fix: Hirth joint mating
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132
nhf/joints.py
132
nhf/joints.py
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@ -4,126 +4,86 @@ import cadquery as Cq
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import nhf.springs as NS
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from nhf import Role
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def hirth_tooth_angle(n_tooth):
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"""
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Angle of one whole tooth
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"""
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return 360 / n_tooth
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@dataclass(frozen=True)
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class HirthJoint:
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"""
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A Hirth joint attached to a cylindrical base
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"""
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# r
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radius: float = 60
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# r_i
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radius_inner: float = 40
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base_height: float = 20
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n_tooth: float = 16
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# h_o
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tooth_height: float = 16
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tooth_height_inner: float = 2
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def __post_init__(self):
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# Ensures tangent doesn't blow up
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assert self.n_tooth >= 5
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assert self.radius > self.radius_inner
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assert self.tooth_height >= self.tooth_height_inner
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@property
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def _theta(self):
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return math.pi / self.n_tooth
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@property
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def tooth_angle(self):
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return hirth_tooth_angle(self.n_tooth)
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return 360 / self.n_tooth
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def generate(self, tag_prefix="", is_mated=False, tol=0.01):
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"""
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is_mated: If set to true, rotate the teeth so they line up at 0 degrees.
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FIXME: The curves don't mate perfectly. See if non-planar lofts can solve
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this issue.
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FIXME: Mate is not exact when number of tooth is low
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"""
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c, s, t = math.cos(self._theta), math.sin(self._theta), math.tan(self._theta)
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span = self.radius * t
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radius_proj = self.radius / c
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span_inner = self.radius_inner * s
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# 2 * raise + (inner tooth height) = (tooth height)
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inner_raise = (self.tooth_height - self.tooth_height_inner) / 2
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# Outer tooth triangle spans 2*theta radians. This profile is the radial
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# profile projected onto a plane `radius` away from the centre of the
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# cylinder. The y coordinates on the edge must drop to compensate.
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# The drop is equal to, via similar triangles
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drop = inner_raise * (radius_proj - self.radius) / (self.radius - self.radius_inner)
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outer = [
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(span, -tol - drop),
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(span, -drop),
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(0, self.tooth_height),
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(-span, -drop),
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(-span, -tol - drop),
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]
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adj = self.radius_inner * c
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# In the case of the inner triangle, it is projected onto a plane `adj` away
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# from the centre. The apex must extrapolate
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# Via similar triangles
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#
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# (inner_raise + tooth_height_inner) -
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# (tooth_height - inner_raise - tooth_height_inner) * ((radius_inner - adj) / (radius - radius_inner))
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apex = (inner_raise + self.tooth_height_inner) - \
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inner_raise * (self.radius_inner - adj) / (self.radius - self.radius_inner)
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inner = [
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(span_inner, -tol),
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(span_inner, inner_raise),
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(0, apex),
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(-span_inner, inner_raise),
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(-span_inner, -tol),
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]
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tooth = (
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phi = math.radians(self.tooth_angle)
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alpha = 2 * math.atan(self.radius / self.tooth_height * math.tan(phi/2))
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#alpha = math.atan(self.radius * math.radians(180 / self.n_tooth) / self.tooth_height)
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gamma = math.radians(90 / self.n_tooth)
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# Tooth half height
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l = self.radius * math.cos(gamma)
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a = self.radius * math.sin(gamma)
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t = a / math.tan(alpha / 2)
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beta = math.asin(t / l)
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dx = self.tooth_height * math.tan(alpha / 2)
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profile = (
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Cq.Workplane('YZ')
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.polyline(inner)
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.polyline([
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(0, 0),
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(dx, self.tooth_height),
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(-dx, self.tooth_height),
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])
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.close()
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.workplane(offset=self.radius - adj)
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.polyline(outer)
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.close()
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.loft(ruled=False, combine=True)
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.extrude(-self.radius)
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.val()
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.rotate((0, 0, 0), (0, 1, 0), math.degrees(beta))
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.moved(Cq.Location((0, 0, self.base_height)))
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)
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angle_offset = hirth_tooth_angle(self.n_tooth) / 2 if is_mated else 0
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h = self.base_height + self.tooth_height
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teeth = (
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core = Cq.Solid.makeCylinder(
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radius=self.radius_inner,
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height=self.tooth_height,
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pnt=(0, 0, self.base_height),
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)
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angle_offset = self.tooth_angle / 2 if is_mated else 0
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result = (
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Cq.Workplane('XY')
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.cylinder(
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radius=self.radius,
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height=self.base_height + self.tooth_height,
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centered=(True, True, False))
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.faces(">Z")
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.tag(f"{tag_prefix}bore")
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.cut(core)
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.polarArray(
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radius=adj,
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radius=self.radius,
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startAngle=angle_offset,
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angle=360,
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count=self.n_tooth)
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.eachpoint(lambda loc: tooth.located(loc))
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.intersect(Cq.Solid.makeCylinder(
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height=h,
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radius=self.radius,
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))
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.cut(Cq.Solid.makeCylinder(
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height=h,
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radius=self.radius_inner,
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))
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.cutEach(
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lambda loc: profile.moved(loc),
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)
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)
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base = (
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Cq.Workplane('XY')
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.cylinder(
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height=self.base_height,
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radius=self.radius,
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centered=(True, True, False))
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.faces(">Z").tag(f"{tag_prefix}bore")
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.union(
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teeth.val().move(Cq.Location((0,0,self.base_height))),
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tol=tol)
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.clean()
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)
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#base.workplane(offset=tooth_height/2).circle(radius=radius,forConstruction=True).tag("mate")
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(
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base
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result
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.polyline([
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(0, 0, self.base_height),
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(0, 0, self.base_height + self.tooth_height)
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@ -131,11 +91,11 @@ class HirthJoint:
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.tag(f"{tag_prefix}mate")
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)
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(
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base
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result
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.polyline([(0, 0, 0), (1, 0, 0)], forConstruction=True)
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.tag(f"{tag_prefix}directrix")
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)
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return base
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return result
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def assembly(self):
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"""
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13
nhf/test.py
13
nhf/test.py
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@ -13,12 +13,15 @@ class TestJoints(unittest.TestCase):
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self.assertIsInstance(
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obj.val().solids(), Cq.Solid,
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msg="Hirth joint must be in one piece")
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def test_joints_hirth_assembly(self):
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j = nhf.joints.HirthJoint()
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assembly = j.assembly()
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isect = binary_intersection(assembly)
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self.assertLess(isect.Volume(), 1e-6,
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"Hirth joint assembly must not have intersection")
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for n_tooth in [16, 20, 24]:
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with self.subTest(n_tooth=n_tooth):
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j = nhf.joints.HirthJoint()
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assembly = j.assembly()
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isect = binary_intersection(assembly)
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self.assertLess(isect.Volume(), 1e-6,
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"Hirth joint assembly must not have intersection")
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def test_joints_comma_assembly(self):
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nhf.joints.comma_assembly()
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def test_torsion_joint(self):
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