# No. 40, Rotary converted into rotary motion: spur-gears with oblique teeth (Brown 1868).
#
# "The teeth of these gears, being oblique, give a more continuous bearing than ordinary spur-gears."
#
# Model (cm): a 24-tooth driver (pitch radius 6) and a 36-tooth follower (pitch radius 9) on parallel
# shafts 15 apart, face 3 wide. Every tooth runs obliquely across the face at 25 deg to the axis
# (right hand on one, left hand on the other, as mating oblique teeth must be): each tooth is eight
# short straight-flanked (20 deg) segments, each one the convex hull of its two end sections, so the
# tooth twists through the face (batch7/gen040.py). The face advance, 3 tan 25 = 1.40, is 0.89 of a
# tooth pitch (pi m = 1.57), so a tooth's bearing slides across the face instead of meeting it all at once.
# Only the driver is motor-driven; the follower turns only through the teeth (ratio -24/36).
number: 40
slug: oblique-tooth-spur-gears
name: Oblique-tooth spur-gears
brown: "Rotary converted into rotary motion. The teeth of these gears, being oblique, give a more continuous bearing than ordinary spur-gears."
units: cm
sim:
  timestep: 0.0002
  integrator: implicitfast
  iterations: 100
  solver: CG
  multiccd: true
  duration_s: 6
  floor: false
bodies:
  - id: ga
    shape: part
    pos: [-6, 0, 0]
    density: 7800
    friction: 0.1
    color: "#e4d9bf"
    pieces:
      - {kind: disc, center: [-6, 0], radius: 5.4, inner: 0.5, y: [-1.5, 1.5]}
      - {kind: rod, from: [-6, -4.5, 0], to: [-6, 4.5, 0], radius: 0.5, color: "#8f8a80"}
      - {kind: loft, a: [[-0.5254, -1.5, 0.1703], [0.3949, -1.5, 0.6494], [0.3451, -1.5, 1.0279], [-0.6679, -1.5, 1.2525]], b: [[-0.5327, -1.125, 0.3297], [0.3733, -1.125, 0.8354], [0.3125, -1.125, 1.2123], [-0.7066, -1.125, 1.4073]], collide: 1}
      - {kind: loft, a: [[-0.5327, -1.125, 0.3297], [0.3733, -1.125, 0.8354], [0.3125, -1.125, 1.2123], [-0.7066, -1.125, 1.4073]], b: [[-0.5446, -0.75, 0.4889], [0.3463, -0.75, 1.0208], [0.2745, -0.75, 1.3958], [-0.7499, -0.75, 1.561]], collide: 1}
      - {kind: loft, a: [[-0.5446, -0.75, 0.4889], [0.3463, -0.75, 1.0208], [0.2745, -0.75, 1.3958], [-0.7499, -0.75, 1.561]], b: [[-0.5612, -0.375, 0.6477], [0.3138, -0.375, 1.2053], [0.2311, -0.375, 1.578], [-0.7976, -0.375, 1.7133]], collide: 1}
      - {kind: loft, a: [[-0.5612, -0.375, 0.6477], [0.3138, -0.375, 1.2053], [0.2311, -0.375, 1.578], [-0.7976, -0.375, 1.7133]], b: [[-0.5824, 0.0, 0.8059], [0.276, 0.0, 1.3888], [0.1825, 0.0, 1.7589], [-0.8497, 0.0, 1.8642]], collide: 1}
      - {kind: loft, a: [[-0.5824, 0.0, 0.8059], [0.276, 0.0, 1.3888], [0.1825, 0.0, 1.7589], [-0.8497, 0.0, 1.8642]], b: [[-0.6081, 0.375, 0.9634], [0.2329, 0.375, 1.5711], [0.1286, 0.375, 1.9383], [-0.9062, 0.375, 2.0134]], collide: 1}
