# No. 143 (Brown 1868): "Circular motion into alternate rectilinear motion. Motion is transmitted through pulley at the left upon the worm-shaft. Worm slides upon shaft, but is made to turn with it by means of a groove cut in shaft, and a key in hub of worm. Worm is carried by a small traversing-frame, which slides upon a horizontal bar of the fixed frame, and the traversing-frame also carries the toothed wheel into which the worm gears. One end of a connecting-rod is attached to fixed frame at the right and the other end to a wrist secured in toothed wheel. On turning worm-shaft, rotary motion is transmitted by worm to wheel, which, as it revolves, is forced by connecting-rod to make an alternating traverse motion."
#
# Model (cm, no gravity; the plate's plane is x-z, depth y): a 18-tooth wheel (module 0.8) lies face-on on the traversing frame, with the worm (a right-hand single thread of 3 turns, 72 convex segments) along x under it, 9.76 below the wheel's centre;
# both are carried by the frame, which slides to and fro on the fixed bar. A worm sliding on a keyed shaft turns with the shaft, so the driven joint is the worm's turn relative to the frame it rides in (180 turns a minute). The wheel is turned by the thread alone (0.0556 of a turn per worm turn). A wrist 4.5 cm from the wheel's centre
# is joined by a 36.2802 cm connecting rod to a pin on the fixed post at the right, so the wheel's turning forces the frame to traverse 8.9999 cm (twice the wrist's radius, a little less). Generator: opencode-runs/batch10/gen143.py.
number: 143
slug: worm-traverse
name: A worm and wheel working a traversing frame
brown: "Circular motion into alternate rectilinear motion. Motion is transmitted through pulley at the left upon the worm-shaft. Worm slides upon shaft, but is made to turn with it by means of a groove cut in shaft, and a key in hub of worm. Worm is carried by a small traversing-frame, which slides upon a horizontal bar of the fixed frame, and the traversing-frame also carries the toothed wheel into which the worm gears. One end of a connecting-rod is attached to fixed frame at the right and the other end to a wrist secured in toothed wheel. On turning worm-shaft, rotary motion is transmitted by worm to wheel, which, as it revolves, is forced by connecting-rod to make an alternating traverse motion."
units: cm
sim:
  timestep: 0.0002
  integrator: implicitfast
  iterations: 100
  solver: CG
  multiccd: true
  duration_s: 13.0
  floor: false
  gravity: 0
bodies:
  - id: frame
    shape: part
    pos: [0, 0, 0]
    mass: 0.5
    color: "#cfc6b4"
    pieces:
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      - {kind: poly, points: [[-1.0, -15.26], [1.0, -15.26], [1.0, 2.2], [-1.0, 2.2]], y: [1.2, 2.4], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[-1.0, -10.36], [1.0, -10.36], [1.0, -9.16], [-1.0, -9.16]], y: [1.2, 2.4], collide: 0, color: "#a89a7e"}
      - {kind: rod, from: [0, -1.0, 0], to: [0, 2.4, 0], radius: 0.7, color: "#8f8a80"}
      - {kind: rod, from: [-8.8, 0, -9.76], to: [-6.6, 0, -9.76], radius: 1.0, color: "#8f8a80"}
      - {kind: rod, from: [6.6, 0, -9.76], to: [8.8, 0, -9.76], radius: 1.0, color: "#8f8a80"}
      - {kind: poly, points: [[-8.8, -11.56], [-6.6, -11.56], [-6.6, -7.96], [-8.8, -7.96]], y: [0.8, 2.4], collide: 0, color: "#a89a7e"}
      - {kind: poly, points: [[6.6, -11.56], [8.8, -11.56], [8.8, -7.96], [6.6, -7.96]], y: [0.8, 2.4], collide: 0, color: "#a89a7e"}
  - id: wheel
    shape: part
    pos: [0, 0, 0]
    mount: frame
    mass: 0.3
    density: 7800
    friction: 0.1
    color: "#e8dec6"
    pieces:
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      - {kind: disc, center: [0.0, 4.5], radius: 1.0, inner: 0.3, y: [-1.3, -0.7], color: "#a89a7e"}
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  - id: worm
    shape: part
    pos: [0, 0, -9.76]
    mount: frame
    density: 7800
    friction: 0.1
    color: "#e4d9bf"
    pieces:
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      - {kind: loft, a: [[1.2341, -0.78, -8.409], [2.9547, -0.78, -8.409], [2.2995, -1.68, -6.8502], [1.8893, -1.68, -6.8502]], b: [[1.3388, -1.1031, -8.6569], [3.0594, -1.1031, -8.6569], [2.4043, -2.3759, -7.3841], [1.994, -2.3759, -7.3841]], collide: 1}
      - {kind: loft, a: [[1.3388, -1.1031, -8.6569], [3.0594, -1.1031, -8.6569], [2.4043, -2.3759, -7.3841], [1.994, -2.3759, -7.3841]], b: [[1.4435, -1.351, -8.98], [3.1641, -1.351, -8.98], [2.509, -2.9098, -8.08], [2.0987, -2.9098, -8.08]], collide: 1}
      - {kind: loft, a: [[1.4435, -1.351, -8.98], [3.1641, -1.351, -8.98], [2.509, -2.9098, -8.08], [2.0987, -2.9098, -8.08]], b: [[1.5483, -1.5068, -9.3562], [3.2688, -1.5068, -9.3562], [2.6137, -3.2455, -8.8904], [2.2034, -3.2455, -8.8904]], collide: 1}
      - {kind: loft, a: [[1.5483, -1.5068, -9.3562], [3.2688, -1.5068, -9.3562], [2.6137, -3.2455, -8.8904], [2.2034, -3.2455, -8.8904]], b: [[1.653, -1.56, -9.76], [3.3736, -1.56, -9.76], [2.7184, -3.36, -9.76], [2.3081, -3.36, -9.76]], collide: 1}
      - {kind: loft, a: [[1.653, -1.56, -9.76], [3.3736, -1.56, -9.76], [2.7184, -3.36, -9.76], [2.3081, -3.36, -9.76]], b: [[1.7577, -1.5068, -10.1638], [3.4783, -1.5068, -10.1638], [2.8231, -3.2455, -10.6296], [2.4129, -3.2455, -10.6296]], collide: 1}
      - {kind: loft, a: [[1.7577, -1.5068, -10.1638], [3.4783, -1.5068, -10.1638], [2.8231, -3.2455, -10.6296], [2.4129, -3.2455, -10.6296]], b: [[1.8624, -1.351, -10.54], [3.583, -1.351, -10.54], [2.9279, -2.9098, -11.44], [2.5176, -2.9098, -11.44]], collide: 1}
      - {kind: loft, a: [[1.8624, -1.351, -10.54], [3.583, -1.351, -10.54], [2.9279, -2.9098, -11.44], [2.5176, -2.9098, -11.44]], b: [[1.9671, -1.1031, -10.8631], [3.6877, -1.1031, -10.8631], [3.0326, -2.3759, -12.1359], [2.6223, -2.3759, -12.1359]], collide: 1}
      - {kind: loft, a: [[1.9671, -1.1031, -10.8631], [3.6877, -1.1031, -10.8631], [3.0326, -2.3759, -12.1359], [2.6223, -2.3759, -12.1359]], b: [[2.0719, -0.78, -11.111], [3.7924, -0.78, -11.111], [3.1373, -1.68, -12.6698], [2.727, -1.68, -12.6698]], collide: 1}
      - {kind: loft, a: [[2.0719, -0.78, -11.111], [3.7924, -0.78, -11.111], [3.1373, -1.68, -12.6698], [2.727, -1.68, -12.6698]], b: [[2.1766, -0.4038, -11.2668], [3.8972, -0.4038, -11.2668], [3.242, -0.8696, -13.0055], [2.8317, -0.8696, -13.0055]], collide: 1}
      - {kind: loft, a: [[2.1766, -0.4038, -11.2668], [3.8972, -0.4038, -11.2668], [3.242, -0.8696, -13.0055], [2.8317, -0.8696, -13.0055]], b: [[2.2813, 0.0, -11.32], [4.0019, 0.0, -11.32], [3.3467, 0.0, -13.12], [2.9365, 0.0, -13.12]], collide: 1}
      - {kind: loft, a: [[2.2813, 0.0, -11.32], [4.0019, 0.0, -11.32], [3.3467, 0.0, -13.12], [2.9365, 0.0, -13.12]], b: [[2.386, 0.4038, -11.2668], [4.1066, 0.4038, -11.2668], [3.4515, 0.8696, -13.0055], [3.0412, 0.8696, -13.0055]], collide: 1}
      - {kind: loft, a: [[2.386, 0.4038, -11.2668], [4.1066, 0.4038, -11.2668], [3.4515, 0.8696, -13.0055], [3.0412, 0.8696, -13.0055]], b: [[2.4907, 0.78, -11.111], [4.2113, 0.78, -11.111], [3.5562, 1.68, -12.6698], [3.1459, 1.68, -12.6698]], collide: 1}
      - {kind: loft, a: [[2.4907, 0.78, -11.111], [4.2113, 0.78, -11.111], [3.5562, 1.68, -12.6698], [3.1459, 1.68, -12.6698]], b: [[2.5955, 1.1031, -10.8631], [4.316, 1.1031, -10.8631], [3.6609, 2.3759, -12.1359], [3.2506, 2.3759, -12.1359]], collide: 1}
