# No. 224 (Brown 1868): "This represents an expanding pulley. On turning pinion, d, to the right or left, a similar motion is imparted to wheel, c, which, by means of
# curved slots cut therein, thrusts the studs fastened to arms of pulley outward or inward, thus augmenting or diminishing the size of the pulley."
#
# Model (cm; the pulley's face in the x-z plane, gravity on): the pulley's hub and its four radial spokes and guides are the frame (the pulley is held still while it is set).
# Wheel c (32 teeth, module 0.5) turns loosely on the hub and has four curved slots, the spirals r = 4.6 + 1.79 (theta - phi) over +-48 degrees about each arm,
# so its studs move 1.79 cm out or in for each radian c turns. Pinion d (10 teeth), its axle in the frame between two arms, gears with c. Each of the four arms slides
# in its guides and carries a stud in one of c's slots and a segment of the pulley's rim. A hand rocks pinion d to the right and left (2 rad either way), the only driven joint;
# so c turns 0.625 rad either way and the arms move 1.12 cm out and in, together (kinematics: 0.5594 cm per radian of d).
# Generator: opencode-runs/batch11/gen224.py.
number: 224
slug: expanding-pulley
name: An expanding pulley
brown: "This represents an expanding pulley. On turning pinion, d, to the right or left, a similar motion is imparted to wheel, c, which, by means of curved slots cut therein, thrusts the studs fastened to arms of pulley outward or inward, thus augmenting or diminishing the size of the pulley."
units: cm
sim:
  timestep: 0.0002
  integrator: implicitfast
  iterations: 100
  solver: PGS
  multiccd: true
  duration_s: 12.0
bodies:
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    shape: part
    pos: [0, 0, 0]
    mass: 0.3
    friction: 0.1
    color: "#d9cfb6"
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      - {kind: poly, points: [[7.3895, -1.2355], [7.4885, -0.2299], [8.3761, -0.6556], [8.343, -0.9911]], y: [-0.5, 0.5], collide: 1}
  - id: pinion
    shape: part
    pos: [7.4246, 0, 7.4246]
    mass: 0.4
    friction: 0.1
    color: "#c9b88f"
    pieces:
      - {kind: poly, points: [[5.6708, 6.3853], [6.3853, 5.6708], [5.4932, 5.2548], [5.2548, 5.4932]], y: [-0.5, 0.5], collide: 2}
      - {kind: poly, points: [[6.6166, 5.553], [7.6147, 5.3949], [7.1375, 4.534], [6.8045, 4.5867]], y: [-0.5, 0.5], collide: 2}
      - {kind: poly, points: [[7.8711, 5.4355], [8.7714, 5.8943], [8.8914, 4.9172], [8.591, 4.7642]], y: [-0.5, 0.5], collide: 2}
      - {kind: poly, points: [[8.955, 6.0778], [9.4137, 6.9782], [10.0851, 6.2582], [9.932, 5.9579]], y: [-0.5, 0.5], collide: 2}
      - {kind: poly, points: [[9.4543, 7.2346], [9.2963, 8.2326], [10.2625, 8.0448], [10.3153, 7.7118]], y: [-0.5, 0.5], collide: 2}
      - {kind: poly, points: [[9.1784, 8.4639], [8.4639, 9.1784], [9.356, 9.5944], [9.5944, 9.356]], y: [-0.5, 0.5], collide: 2}
      - {kind: poly, points: [[8.2326, 9.2963], [7.2346, 9.4543], [7.7118, 10.3153], [8.0448, 10.2625]], y: [-0.5, 0.5], collide: 2}
      - {kind: poly, points: [[6.9782, 9.4137], [6.0778, 8.955], [5.9579, 9.932], [6.2582, 10.0851]], y: [-0.5, 0.5], collide: 2}
      - {kind: poly, points: [[5.8943, 8.7714], [5.4355, 7.8711], [4.7642, 8.591], [4.9172, 8.8914]], y: [-0.5, 0.5], collide: 2}
      - {kind: poly, points: [[5.3949, 7.6147], [5.553, 6.6166], [4.5867, 6.8045], [4.534, 7.1375]], y: [-0.5, 0.5], collide: 2}
      - {kind: disc, center: [7.4246, 7.4246], radius: 1.955, y: [-0.5, 0.5], collide: 0}
      - {kind: disc, center: [7.4246, 7.4246], radius: 0.45, y: [-1.6, 2.2], collide: 0, color: "#8f8a80"}   # its axle
      - {kind: poly, points: [[7.4246, 7.9746], [6.8746, 7.4246], [7.4246, 6.8746], [7.9746, 7.4246]], y: [-2.2, -1.6], collide: 0, color: "#8f8a80"}   # the square for the key
  - id: arm0
    shape: part
    pos: [4.6, 0, 0.0]
    mass: 0.12
    friction: 0.1
    color: "#b8ad97"
