# No. 205 (Brown 1868): "Represents a wheel driven by a pinion of two teeth. The pinion consists in reality of two cams, which gear with two distinct series of teeth on opposite sides of the wheel, the teeth of one series alternating in position with those of the other."
#
# Model (cm; drawing plane x-z, shafts along y): the wheel carries two rows of 14 pins standing out of its two faces on a circle of radius 10, the back
# row midway between the front. Below it the pinion's shaft carries two one-lobed cams, the front one in the plane of the front pins and the back one,
# half a turn round, in the plane of the back pins. Each cam's outline is the largest the pins leave free when wheel and pinion turn together at
# 0.714 : 10 (one pin of a row per pinion turn), less 0.05 clearance, kept to a 200-degree lobe and cut to the hub elsewhere. So the
# front cam drives the front row for part of a turn, then the back cam the back row, and between them the wheel goes round continuously, a pin's pitch of
# a row (1/14 turn) per pinion turn. Only the pinion is driven (30 rpm). Generator: opencode-runs/batch11/gen205.py.
number: 205
slug: two-tooth-pinion
name: A wheel driven by a pinion of two teeth
brown: "Represents a wheel driven by a pinion of two teeth. The pinion consists in reality of two cams, which gear with two distinct series of teeth on opposite sides of the wheel, the teeth of one series alternating in position with those of the other."
units: cm
sim:
  timestep: 0.0002
  integrator: implicitfast
  iterations: 100
  solver: CG
  multiccd: true
  duration_s: 8.0
  floor: false
bodies:
  - id: wheel
    shape: part
    pos: [0, 0, 10.7143]
    density: 2700
    friction: 0.1
    color: "#e4d9bf"
    pieces:
      - {kind: disc, center: [0, 10.7143], radius: 9.1, y: [-0.3, 0.3], collide: 0}   # the wheel
      - {kind: disc, center: [0, 10.7143], radius: 1.2, y: [-0.8, 0.8], collide: 0, color: "#8f8a80"}   # its hub
      - {kind: disc, center: [0.0, 0.7143], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [4.3388, 1.7046], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [7.8183, 4.4794], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [9.7493, 8.4891], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [9.7493, 12.9395], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [7.8183, 16.9492], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [4.3388, 19.724], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [0.0, 20.7143], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [-4.3388, 19.724], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [-7.8183, 16.9492], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [-9.7493, 12.9395], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [-9.7493, 8.4891], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [-7.8183, 4.4794], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [-4.3388, 1.7046], radius: 0.4, y: [-1.4, 0.0], collide: 1}
      - {kind: disc, center: [2.2252, 0.965], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [6.2349, 2.896], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [9.0097, 6.3754], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [10.0, 10.7143], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [9.0097, 15.0531], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [6.2349, 18.5326], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [2.2252, 20.4636], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [-2.2252, 20.4636], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [-6.2349, 18.5326], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [-9.0097, 15.0531], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [-10.0, 10.7143], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [-9.0097, 6.3754], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [-6.2349, 2.896], radius: 0.4, y: [0.0, 1.4], collide: 1}
      - {kind: disc, center: [-2.2252, 0.965], radius: 0.4, y: [0.0, 1.4], collide: 1}
  - id: pinion
    shape: part
    pos: [0, 0, 0]
    density: 7800
    friction: 0.1
    color: "#c9b88f"
    pieces:
      - {kind: disc, center: [0, 0], radius: 0.5, y: [-3.0, -1.5], collide: 0, color: "#8f8a80"}   # the shaft, outside the cams
      - {kind: disc, center: [0, 0], radius: 0.5, y: [1.5, 3.0], collide: 0, color: "#8f8a80"}
      - {kind: disc, center: [0, 0], radius: 4.0, inner: 3.2, y: [3.6, 4.4], collide: 0, color: "#8f8a80"}   # a fly-wheel on the shaft, behind
      - {kind: disc, center: [0, 0], radius: 0.5, y: [3.0, 4.6], collide: 0, color: "#8f8a80"}
      - {kind: disc, center: [0, 0], radius: 0.28, y: [-1.5, 1.5], collide: 0, color: "#8f8a80"}   # and between them, slim where the pins pass
      - {kind: poly, points: [[0.0, 0.0], [1.6323, 0.0], [1.6253, 0.0142]], y: [-1.3, -0.5], collide: 2}
      - {kind: poly, points: [[0.0, 0.0], [1.6253, 0.0142], [1.6183, 0.0282]], y: [-1.3, -0.5], collide: 2}
      - {kind: poly, points: [[0.0, 0.0], [1.6183, 0.0282], [1.611, 0.0422]], y: [-1.3, -0.5], collide: 2}
      - {kind: poly, points: [[0.0, 0.0], [1.611, 0.0422], [1.6037, 0.056]], y: [-1.3, -0.5], collide: 2}
      - {kind: poly, points: [[0.0, 0.0], [1.6037, 0.056], [1.5962, 0.0697]], y: [-1.3, -0.5], collide: 2}
      - {kind: poly, points: [[0.0, 0.0], [1.5962, 0.0697], [1.5886, 0.0833]], y: [-1.3, -0.5], collide: 2}
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  - id: frame
    shape: frame
    color: "#8f8a80"
    rods:
      - {from: [0, -2.2, 10.7143], to: [0, 2.2, 10.7143], radius: 0.5}
      - {from: [0, 4.6, 0], to: [0, 5.6, 0], radius: 0.8}
joints:
  - {id: j_pinion, type: hinge, body: pinion, axis: [0, -1, 0], damping: 0.001}   # the one driven joint; +: counter-clockwise
  - {id: j_wheel, type: hinge, body: wheel, axis: [0, -1, 0], damping: 0.02, frictionloss: 0.05}   # a load: the wheel stops whenever no cam pushes it
contact: {solref: [0.002, 1.0], solimp: [0.95, 0.99, 0.0005], margin: 0}
driver: {joint: j_pinion, kind: velocity, rpm: 30, kv: 0.3, max_torque: 5}
checks:
  - {type: ratio, out: j_wheel, in: j_pinion, expect: -0.07143, tol: 0.00214, settle_s: 1, window_s: 6}
  - {type: penetration, max: 0.001, settle_s: 0.5}
camera: {target: [0, 0, 6.3571], position: [-14, -70, 9.3571], fov: 34}
display:
  output: j_wheel
  labels: {j_pinion: "Two-toothed pinion (driver)", j_wheel: "Wheel (14 pins a side)"}
  proof: {label: "Cams out of contact", sub: "the pinion turns alone: the wheel stands"}