      - {kind: loft, a: [[2.5955, 1.1031, -10.8631], [4.316, 1.1031, -10.8631], [3.6609, 2.3759, -12.1359], [3.2506, 2.3759, -12.1359]], b: [[2.7002, 1.351, -10.54], [4.4208, 1.351, -10.54], [3.7656, 2.9098, -11.44], [3.3553, 2.9098, -11.44]], collide: 1}
      - {kind: loft, a: [[2.7002, 1.351, -10.54], [4.4208, 1.351, -10.54], [3.7656, 2.9098, -11.44], [3.3553, 2.9098, -11.44]], b: [[2.8049, 1.5068, -10.1638], [4.5255, 1.5068, -10.1638], [3.8703, 3.2455, -10.6296], [3.46, 3.2455, -10.6296]], collide: 1}
      - {kind: loft, a: [[2.8049, 1.5068, -10.1638], [4.5255, 1.5068, -10.1638], [3.8703, 3.2455, -10.6296], [3.46, 3.2455, -10.6296]], b: [[2.9096, 1.56, -9.76], [4.6302, 1.56, -9.76], [3.9751, 3.36, -9.76], [3.5648, 3.36, -9.76]], collide: 1}
  - id: conrod
    shape: part
    pos: [0.0, 0, 4.5]
    mount: wheel
    mass: 0.1
    color: "#c4baa2"
    pieces:
      - {kind: poly, points: [[0.0806, 5.145], [36.0806, 0.645], [35.9194, -0.645], [-0.0806, 3.855]], y: [-2.1, -1.4], collide: 0, color: "#c4baa2"}
      - {kind: disc, center: [0.0, 4.5], radius: 1.0, inner: 0.3, y: [-2.1, -1.4]}
      - {kind: disc, center: [36.0, 0.0], radius: 1.0, inner: 0.3, y: [-2.1, -1.4]}
  - id: base
    shape: part
    pos: [0, 0, 0]
    fixed: true
    color: "#9b917c"
    pieces:
      - {kind: poly, points: [[-30.0, -17.66], [39.0, -17.66], [39.0, -16.06], [-30.0, -16.06]], y: [0.6, 3.0], collide: 0, color: "#9b917c"}
      - {kind: poly, points: [[36.0, -17.66], [39.0, -17.66], [39.0, 6.0], [36.0, 6.0]], y: [0.6, 3.0], collide: 0, color: "#9b917c"}
      - {kind: rod, from: [36.0, -1.4, 0.0], to: [36.0, 0.8, 0.0], radius: 0.6, color: "#8f8a80"}
      - {kind: rod, from: [-26, 0, -9.76], to: [26, 0, -9.76], radius: 0.5, color: "#a49f93", collide: 0}
joints:
  - {id: j_f, type: slide, body: frame, axis: [1, 0, 0], damping: 0.05}   # the traversing frame on its bar; + : to the right
  - {id: j_wh, type: hinge, body: wheel, axis: [0, 1, 0], damping: 0.01}               # the toothed wheel; + : clockwise
  - {id: j_wo, type: hinge, body: worm, axis: [1, 0, 0], damping: 0.001}               # the one driven joint: the worm turning with its shaft
  - {id: j_r, type: hinge, body: conrod, axis: [0, 1, 0], damping: 0.005}
pins:
  - {id: pin_f, a: conrod, b: base, at: [36.0, 0, 0.0]}
contact: {solref: [0.002, 1.0], solimp: [0.98, 0.99, 0.0002], margin: 0}
driver: {joint: j_wo, kind: velocity, rpm: 180.0, kv: 2.0, max_torque: 1.0}
checks:
  - {type: ratio, out: j_wh, in: j_wo, expect: 0.0556, tol: 0.002, settle_s: 1, window_s: 11.0}
  - {type: follow, out: j_f, in: j_wh, expect: 0.0438, tol: 0.0022, min_r2: 0.97, settle_s: 2.4, window_s: 1.0}
  - {type: follow, out: j_f, in: j_wh, expect: -0.0437, tol: 0.0022, min_r2: 0.97, settle_s: 5.6, window_s: 1.0}
  - {type: follow, out: j_f, in: j_wh, expect: 0.0438, tol: 0.0022, min_r2: 0.97, settle_s: 8.4, window_s: 1.0}
  - {type: follow, out: j_f, in: j_wh, expect: -0.0437, tol: 0.0022, min_r2: 0.97, settle_s: 11.6, window_s: 1.0}
  - {type: follow, out: j_f, in: j_wh, expect: -0.0418, tol: 0.0021, min_r2: 0.97, settle_s: 6.0, window_s: 1.0}
  - {type: position, joint: j_f, min: -5.1801, max: 4.6198, settle_s: 0.0, window_s: 12.0}
  - {type: penetration, max: 0.001, settle_s: 0.5}
camera: {target: [9.0, 0, -10.5], position: [9.0, -85.0, -10.5], fov: 34}
display:
  output: j_f
  labels: {j_wo: "Worm (driver)", j_wh: "Toothed wheel", j_f: "Traversing frame"}
  proof: {label: "Thread out of contact", sub: "the worm turns alone: the wheel and frame stand still"}