    pieces:
      - {kind: disc, center: [4.6, 0.0], radius: 0.4, y: [-0.7, 0.8], collide: 2, color: "#8f8a80"}   # the stud, in its slot
      - {kind: poly, points: [[4.0, -0.6], [4.0, 0.6], [11.0, 0.6], [11.0, -0.6]], y: [0.75, 1.45], collide: 0}   # the arm, behind the wheel
      - {kind: poly, points: [[10.2714, -3.3374], [10.432, -2.7952], [11.3979, -3.0541], [11.2225, -3.6464]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.432, -2.7952], [10.564, -2.2454], [11.5421, -2.4534], [11.3979, -3.0541]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.564, -2.2454], [10.667, -1.6895], [11.6547, -1.8459], [11.5421, -2.4534]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.667, -1.6895], [10.7408, -1.1289], [11.7354, -1.2334], [11.6547, -1.8459]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.7408, -1.1289], [10.7852, -0.5652], [11.7838, -0.6176], [11.7354, -1.2334]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.7852, -0.5652], [10.8, 0.0], [11.8, 0.0], [11.7838, -0.6176]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.8, 0.0], [10.7852, 0.5652], [11.7838, 0.6176], [11.8, 0.0]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.7852, 0.5652], [10.7408, 1.1289], [11.7354, 1.2334], [11.7838, 0.6176]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.7408, 1.1289], [10.667, 1.6895], [11.6547, 1.8459], [11.7354, 1.2334]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.667, 1.6895], [10.564, 2.2454], [11.5421, 2.4534], [11.6547, 1.8459]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.564, 2.2454], [10.432, 2.7952], [11.3979, 3.0541], [11.5421, 2.4534]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[10.432, 2.7952], [10.2714, 3.3374], [11.2225, 3.6464], [11.3979, 3.0541]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}   # a segment of the pulley's rim
  - id: arm1
    shape: part
    pos: [0.0, 0, 4.6]
    mass: 0.12
    friction: 0.1
    color: "#b8ad97"
    pieces:
      - {kind: disc, center: [0.0, 4.6], radius: 0.4, y: [-0.7, 0.8], collide: 2, color: "#8f8a80"}   # the stud, in its slot
      - {kind: poly, points: [[0.6, 4.0], [-0.6, 4.0], [-0.6, 11.0], [0.6, 11.0]], y: [0.75, 1.45], collide: 0}   # the arm, behind the wheel
      - {kind: poly, points: [[3.3374, 10.2714], [2.7952, 10.432], [3.0541, 11.3979], [3.6464, 11.2225]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[2.7952, 10.432], [2.2454, 10.564], [2.4534, 11.5421], [3.0541, 11.3979]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[2.2454, 10.564], [1.6895, 10.667], [1.8459, 11.6547], [2.4534, 11.5421]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[1.6895, 10.667], [1.1289, 10.7408], [1.2334, 11.7354], [1.8459, 11.6547]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[1.1289, 10.7408], [0.5652, 10.7852], [0.6176, 11.7838], [1.2334, 11.7354]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[0.5652, 10.7852], [0.0, 10.8], [0.0, 11.8], [0.6176, 11.7838]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[0.0, 10.8], [-0.5652, 10.7852], [-0.6176, 11.7838], [0.0, 11.8]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-0.5652, 10.7852], [-1.1289, 10.7408], [-1.2334, 11.7354], [-0.6176, 11.7838]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-1.1289, 10.7408], [-1.6895, 10.667], [-1.8459, 11.6547], [-1.2334, 11.7354]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-1.6895, 10.667], [-2.2454, 10.564], [-2.4534, 11.5421], [-1.8459, 11.6547]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-2.2454, 10.564], [-2.7952, 10.432], [-3.0541, 11.3979], [-2.4534, 11.5421]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-2.7952, 10.432], [-3.3374, 10.2714], [-3.6464, 11.2225], [-3.0541, 11.3979]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}   # a segment of the pulley's rim
  - id: arm2
    shape: part
    pos: [-4.6, 0, 0.0]
    mass: 0.12
    friction: 0.1
    color: "#b8ad97"
    pieces:
