432 lines
14 KiB
Python
432 lines
14 KiB
Python
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from dataclasses import dataclass, field
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from typing import Optional
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import math
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import cadquery as Cq
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from nhf.parts.springs import TorsionSpring
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from nhf import Role
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import nhf.utils
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TOL = 1e-6
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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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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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@property
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def tooth_angle(self):
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return 360 / self.n_tooth
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@property
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def total_height(self):
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return self.base_height + self.tooth_height
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@property
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def joint_height(self):
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return 2 * self.base_height + self.tooth_height
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def generate(self, 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: Mate is not exact when number of tooth is low
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"""
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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([
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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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.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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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("bore")
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.cut(core)
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.polarArray(
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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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.cutEach(
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lambda loc: profile.moved(loc),
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)
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)
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(
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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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], forConstruction=True)
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.tag("mate")
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)
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(
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result
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.polyline([(0, 0, 0), (1, 0, 0)], forConstruction=True)
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.tag("dirX")
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)
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(
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result
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.polyline([(0, 0, 0), (0, 1, 0)], forConstruction=True)
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.tag("dirY")
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)
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return result
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def add_constraints(self,
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assembly: Cq.Assembly,
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parent: str,
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child: str,
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offset: int = 0):
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angle = offset * self.tooth_angle
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(
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assembly
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.constrain(f"{parent}?mate", f"{child}?mate", "Plane")
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.constrain(f"{parent}?dirX", f"{child}?dirX",
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"Axis", param=angle)
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.constrain(f"{parent}?dirY", f"{child}?dirX",
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"Axis", param=90 - angle)
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)
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def assembly(self, offset: int = 1):
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"""
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Generate an example assembly
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"""
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tab = (
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Cq.Workplane('XY')
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.box(100, 10, 2, centered=False)
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)
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obj1 = (
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self.generate()
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.faces(tag="bore")
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.cboreHole(
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diameter=10,
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cboreDiameter=20,
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cboreDepth=3)
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.union(tab)
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)
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obj2 = (
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self.generate(is_mated=True)
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.union(tab)
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)
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result = (
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Cq.Assembly()
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.addS(obj1, name="obj1", role=Role.PARENT)
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.addS(obj2, name="obj2", role=Role.CHILD)
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)
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self.add_constraints(
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result,
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parent="obj1",
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child="obj2",
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offset=offset)
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return result.solve()
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@dataclass
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class TorsionJoint:
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"""
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This jonit consists of a rider puck on a track puck. IT is best suited if
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the radius has to be small and vertical space is abundant.
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The rider part consists of:
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1. A cylinderical base
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2. A annular extrusion with the same radius as the base, but with slots
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carved in
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3. An annular rider
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The track part consists of:
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1. A cylindrical base
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2. A slotted annular extrusion where the slot allows the spring to rest
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3. An outer and an inner annuli which forms a track the rider can move on
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"""
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spring: TorsionSpring = field(default_factory=lambda: TorsionSpring(
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mass=float('nan'),
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radius=10.0,
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thickness=2.0,
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height=15.0,
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tail_length=35.0,
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right_handed=False,
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))
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# Radius limit for rotating components
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radius_track: float = 40
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radius_rider: float = 38
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track_disk_height: float = 10
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rider_disk_height: float = 8
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radius_axle: float = 6
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# If true, cover the spring hole. May make it difficult to insert the spring
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# considering the stiffness of torsion spring steel.
