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double-universal-joint.py
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from madcad import *
from madcad.joints import *
from itertools import accumulate
settings.resolution = ('rad', 0.1)
# profile separating the bottom and top part allowing them to move around each other and using the maximum volume for the part robustness
def cardan_sphereprofile(maxangle=0.5):
s = icosphere(O, 1)
d = vec3(cos(maxangle), 0, sin(maxangle))
a = normalize(d+1*Y)
return wire([
ArcCentered(Axis(O, d*vec3(-1,1,1)), a*vec3(-1,-1,1), a*vec3(-1,1,1)),
ArcCentered(Axis(O, -Y), a*vec3(-1,1,1), a),
ArcCentered(Axis(O, d), a, a*vec3(1,-1,1)),
ArcCentered(Axis(O, Y), a*vec3(1,-1,1), a*vec3(-1,-1,1)),
])
# generate a side of the universal joint
def cardan_side(rint, rext, rtop, thickness, height):
margin = 0.1*rint
profile = cardan_sphereprofile(0.5) .transform(rext*thickness*0.95)
body = union(
icosphere(O, rext),
revolution(wire([
Softened([
vec3(rext*0.9, 0, height*0.2),
vec3(rext*0.6, 0, height*0.4),
vec3(rtop*1.5, 0, height*0.7),
vec3(rtop*1.5, 0, height-0.5*rtop)]),
Wire([
vec3(rtop*1.5, 0, height-0.5*rtop),
vec3(rtop*1.1, 0, height),
vec3(rtop, 0, height),
vec3(rtop, 0, height*0.55),
vec3(0, 0, height*0.55),
]).segmented(),
])) .flip() .qualify('junction'),
)
body.mergeclose()
shape = intersection(
inflate(extrusion(profile.flip(), mat3(5)), -margin),
body + icosphere(O, thickness*rext).flip(),
)
rscrew = stfloor(0.6*rtop)/2
pocket = extrusion(flatsurface(convexoutline(web([
Circle(Axis(vec3(0, rtop*1.8, rext*thickness + 2*rscrew), Y), 2.7*rscrew),
Segment(
vec3(+rtop, rtop*1.5, height),
vec3(-rtop, rtop*1.5, height)),
]))), rext*Y).orient()
pocket = union(pocket,
extrusion(
flatsurface(Circle(Axis(vec3(0, rtop*1.35, height - 1.5*rtop), -Y), 2.7*rscrew)),
rtop*Y))
removal = union(
pocket + pocket.transform(scaledir(Y, -1)).flip(),
( cylinder(
vec3(0, rext, rext*thickness + 2*rscrew),
vec3(0, -rext, rext*thickness + 2*rscrew),
rscrew*1.2)
+ cylinder(
vec3(0, rext, height - 1.5*rtop),
vec3(0, -rext, height - 1.5*rtop),
rscrew*1.2)
).qualify('hole'),
)
shape = difference(shape, removal)
hole = revolution(wire([
vec3(rint+0.1*rext, rext, 0),
vec3(rint, rext-rint*0.3, 0),
vec3(rint, 0, 0),
]).segmented().flip(), Axis(O,Y)) .qualify('axis', 'joint')
result = intersection(
shape,
hole + hole.transform(scaledir(Y,-1)).flip(),
)
result = result.finish()
sep = square((O+1e-5*Y,Y), rext*5)
return Solid(
right = difference(result, sep),
left = intersection(result, sep),
b1 = bolt(
vec3(0, rtop*1.8, rext*thickness + 2*rscrew),
vec3(0, -rtop*1.8, rext*thickness + 2*rscrew),
rscrew),
b3 = bolt(
vec3(0, rtop*1.3, height - 1.5*rtop),
vec3(0, -rtop*1.3, height - 1.5*rtop),
rscrew),
annotations = [
note_radius(result.group('axis')),
note_radius(result.group('hole')),
],
)
# just like madcad.standard.bolt but with annotations added
def bolt(a, b, radius, washera=False, washerb=False):
dir = normalize(b-a)
rwasher = washer(2*radius)
thickness = rwasher['part'].box().width.z
rscrew = screw(radius*2, distance(a,b) + 3*radius)
rnut = nut(radius*2)
return Solid(
screw = rscrew.place((Revolute, rscrew['axis'], Axis(a-thickness*dir, -dir))),
nut = rnut.place((Revolute, rnut['top'], Axis(b+thickness*dir, -dir))),
w1 = rwasher.place((Revolute, rwasher['top'], Axis(b, -dir))),
w2 = rwasher.place((Revolute, rwasher['top'], Axis(a, dir))),
)