      - {kind: disc, center: [-4.6, 0.0], radius: 0.4, y: [-0.7, 0.8], collide: 2, color: "#8f8a80"}   # the stud, in its slot
      - {kind: poly, points: [[-4.0, 0.6], [-4.0, -0.6], [-11.0, -0.6], [-11.0, 0.6]], y: [0.75, 1.45], collide: 0}   # the arm, behind the wheel
      - {kind: poly, points: [[-10.2714, 3.3374], [-10.432, 2.7952], [-11.3979, 3.0541], [-11.2225, 3.6464]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.432, 2.7952], [-10.564, 2.2454], [-11.5421, 2.4534], [-11.3979, 3.0541]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.564, 2.2454], [-10.667, 1.6895], [-11.6547, 1.8459], [-11.5421, 2.4534]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.667, 1.6895], [-10.7408, 1.1289], [-11.7354, 1.2334], [-11.6547, 1.8459]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.7408, 1.1289], [-10.7852, 0.5652], [-11.7838, 0.6176], [-11.7354, 1.2334]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.7852, 0.5652], [-10.8, 0.0], [-11.8, 0.0], [-11.7838, 0.6176]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.8, 0.0], [-10.7852, -0.5652], [-11.7838, -0.6176], [-11.8, 0.0]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.7852, -0.5652], [-10.7408, -1.1289], [-11.7354, -1.2334], [-11.7838, -0.6176]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.7408, -1.1289], [-10.667, -1.6895], [-11.6547, -1.8459], [-11.7354, -1.2334]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.667, -1.6895], [-10.564, -2.2454], [-11.5421, -2.4534], [-11.6547, -1.8459]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.564, -2.2454], [-10.432, -2.7952], [-11.3979, -3.0541], [-11.5421, -2.4534]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-10.432, -2.7952], [-10.2714, -3.3374], [-11.2225, -3.6464], [-11.3979, -3.0541]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}   # a segment of the pulley's rim
  - id: arm3
    shape: part
    pos: [-0.0, 0, -4.6]
    mass: 0.12
    friction: 0.1
    color: "#b8ad97"
    pieces:
      - {kind: disc, center: [-0.0, -4.6], radius: 0.4, y: [-0.7, 0.8], collide: 2, color: "#8f8a80"}   # the stud, in its slot
      - {kind: poly, points: [[-0.6, -4.0], [0.6, -4.0], [0.6, -11.0], [-0.6, -11.0]], y: [0.75, 1.45], collide: 0}   # the arm, behind the wheel
      - {kind: poly, points: [[-3.3374, -10.2714], [-2.7952, -10.432], [-3.0541, -11.3979], [-3.6464, -11.2225]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-2.7952, -10.432], [-2.2454, -10.564], [-2.4534, -11.5421], [-3.0541, -11.3979]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-2.2454, -10.564], [-1.6895, -10.667], [-1.8459, -11.6547], [-2.4534, -11.5421]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-1.6895, -10.667], [-1.1289, -10.7408], [-1.2334, -11.7354], [-1.8459, -11.6547]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-1.1289, -10.7408], [-0.5652, -10.7852], [-0.6176, -11.7838], [-1.2334, -11.7354]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-0.5652, -10.7852], [-0.0, -10.8], [-0.0, -11.8], [-0.6176, -11.7838]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-0.0, -10.8], [0.5652, -10.7852], [0.6176, -11.7838], [-0.0, -11.8]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[0.5652, -10.7852], [1.1289, -10.7408], [1.2334, -11.7354], [0.6176, -11.7838]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[1.1289, -10.7408], [1.6895, -10.667], [1.8459, -11.6547], [1.2334, -11.7354]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[1.6895, -10.667], [2.2454, -10.564], [2.4534, -11.5421], [1.8459, -11.6547]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[2.2454, -10.564], [2.7952, -10.432], [3.0541, -11.3979], [2.4534, -11.5421]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[2.7952, -10.432], [3.3374, -10.2714], [3.6464, -11.2225], [3.0541, -11.3979]], y: [-1.2, 1.45], collide: 0, color: "#a89a7e"}   # a segment of the pulley's rim
  - id: frame
    shape: part
