') + plt.plot(cos(theta2)*ri2,sin(theta2)*ri2,'ro') + plt.show() + + + return + +def geom_involute_left(rbase,xycenter,theta0,phi1,phi2,N): + + rbase = np.float64(rbase) + xycenter = np.float64(xycenter) + theta0 = np.float64(theta0) + phi1 = np.float64(phi1) + phi2 = np.float64(phi2) + N = np.int32(N) + + xy = np.zeros((2,N),dtype=np.float64) + phi = np.linspace(phi1,phi2,N) + xy[0,:] = cos(phi-theta0) + (phi)*sin(phi-theta0) + xy[1,:] = sin(phi-theta0) - (phi)*cos(phi-theta0) + xy[0,:] = rbase*xy[0,:] + xycenter[0] + xy[1,:] = rbase*xy[1,:] + xycenter[1] + + return xy + +def geom_involute_right(rbase, xycenter, theta0, phi1, phi2, N): + + rbase = np.float64(rbase) + xycenter = np.float64(xycenter) + theta0 = np.float64(theta0) + phi1 = np.float64(phi1) + phi2 = np.float64(phi2) + N = np.int32(N) + + xy = np.zeros((2,N),dtype=np.float64) + phi = np.linspace(-phi1,-phi2,N) + xy[0,:] = cos(phi-theta0) + (phi)*sin(phi-theta0) + xy[1,:] = sin(phi-theta0) - (phi)*cos(phi-theta0) + xy[0,:] = rbase*xy[0,:] + xycenter[0] + xy[1,:] = rbase*xy[1,:] + xycenter[1] + + return xy + +def delta_involute_left(phi,theta0,rbase): + + dxy = np.zeros(2,dtype=np.float64) + dxy[0] = cos(phi-theta0)*(phi)*rbase + dxy[1] = sin(phi-theta0)*(phi)*rbase + return dxy + +def delta_involute_right(phi,theta0,rbase): + + dxy = np.zeros(2,dtype=np.float64) + dxy[0] = cos(phi-theta0)*(phi)*rbase + dxy[1] = -sin(phi-theta0)*(phi)*rbase + + return dxy + +def geom_circulararc(r,xycenter,theta0,theta1,N): + + r = np.float64(r) + xycenter = np.float64(xycenter) + theta0 = np.float64(theta0) + theta1 = np.float64(theta1) + N = np.int32(N) + + th = np.linspace(theta0,theta1,N) + xy = np.zeros((2,N),dtype=np.float64) + + for I in range(0,N): + xy[0,I] = xycenter[0] + r*cos(th[I]) + xy[1,I] = xycenter[1] + r*sin(th[I]) + + return xy + +def geom_circle(r,N): + + r = np.float64(r) + N = np.int32(N) + + th = np.linspace(0,2.0*pi,N-1) + xy = np.zeros((2,N),dtype=np.float64) + + for I in range(0,N-1): + xy[0,I] = r*cos(th[I]) + xy[1,I] = r*sin(th[I]) + + xy[0,N-1] = xy[0,0] + xy[1,N-1] = xy[1,0] + + + return xy + +def geom_cubicspline(xy0,dxy0,xy1,dxy1,N,r0=1.5,r1=1.5): + + xy0 = np.float64(xy0) + dxy0 = np.float64(dxy0) + xy1 = np.float64(xy1) + dxy1 = np.float64(dxy1) + + L = xy1-xy0 #two lengthscales + + dxy0s = vnormalize(dxy0)*r0 + dxy1s = vnormalize(dxy1)*r1 + + if(L[0]<0): + dxy0s[0] = -dxy0s[0] + dxy1s[0] = -dxy1s[0] + if(L[1]<0): + dxy0s[1] = -dxy0s[1] + dxy1s[1] = -dxy1s[1] + + xy = np.zeros((2,N)) + xys = np.zeros((2,N)) + + ax = np.zeros((4,1)) + ay = np.zeros((4,1)) + bx = np.float64([[0],[1],[dxy0s[0]],[dxy1s[0]]]) + by = np.float64([[0],[1],[dxy0s[1]],[dxy1s[1]]]) + + A = np.array([[1,0,0,0],[1,1,1,1],[0,1,0,0],[0,1,2,3]],dtype=np.float64) + Ai = np.linalg.inv(A) + + ax = np.matmul(Ai,bx) + ay = np.matmul(Ai,by) + + t = np.linspace(0,1,N) + o = np.ones(t.shape,dtype=np.float64) + + xys[0,:] = ax[0]*o+ax[1]*t+ax[2]*(t**2)+ax[3]*(t**3) + xys[1,:] = ay[0]*o+ay[1]*t+ay[2]*(t**2)+ay[3]*(t**3) + + xy[0,:] = xys[0,:]*L[0]+xy0[0] + xy[1,:] = xys[1,:]*L[1]+xy0[1] + + + return xy + +def test_geom_cubic_spline(): + + xy = geom_cubicspline([0,0],[0,55],[1,1],[1,0],100) + + plt.plot(xy[0,:],xy[1,:],'k') + plt.show() + + return + +# def geom_twoline_arc(p1,l1,p2,l2,r,N): + +# ##future work .... + +# return xy + +#Oriented two-point arc. Circle joins p1 to p2 with radius r, offset dual to p1p2 +def geom_twopoint_arc(p1,p2,r,N): + + p0 = 0.5*(p1+p2) + l = (p2-p1) + l = vnormalize(l) + n = vdual(l) + b = vnorm(p2-p1)/2.0 + + xy = None + + if(b<=r): + a = sqrt(r*r-b*b) + pc = p0 + a*n + th1 = geom_arg(p1-pc) + th2 = geom_arg(p2-pc) + if(th2Ri+f): + #Scenario2 base circle is outside of inner circle + + + + + theta1 = -thw/2.0 + thetaoff1 = -thw/4.0-thetad+add_sideclearance/Rp + + [phid5,thetad5,rd5] = involute_r(Ro,Rb) + + phid4 = 0; theta4 = thetaoff1; r4 = Rb + theta3 = theta4; r3 = Ri+f + theta2 = theta3 - f/Ri; r2 = Ri + theta5 = thetaoff1+thetad5 + + #theta3 = thetaoff1+thetad3 + #theta2 = theta3 - f/Ri + #theta4 = thetaoff1 + thetad4 + + xy2 = r2*np.float64([cos(theta2),sin(theta2)]) + xy3 = r3*np.float64([cos(theta3),sin(theta3)]) + dxy2 = np.float64([-sin(theta2),cos(theta2)]) + dxy3 = np.float64([cos(theta3),sin(theta3)]) + + xy4 = r4*np.float64([cos(theta4),sin(theta4)]) + + cxy1 = geom_circulararc(Ri,[0,0],theta1,theta2,Npts) + cxy2 = geom_cubicspline(xy2,dxy2,xy3,dxy3,Npts) + cxy3 = np.float64([[xy3[0],xy4[0]],[xy3[1],xy4[1]]]) + cxy4 = geom_involute_left(Rb,[0,0],-thetaoff1,0,phid5,Npts) + cxy5 = geom_circulararc(Ro,[0,0],theta5,-theta5,Npts) + ### reflect + cxy6 = np.copy(cxy4); cxy6[1,:] = -cxy4[1,:] + cxy7 = np.copy(cxy3); cxy7[1,:] = -cxy3[1,:] + cxy8 = np.copy(cxy2); cxy8[1,:] = -cxy2[1,:] + cxy9 = np.copy(cxy1); cxy9[1,:] = -cxy1[1,:] + + prof = geom_join_curve(cxy1,cxy2) + prof = geom_join_curve(prof,cxy3) + prof = geom_join_curve(prof,cxy4) + prof = geom_join_curve(prof,cxy5) + prof = geom_join_curve(prof,cxy6) + prof = geom_join_curve(prof,cxy7) + prof = geom_join_curve(prof,cxy8) + prof = geom_join_curve(prof,cxy9) + + #debug profile + # plt.plot(circp[0,:],circp[1,:],'r--') + # plt.plot(circi[0,:],circi[1,:],'k--') + # plt.plot(circb[0,:],circb[1,:],'b--') + # plt.plot(circo[0,:],circo[1,:],'k--') + + # plt.plot(cxy1[0,:],cxy1[1,:],'r') + # plt.plot(cxy2[0,:],cxy2[1,:],'r') + # plt.plot(cxy3[0,:],cxy3[1,:],'r') + # plt.plot(cxy4[0,:],cxy4[1,:],'r') + # plt.plot(cxy5[0,:],cxy5[1,:],'r') + # plt.plot(cxy6[0,:],cxy6[1,:],'r') + # plt.plot(cxy7[0,:],cxy7[1,:],'r') + # plt.plot(cxy8[0,:],cxy8[1,:],'r') + # plt.plot(cxy9[0,:],cxy9[1,:],'r') + + # plt.plot(prof[0,:],prof[1,:],'g--') + # plt.plot(xy2[0],xy2[1],'rd') + # plt.plot(xy3[0],xy3[1],'rd') + + # plt.axis("equal") + # plt.show() + + + pass + + gearprof = np.copy(prof) + for I in range(0,int(N)-1): + prof = geom_rotate(prof,thw) + #plt.plot(prof[0,:],prof[1,:]) + gearprof = geom_join_curve(gearprof,prof) + + # plt.plot(gearprof[0,:],gearprof[1,:],'k') + # plt.axis("equal") + # plt.show() + + + return [gearprof, gearpars] + +def test_genpitchseries(**kwargs): + diametral_pitch = kwargs["diametral_pitch"] + N = kwargs["N"] + + for I in range(0,len(diametral_pitch)): + for J in range(0,len(N)): + dd = diametral_pitch[I] + NN = N[J] + + [gearprof1, gearpars1] = spurgear_profile(Npts = 30, diametral_pitch=dd, N=NN, phi=20,add_sideclearance=0.003,add_outerclearance=0.003) + gname = "gear_{:d}_{:d}".format(dd,NN) + fname = "{}_v1.scad".format(gname) + save_closedcontour_scad(gearprof1,fname,gname) + + +def test_spurgear_profile(): + + [gearprof1, gearpars1] = spurgear_profile(Npts = 10, diametral_pitch=36, N=72, phi=20,add_sideclearance=0.003,add_outerclearance=0.003) + [gearprof2, gearpars2] = spurgear_profile(Npts = 10, diametral_pitch=36, N=54, phi=20,add_sideclearance=0.003,add_outerclearance=0.003) + + print("Gearpars1:") + print(gearpars1) + print("Gearpars2:") + print(gearpars2) + + off = 0.5*(gearpars1["pitch_diameter"]+gearpars2["pitch_diameter"]) + thw = 2*pi/gearpars2["num_teeth"] + dth = -0.285 + GR = gearpars1["num_teeth"]/gearpars2["num_teeth"] + + gearprof2 = geom_rotate(gearprof2,thw/2.0+dth) + gearprof1 = geom_rotate(gearprof1,-dth/GR) + + save_closedcontour_scad(gearprof1,"gear_36_72_v1.scad","gear_36_72") + save_closedcontour_scad(gearprof2,"gear_36_54_v1.scad","gear_36_54") + + plt.figure(1) + plt.plot(gearprof1[0,:],gearprof1[1,:],'b',linewidth=1) + plt.plot(gearprof1[0,0],gearprof1[1,0],'bo') + plt.plot(gearprof2[0,:]+off,gearprof2[1,:],'r',linewidth=1) + plt.axis("equal") + plt.show() + +## racks + +#Ref Machinery's Handbook,28, pp 2043. +#This references ANSI B6.1-1968 R1974 +def linearrack_ANSI_proportions(**kwargs): + + P = 48 + N = 18 + phi = 20 + + add_clearance = 0.000 + add_outerclearance = 0.000 + add_sideclearance = 0.000 + + if("pressure_angle" in kwargs): + phi = np.float64(kwargs["pressure_angle"]) + if("phi" in kwargs): + phi = np.float64(kwargs["phi"]) + + if("num_teeth" in kwargs): + N = np.float64(np.int32(kwargs["num_teeth"])) + if("N" in kwargs): + N = np.float64(np.int32(kwargs["N"])) + + if("diametral_pitch" in kwargs): + P = np.float64(kwargs["diametral_pitch"]) + Cp = pi/P + if("P" in kwargs): + P = np.float64(kwargs["P"]) + Cp = pi/P + + if("circular_pitch" in kwargs): + Cp = np.float64(kwargs["circular_pitch"]) + P = pi/Cp + if("Cp" in kwargs): + Cp = np.float64(kwargs["Cp"]) + P = pi/Cp + + + a = 1.000/P #addendum + b = 1.200/P + 0.002 #dedendum + c = 0.200/P + 0.002 #clearance + f = 0.300/P #fillet radius + + if("addendum" in kwargs): + a = np.float64(kwargs["addendum"]) + if("dedendum" in kwargs): + b = np.float64(kwargs["dedendum"]) + if("clearance" in kwargs): + c = np.float64(kwargs["clearance"]) + if("fillet_radius" in kwargs): + f = np.float64(kwargs["fillet_radius"]) + if("add_clearance" in kwargs): + add_clearance = np.float64(kwargs["add_clearance"]) + if("add_outerclearance" in kwargs): + add_outerclearance = np.float64(kwargs["add_outerclearance"]) + if("add_sideclearance" in kwargs): + add_sideclearance = np.float64(kwargs["add_sideclearance"]) + + + Ho = a - add_outerclearance + Hi = -b - c - add_clearance + t = Cp/2 - 2*add_sideclearance + + Hb = 1.50*Hi + L = N*Cp + + if("bottom_height" in kwargs): + Hb = np.float64(kwargs["bottom_height"]) + if("Hb" in kwargs): + Hb = np.float64(kwargs["Hb"]) + + rackpars = dict() + + rackpars["pressure_angle"] = phi + rackpars["num_teeth"] = N + rackpars["diametral_pitch"] = P + rackpars["circular_pitch"] = Cp + + rackpars["outer_height"] = Ho + rackpars["pitch_height"] = 0.0 + rackpars["inner_height"] = Hi + rackpars["bottom_height"] = Hb + rackpars["length"] = L + + rackpars["addendum"] = a + rackpars["dedendum"] = b + rackpars["clearance"] = c + rackpars["fillet_radius"] = f + rackpars["tooth_thickness"] = t + rackpars["add_clearance"] = add_clearance + rackpars["add_outerclearance"] = add_outerclearance + rackpars["add_sideclearance"] = add_sideclearance + + return rackpars + +def linearrack_profile(**kwargs): + + rackpars = linearrack_ANSI_proportions(**kwargs) + rackprofile = None + + Npts = 10 + if("Npts" in kwargs): + Npts = kwargs["Npts"] + + phi = rackpars["pressure_angle"] + N = rackpars["num_teeth"] + P = rackpars["diametral_pitch"] + Cp = rackpars["circular_pitch"] + + Ho = rackpars["outer_height"] + Hp = rackpars["pitch_height"] + Hi = rackpars["inner_height"] + Hb = rackpars["bottom_height"] + L = rackpars["length"] + + a = rackpars["addendum"] + b = rackpars["dedendum"] + c = rackpars["clearance"] + f = rackpars["fillet_radius"] + t = rackpars["tooth_thickness"] + add_clearance = rackpars["add_clearance"] + add_outerclearance = rackpars["add_outerclearance"] + add_sideclearance = rackpars["add_sideclearance"] + + x1 = 0 + x2 = Cp/4.0 - add_sideclearance - sin(pi/180*phi)*a + x3 = Cp/4.0 - add_sideclearance + sin(pi/180*phi)*b -sin(pi/180*phi)*f + x4 = Cp/4.0 - add_sideclearance + sin(pi/180*phi)*b + f + x5 = Cp - x4 + x6 = Cp - x3 + x7 = Cp - x2 + x8 = Cp + + y1 = Ho + y2 = Ho + y3 = Hi + cos(pi/180*phi)*f + y4 = Hi + y5 = y4 + y6 = y3 + y7 = y2 + y8 = y1 + + d3 = np.float64([x3-x2,y3-y2]) + d6 = np.float64([x7-x6,y7-y6]) + + cxy1 = geom_lineseg([x1,y1],[x2,y2]) + cxy2 = geom_lineseg([x2,y2],[x3,y3]) + cxy3 = geom_cubicspline(np.float64([x3,y3]),d3,np.float64([x4,y4]),np.float64([1,0]),Npts) + cxy4 = geom_lineseg([x4,y4],[x5,y5]) + cxy5 = geom_cubicspline([x5,y5],[1,0],[x6,y6],d6,Npts) + cxy6 = geom_lineseg([x6,y6],[x7,y7]) + cxy7 = geom_lineseg([x7,y7],[x8,y8]) + + prof = np.copy(cxy1) + prof = geom_join_curve(prof,cxy2) + prof = geom_join_curve(prof,cxy3) + prof = geom_join_curve(prof,cxy4) + prof = geom_join_curve(prof,cxy5) + prof = geom_join_curve(prof,cxy6) + prof = geom_join_curve(prof,cxy7) + + rackprofile = np.copy(prof) + for I in range(0,int(N)-1): + prof = geom_translate(prof,[Cp,0]) + rackprofile = geom_join_curve(rackprofile,prof) + + bxy0 = geom_lineseg([0,Ho],[0,Hb]) + bxy1 = geom_lineseg([L,Ho],[L,Hb]) + bxy2 = geom_lineseg([0,Hb],[L,Hb]) + + rackprofile = geom_join_curve(rackprofile,bxy0) + rackprofile = geom_join_curve(rackprofile,bxy1) + rackprofile = geom_join_curve(rackprofile,bxy2) + + rackprofile = geom_closecontour(rackprofile) + + return [rackprofile,kwargs] + +def test_linearrack_profile(): + + [rackprofile, rackpars] = linearrack_profile(diametral_pitch=36,N=10,phi=20,Hb=-0.25) + print(rackpars) + save_closedcontour_scad(rackprofile,"rack36.scad","rack36") + + return + +def save_closedcontour_scad(contour, fname, modulename="mycontour"): + + try: + fp = open(fname,"w+") + except: + printf("{} could not be opened for writing.\n".format(fname)) + return + + contour = np.float64(contour) + + fp.writelines("// openscad\n\n") + fp.writelines("module {}()\n".format(modulename)) + fp.writelines("{\n") + + N = contour.shape[1] + + fp.writelines("pts = [") + for I in range(0,N): + if(I>/Metadata 2 0 R/Pages 3 0 R/StructTreeRoot 5 0 R/Type/Catalog>> endobj 2 0 obj <>stream + + + + + 2021-07-22T08:26:49-05:00 + 2021-07-22T08:26:49-05:00 + 2021-07-22T08:26:49-05:00 + Adobe InDesign 16.3 (Windows) + application/pdf + uuid:5f9f843e-5d52-4084-9cb7-b33493035754 + uuid:54d6d1fd-2167-4e17-a6d6-c708593ce025 + Adobe PDF Library 15.0 + False + + + + + + + + + + + + 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