      - {kind: loft, a: [[-0.6081, 0.375, 0.9634], [0.2329, 0.375, 1.5711], [0.1286, 0.375, 1.9383], [-0.9062, 0.375, 2.0134]], b: [[-0.6385, 0.75, 1.1201], [0.1845, 0.75, 1.752], [0.0695, 0.75, 2.1161], [-0.9671, 0.75, 2.161]], collide: 1}
      - {kind: loft, a: [[-0.6385, 0.75, 1.1201], [0.1845, 0.75, 1.752], [0.0695, 0.75, 2.1161], [-0.9671, 0.75, 2.161]], b: [[-0.6734, 1.125, 1.2759], [0.1308, 1.125, 1.9315], [0.0053, 1.125, 2.2921], [-1.0322, 1.125, 2.3068]], collide: 1}
      - {kind: loft, a: [[-0.6734, 1.125, 1.2759], [0.1308, 1.125, 1.9315], [0.0053, 1.125, 2.2921], [-1.0322, 1.125, 2.3068]], b: [[-0.7129, 1.5, 1.4306], [0.0719, 1.5, 2.1093], [-0.0641, 1.5, 2.4661], [-1.1015, 1.5, 2.4505]], collide: 1}
      - {kind: loft, a: [[-0.756, -1.5, 1.5814], [0.009, -1.5, 2.2824], [-0.1371, -1.5, 2.6351], [-1.1737, -1.5, 2.5898]], b: [[-0.8043, -1.125, 1.7335], [-0.0601, -1.125, 2.4565], [-0.2164, -1.125, 2.8048], [-1.2512, -1.125, 2.7294]], collide: 1}
      - {kind: loft, a: [[-0.8043, -1.125, 1.7335], [-0.0601, -1.125, 2.4565], [-0.2164, -1.125, 2.8048], [-1.2512, -1.125, 2.7294]], b: [[-0.857, -0.75, 1.8842], [-0.1342, -0.75, 2.6286], [-0.3006, -0.75, 2.9722], [-1.3328, -0.75, 2.8666]], collide: 1}
      - {kind: loft, a: [[-0.857, -0.75, 1.8842], [-0.1342, -0.75, 2.6286], [-0.3006, -0.75, 2.9722], [-1.3328, -0.75, 2.8666]], b: [[-0.9141, -0.375, 2.0333], [-0.2133, -0.375, 2.7984], [-0.3896, -0.375, 3.137], [-1.4183, -0.375, 3.0014]], collide: 1}
      - {kind: loft, a: [[-0.9141, -0.375, 2.0333], [-0.2133, -0.375, 2.7984], [-0.3896, -0.375, 3.137], [-1.4183, -0.375, 3.0014]], b: [[-0.9755, 0.0, 2.1806], [-0.2973, 0.0, 2.9658], [-0.4834, 0.0, 3.2991], [-1.5077, 0.0, 3.1336]], collide: 1}
      - {kind: loft, a: [[-0.9755, 0.0, 2.1806], [-0.2973, 0.0, 2.9658], [-0.4834, 0.0, 3.2991], [-1.5077, 0.0, 3.1336]], b: [[-1.0412, 0.375, 2.3261], [-0.3861, 0.375, 3.1307], [-0.5819, 0.375, 3.4585], [-1.6009, 0.375, 3.2632]], collide: 1}
      - {kind: loft, a: [[-1.0412, 0.375, 2.3261], [-0.3861, 0.375, 3.1307], [-0.5819, 0.375, 3.4585], [-1.6009, 0.375, 3.2632]], b: [[-1.1111, 0.75, 2.4696], [-0.4797, 0.75, 3.293], [-0.685, 0.75, 3.6149], [-1.6979, 0.75, 3.39]], collide: 1}
      - {kind: loft, a: [[-1.1111, 0.75, 2.4696], [-0.4797, 0.75, 3.293], [-0.685, 0.75, 3.6149], [-1.6979, 0.75, 3.39]], b: [[-1.1851, 1.125, 2.611], [-0.578, 1.125, 3.4525], [-0.7926, 1.125, 3.7683], [-1.7985, 1.125, 3.5139]], collide: 1}
      - {kind: loft, a: [[-1.1851, 1.125, 2.611], [-0.578, 1.125, 3.4525], [-0.7926, 1.125, 3.7683], [-1.7985, 1.125, 3.5139]], b: [[-1.2633, 1.5, 2.7502], [-0.681, 1.5, 3.609], [-0.9046, 1.5, 3.9184], [-1.9027, 1.5, 3.6349]], collide: 1}
      - {kind: loft, a: [[-1.344, -1.5, 2.8848], [-0.7865, -1.5, 3.7599], [-1.0189, -1.5, 4.0627], [-2.0085, -1.5, 3.7507]], b: [[-1.43, -1.125, 3.0192], [-0.8983, -1.125, 3.9102], [-1.1394, -1.125, 4.2062], [-2.1195, -1.125, 3.8655]], collide: 1}