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spring_hole_cover_track: bool = False
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spring_hole_cover_rider: bool = False
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groove_radius_outer: float = 35
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groove_radius_inner: float = 20
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# Gap on inner groove to ease movement
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groove_inner_gap: float = 0.2
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groove_depth: float = 5
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rider_gap: float = 1
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rider_n_slots: float = 4
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# Degrees of the first and last rider slots
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rider_slot_begin: float = 0
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rider_slot_span: float = 90
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def __post_init__(self):
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assert self.radius_track > self.groove_radius_outer
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assert self.radius_rider > self.groove_radius_outer > self.groove_radius_inner + self.groove_inner_gap
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assert self.groove_radius_inner > self.spring.radius > self.radius_axle
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assert self.spring.height > self.groove_depth, "Groove is too deep"
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assert self.groove_depth < self.spring.height - self.spring.thickness * 2
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if self.rider_n_slots == 1:
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assert self.rider_slot_span == 0.0, "Non-zero span is impossible with multiple riders"
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@property
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def total_height(self):
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"""
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Total height counting from bottom to top
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"""
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return self.track_disk_height + self.rider_disk_height + self.spring.height
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@property
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def radius(self):
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"""
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Maximum radius of this joint
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"""
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return max(self.radius_rider, self.radius_track)
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def _slot_polygon(self, flip: bool=False):
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r1 = self.spring.radius_inner
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r2 = self.spring.radius
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flip = flip != self.spring.right_handed
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if flip:
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r1 = -r1
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r2 = -r2
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return [
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(0, r2),
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(self.spring.tail_length, r2),
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(self.spring.tail_length, r1),
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(0, r1),
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]
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def _directrix(self, height, theta=0):
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c, s = math.cos(theta), math.sin(theta)
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r2 = self.spring.radius
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l = self.spring.tail_length
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if self.spring.right_handed:
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r2 = -r2
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# This is (0, r2) and (l, r2) transformed by right handed rotation
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# matrix `[[c, -s], [s, c]]`
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return [
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(-s * r2, c * r2, height),
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(c * l - s * r2, s * l + c * r2, height),
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]
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def track(self):
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# TODO: Cover outer part of track only. Can we do this?
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groove_profile = (
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Cq.Sketch()
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.circle(self.radius_track)
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.circle(self.groove_radius_outer, mode='s')
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.circle(self.groove_radius_inner, mode='a')
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.circle(self.spring.radius, mode='s')
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)
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spring_hole_profile = (
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Cq.Sketch()
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.circle(self.radius_track)
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.circle(self.spring.radius, mode='s')
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)
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slot_height = self.spring.thickness
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if not self.spring_hole_cover_track:
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slot_height += self.groove_depth
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slot = (
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Cq.Workplane('XY')
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.sketch()
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.polygon(self._slot_polygon(flip=False))
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.finalize()
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.extrude(slot_height)
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.val()
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)
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result = (
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Cq.Workplane('XY')
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.cylinder(
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radius=self.radius_track,
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height=self.track_disk_height,
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centered=(True, True, False))
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.faces('>Z')
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.tag("spring")
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.placeSketch(spring_hole_profile)
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.extrude(self.spring.thickness)
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# If the spring hole profile is not simply connected, this workplane
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# will have to be created from the `spring-mate` face.
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.faces('>Z')
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.placeSketch(groove_profile)
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.extrude(self.groove_depth)
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.faces('>Z')
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.hole(self.radius_axle * 2)
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.cut(slot.moved(Cq.Location((0, 0, self.track_disk_height))))
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)
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result.faces("<Z").tag("bot")
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# Insert directrix
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result.polyline(self._directrix(self.track_disk_height),
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forConstruction=True).tag("dir")
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return result
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def rider(self, rider_slot_begin=None, reverse_directrix_label=False):
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if not rider_slot_begin:
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rider_slot_begin = self.rider_slot_begin
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def slot(loc):
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wire = Cq.Wire.makePolygon(self._slot_polygon(flip=False))
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face = Cq.Face.makeFromWires(wire)
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return face.located(loc)
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wall_profile = (
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Cq.Sketch()
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.circle(self.radius_rider, mode='a')
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.circle(self.spring.radius, mode='s')
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.parray(
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r=0,
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a1=rider_slot_begin,
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da=self.rider_slot_span,
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n=self.rider_n_slots)
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.each(slot, mode='s')
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#.circle(self._radius_wall, mode='a')
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)
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contact_profile = (
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Cq.Sketch()
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.circle(self.groove_radius_outer, mode='a')
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.circle(self.groove_radius_inner + self.groove_inner_gap, mode='s')
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)
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if not self.spring_hole_cover_rider:
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contact_profile = (
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contact_profile
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.parray(
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r=0,
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a1=rider_slot_begin,
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da=self.rider_slot_span,
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n=self.rider_n_slots)
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.each(slot, mode='s')
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.reset()
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)
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#.circle(self._radius_wall, mode='a')
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middle_height = self.spring.height - self.groove_depth - self.rider_gap - self.spring.thickness
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result = (
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Cq.Workplane('XY')
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.cylinder(
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radius=self.radius_rider,
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height=self.rider_disk_height,
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centered=(True, True, False))
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.faces('>Z')
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.tag("spring")
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.workplane()
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.placeSketch(wall_profile)
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.extrude(middle_height)
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.faces(tag="spring")
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.workplane()
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# The top face might not be in one piece.