# central part of the universal joint
def moyeu(brext, rext, thickness, brint=None, slot=False):
if not brint:
brint = brext - stceil(1/8*brext)
xint = sqrt((thickness*rext)**2 - brext**2)
profile = Wire([
(rext - 0.2*brext)*X,
(rext - 0.2*brext)*X + 0.99*brint*Z,
xint*X - 0.2*brext*X + 0.99*brint*Z,
xint*X - 0.2*brext*X + 1.1*brext*Z,
xint*X - 0.3*brext*X + 1.1*brext*Z
]) .segmented()
profile.qualify('axis', select=1)
chamfer(profile, [1], radius=0.1*brext)
tip = revolution(profile, Axis(O,X))
tip.finish()
if slot:
tip = difference(tip, union(
brick(vec3(xint-0.15*rint, -0.1*rint, 0.1*rint), vec3(rext, 0.1*rint, 2*rint)),
brick(vec3(xint-0.1*rint, -rint, 0.5*rint), vec3(rext*2, rint, 2*rint)),
))
tubes = repeat(tip, 4, rotatearound(pi/2, Axis(O,Z)))
moyeu = tubes + junction(
tubes.flip(),
tangents='tangent', weight=-1,
)
moyeu
bearing = slidebearing(
dint = 2*brint,
thickness = brext-brint,
h = stceil((1-thickness)*rext + 0.2*rint),
) .transform(translate((rext - 0.2*rint)*X) * rotate(pi/2,Y))
return Solid(
part = moyeu,
bearings = [
bearing.transform(rotate(i*pi/2, Z))
for i in range(4)
],
annotations = [
note_radius(moyeu.group('axis').islands()[0]),
],
)
# generate the parts
rint = 16/2
rext = 40/2
thickness = 0.7
side = cardan_side(rint*1.02, rext, rext*0.25, thickness, rext*2)
lower = side.transform(rotate(pi/2,Z) * rotate(pi,Y) * rotate(0.5,X))
upper = side.transform(translate(2*rext*Z) * rotate(pi/2,Z) * rotate(0.5,X))
central = moyeu(rint, rext, thickness)
central_lower = central.transform(rotate(-0.5,Y))
central_upper = central.transform(translate(2*rext*Z) * rotate(0.5,Y))
# TODO allow it to move with a kinematic
# add visual annotations
part = central['bearings'][0]['part']
islands = part.group(2).islands()
central['bearings'][0]['annotations'] = [
note_radius(part.group(1)),
note_radius(part.group(0)),
note_distance_planes(islands[0], islands[1]),
]
# display the result
#show([upper, lower, central])
# generate a side of the universal joint
def cardan_middle(rint, rext, rtop, thickness, height):
margin = 0.1*rint
profile = cardan_sphereprofile(0.45) .transform(rext*thickness*0.95)
body = union(
icosphere(O, rext) + icosphere(O + 2*rext*Z, rext),
revolution(wire([
Softened([
vec3(rext*0.9, 0, height*0.2),
vec3(rext*0.6, 0, height*0.4),
vec3(rext*0.6, 0, 2*rext - height*0.4),
vec3(rext*0.9, 0, 2*rext - height*0.2)]),
])) .flip() .qualify('junction'),
)
body.mergeclose()
shape = intersection(
intersection(
inflate(extrusion(profile.flip(), mat3(5)), -margin),
inflate(extrusion(profile, mat3(5)).transform(scaledir(Z, -1)).transform(2*rext*Z), -margin),
),
body + icosphere(O, thickness*rext).flip() + icosphere(O + 2*rext*Z, thickness*rext).flip(),
)
rscrew = stfloor(0.6*rtop)/2
removal = bolt_slot(
vec3(0, 0.5*rext, rext),
vec3(0, -0.5*rext, rext),
2*rscrew*1.2).flip()
shape = difference(shape, removal)
hole = revolution(wire([
vec3(rint+0.1*rext, rext, 0),
vec3(rint, rext-rint*0.3, 0),
vec3(rint, 0, 0),
]).segmented().flip(), Axis(O,Y)) .qualify('axis', 'joint')
result = intersection(
shape,
hole + hole.transform(scaledir(Y,-1)).flip()
+ hole.transform(translate(2*rext*Z)) + hole.transform(translate(2*rext*Z) * mat4(scaledir(Y,-1))).flip(),
)
result = result.finish()
sep = square((O+1e-5*Y,Y), rext*5)
return Solid(
right = difference(result, sep),
left = intersection(result, sep),
b1 = bolt(
vec3(0, 0.5*rext, rext),
vec3(0, -0.5*rext, rext),
rscrew),
)
middle = cardan_middle(rint*1.02, rext, rext*0.25, thickness, rext*2)