    pos: [0, 0, 0]
    fixed: true
    density: 7800
    color: "#cfc6b4"
    pieces:
      - {kind: disc, center: [0.0, 0.0], radius: 1.6, y: [-0.9, 2.2], collide: 0, color: "#8f8a80"}   # the hub
      - {kind: disc, center: [0.0, 0.0], radius: 2.4, y: [-1.3, -0.6], collide: 0, color: "#8f8a80"}   # the collar keeping c on it
      - {kind: poly, points: [[1.0, -1.0], [1.0, 1.0], [9.6, 1.0], [9.6, -1.0]], y: [1.5, 2.2], collide: 0}
      - {kind: poly, points: [[7.2, -0.62], [7.2, -0.95], [9.4, -0.95], [9.4, -0.62]], y: [0.7, 1.5], collide: 0}
      - {kind: poly, points: [[7.2, 0.62], [7.2, 0.95], [9.4, 0.95], [9.4, 0.62]], y: [0.7, 1.5], collide: 0}
      - {kind: poly, points: [[1.0, 1.0], [-1.0, 1.0], [-1.0, 9.6], [1.0, 9.6]], y: [1.5, 2.2], collide: 0}
      - {kind: poly, points: [[0.62, 7.2], [0.95, 7.2], [0.95, 9.4], [0.62, 9.4]], y: [0.7, 1.5], collide: 0}
      - {kind: poly, points: [[-0.62, 7.2], [-0.95, 7.2], [-0.95, 9.4], [-0.62, 9.4]], y: [0.7, 1.5], collide: 0}
      - {kind: poly, points: [[-1.0, 1.0], [-1.0, -1.0], [-9.6, -1.0], [-9.6, 1.0]], y: [1.5, 2.2], collide: 0}
      - {kind: poly, points: [[-7.2, 0.62], [-7.2, 0.95], [-9.4, 0.95], [-9.4, 0.62]], y: [0.7, 1.5], collide: 0}
      - {kind: poly, points: [[-7.2, -0.62], [-7.2, -0.95], [-9.4, -0.95], [-9.4, -0.62]], y: [0.7, 1.5], collide: 0}
      - {kind: poly, points: [[-1.0, -1.0], [1.0, -1.0], [1.0, -9.6], [-1.0, -9.6]], y: [1.5, 2.2], collide: 0}
      - {kind: poly, points: [[-0.62, -7.2], [-0.95, -7.2], [-0.95, -9.4], [-0.62, -9.4]], y: [0.7, 1.5], collide: 0}
      - {kind: poly, points: [[0.62, -7.2], [0.95, -7.2], [0.95, -9.4], [0.62, -9.4]], y: [0.7, 1.5], collide: 0}
      - {kind: poly, points: [[8.3246, 7.4246], [8.204, 7.8746], [7.8746, 8.204], [7.4246, 8.3246], [6.9746, 8.204], [6.6452, 7.8746], [6.5246, 7.4246], [6.6452, 6.9746], [6.9746, 6.6452], [7.4246, 6.5246], [7.8746, 6.6452], [8.204, 6.9746]], y: [1.5, 2.2], collide: 0}   # the pinion's bearing
      - {kind: poly, points: [[-1.0, 0.0], [1.0, 0.0], [8.1246, 6.7246], [6.7246, 8.1246]], y: [1.5, 2.2], collide: 0}
joints:
  - {id: j_d, type: hinge, body: pinion, axis: [0, -1, 0], damping: 0.002}   # the one driven joint; +: counter-clockwise
  - {id: j_c, type: hinge, body: wheel, axis: [0, -1, 0], damping: 0.05, frictionloss: 0.005}   # +: counter-clockwise
  - {id: j_a0, type: slide, body: arm0, axis: [1.0, 0, 0.0], damping: 0.02}   # +: outward
  - {id: j_a1, type: slide, body: arm1, axis: [0.0, 0, 1.0], damping: 0.02}   # +: outward
  - {id: j_a2, type: slide, body: arm2, axis: [-1.0, 0, 0.0], damping: 0.02}   # +: outward
  - {id: j_a3, type: slide, body: arm3, axis: [-0.0, 0, -1.0], damping: 0.02}   # +: outward
contact: {solref: [0.002, 1.0], solimp: [0.95, 0.99, 0.0005], margin: 0}
driver: {joint: j_d, kind: velocity, rpm: 0, swing: {amplitude: 2, hz: 0.1}, kv: 2.0, max_torque: 20}
checks:
  - {type: follow, out: j_c, in: j_d, expect: -0.3125, tol: 0.01, min_r2: 0.995, settle_s: 0.5, window_s: 10}   # c turns the other way, 10/32
  - {type: follow, out: j_a0, in: j_d, expect: 0.005594, tol: 0.000280, min_r2: 0.99, settle_s: 0.5, window_s: 10}   # 0.5594 cm out per radian of d
  - {type: follow, out: j_a1, in: j_a0, expect: 1.0, tol: 0.05, min_r2: 0.98, settle_s: 0.5, window_s: 10}
  - {type: follow, out: j_a2, in: j_a0, expect: 1.0, tol: 0.05, min_r2: 0.98, settle_s: 0.5, window_s: 10}
  - {type: follow, out: j_a3, in: j_a0, expect: 1.0, tol: 0.05, min_r2: 0.98, settle_s: 0.5, window_s: 10}   # the arms together
  - {type: penetration, max: 0.001, settle_s: 0.5}
camera: {target: [0.0, 0, -3.0], position: [6.0, -72.0, 8.0], fov: 34}
display:
  output: j_a0
  labels: {j_d: "Pinion d (driver)", j_c: "Wheel c", j_a0: "Arm, right", j_a1: "Arm, top", j_a2: "Arm, left", j_a3: "Arm, bottom"}
  proof: {label: "Studs and teeth out of contact", sub: "the pinion turns but the pulley keeps its size"}