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.workplane(offset=middle_height)
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.placeSketch(contact_profile)
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.extrude(self.groove_depth + self.rider_gap)
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.faces(tag="spring")
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.workplane()
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.circle(self.spring.radius_inner)
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.extrude(self.spring.height)
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.faces("<Z")
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.workplane()
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.hole(self.radius_axle * 2)
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)
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|
|
theta_begin = -math.radians(rider_slot_begin)
|
||
|
|
theta_span = math.radians(self.rider_slot_span)
|
||
|
|
if self.rider_n_slots <= 1:
|
||
|
|
theta_step = 0
|
||
|
|
elif abs(math.remainder(self.rider_slot_span, 360)) < TOL:
|
||
|
|
theta_step = theta_span / self.rider_n_slots
|
||
|
|
else:
|
||
|
|
theta_step = theta_span / (self.rider_n_slots - 1)
|
||
|
|
for i in range(self.rider_n_slots):
|
||
|
|
theta = theta_begin - i * theta_step
|
||
|
|
j = self.rider_n_slots - i - 1 if reverse_directrix_label else i
|
||
|
|
result.polyline(self._directrix(self.rider_disk_height, theta),
|
||
|
|
forConstruction=True).tag(f"dir{j}")
|
||
|
|
return result
|
||
|
|
|
||
|
|
def rider_track_assembly(self, directrix: int = 0, deflection: float = 0):
|
||
|
|
rider = self.rider()
|
||
|
|
track = self.track()
|
||
|
|
spring = self.spring.assembly(deflection=deflection)
|
||
|
|
result = (
|
||
|
|
Cq.Assembly()
|
||
|
|
.addS(spring, name="spring", role=Role.DAMPING)
|
||
|
|
.addS(track, name="track", role=Role.PARENT)
|
||
|
|
.addS(rider, name="rider", role=Role.CHILD)
|
||
|
|
)
|
||
|
|
TorsionJoint.add_constraints(
|
||
|
|
result,
|
||
|
|
rider="rider", track="track", spring="spring",
|
||
|
|
directrix=directrix)
|
||
|
|
return result.solve()
|
||
|
|
|
||
|
|
@staticmethod
|
||
|
|
def add_constraints(assembly: Cq.Assembly,
|
||
|
|
spring: str,
|
||
|
|
rider: Optional[str] = None,
|
||
|
|
track: Optional[str] = None,
|
||
|
|
directrix: int = 0):
|
||
|
|
"""
|
||
|
|
Add the necessary constraints to a RT assembly
|
||
|
|
"""
|
||
|
|
if track:
|
||
|
|
(
|
||
|
|
assembly
|
||
|
|
.constrain(f"{track}?spring", f"{spring}?top", "Plane")
|
||
|
|
.constrain(f"{track}?dir", f"{spring}?dir_top",
|
||
|
|
"Axis", param=0)
|
||
|
|
)
|
||
|
|
if rider:
|
||
|
|
(
|
||
|
|
assembly
|
||
|
|
.constrain(f"{rider}?spring", f"{spring}?bot", "Plane")
|
||
|
|
.constrain(f"{rider}?dir{directrix}", f"{spring}?dir_bot",
|
||
|
|
"Axis", param=0)
|
||
|
|
)
|