      - {kind: loft, a: [[-1.43, -1.125, 3.0192], [-0.8983, -1.125, 3.9102], [-1.1394, -1.125, 4.2062], [-2.1195, -1.125, 3.8655]], b: [[-1.5199, -0.75, 3.1511], [-1.0144, -0.75, 4.0572], [-1.264, -0.75, 4.346], [-2.2337, -0.75, 3.9769]], collide: 1}
      - {kind: loft, a: [[-1.5199, -0.75, 3.1511], [-1.0144, -0.75, 4.0572], [-1.264, -0.75, 4.346], [-2.2337, -0.75, 3.9769]], b: [[-1.6137, -0.375, 3.2803], [-1.1347, -0.375, 4.2007], [-1.3927, -0.375, 4.4822], [-2.3512, -0.375, 4.0849]], collide: 1}
      - {kind: loft, a: [[-1.6137, -0.375, 3.2803], [-1.1347, -0.375, 4.2007], [-1.3927, -0.375, 4.4822], [-2.3512, -0.375, 4.0849]], b: [[-1.7111, 0.0, 3.4067], [-1.2592, 0.0, 4.3407], [-1.5253, 0.0, 4.6145], [-2.4718, 0.0, 4.1895]], collide: 1}
      - {kind: loft, a: [[-1.7111, 0.0, 3.4067], [-1.2592, 0.0, 4.3407], [-1.5253, 0.0, 4.6145], [-2.4718, 0.0, 4.1895]], b: [[-1.8122, 0.375, 3.5303], [-1.3877, 0.375, 4.477], [-1.6616, 0.375, 4.743], [-2.5954, 0.375, 4.2906]], collide: 1}
      - {kind: loft, a: [[-1.8122, 0.375, 3.5303], [-1.3877, 0.375, 4.477], [-1.6616, 0.375, 4.743], [-2.5954, 0.375, 4.2906]], b: [[-1.9169, 0.75, 3.6508], [-1.5201, 0.75, 4.6095], [-1.8017, 0.75, 4.8674], [-2.7219, 0.75, 4.388]], collide: 1}
      - {kind: loft, a: [[-1.9169, 0.75, 3.6508], [-1.5201, 0.75, 4.6095], [-1.8017, 0.75, 4.8674], [-2.7219, 0.75, 4.388]], b: [[-2.025, 1.125, 3.7682], [-1.6564, 1.125, 4.7381], [-1.9453, 1.125, 4.9876], [-2.8511, 1.125, 4.4816]], collide: 1}
      - {kind: loft, a: [[-2.025, 1.125, 3.7682], [-1.6564, 1.125, 4.7381], [-1.9453, 1.125, 4.9876], [-2.8511, 1.125, 4.4816]], b: [[-2.1365, 1.5, 3.8825], [-1.7963, 1.5, 4.8627], [-2.0924, 1.5, 5.1037], [-2.9831, 1.5, 4.5715]], collide: 1}
      - {kind: loft, a: [[-2.2493, -1.5, 3.9915], [-1.9373, -1.5, 4.9811], [-2.2401, -1.5, 5.2135], [-3.1152, -1.5, 4.656]], b: [[-2.3672, -1.125, 4.0991], [-2.0841, -1.125, 5.0974], [-2.3937, -1.125, 5.3208], [-3.2521, -1.125, 4.7381]], collide: 1}
      - {kind: loft, a: [[-2.3672, -1.125, 4.0991], [-2.0841, -1.125, 5.0974], [-2.3937, -1.125, 5.3208], [-3.2521, -1.125, 4.7381]], b: [[-2.4882, -0.75, 4.2033], [-2.2343, -0.75, 5.2093], [-2.5502, -0.75, 5.4237], [-3.3914, -0.75, 4.8162]], collide: 1}
      - {kind: loft, a: [[-2.4882, -0.75, 4.2033], [-2.2343, -0.75, 5.2093], [-2.5502, -0.75, 5.4237], [-3.3914, -0.75, 4.8162]], b: [[-2.6121, -0.375, 4.3038], [-2.3877, -0.375, 5.3168], [-2.7098, -0.375, 5.5219], [-3.5328, -0.375, 4.8901]], collide: 1}
      - {kind: loft, a: [[-2.6121, -0.375, 4.3038], [-2.3877, -0.375, 5.3168], [-2.7098, -0.375, 5.5219], [-3.5328, -0.375, 4.8901]], b: [[-2.739, 0.0, 4.4007], [-2.5442, 0.0, 5.4198], [-2.8721, 0.0, 5.6154], [-3.6764, 0.0, 4.9599]], collide: 1}
      - {kind: loft, a: [[-2.739, 0.0, 4.4007], [-2.5442, 0.0, 5.4198], [-2.8721, 0.0, 5.6154], [-3.6764, 0.0, 4.9599]], b: [[-2.8686, 0.375, 4.4939], [-2.7036, 0.375, 5.5182], [-3.037, 0.375, 5.7042], [-3.8219, 0.375, 5.0256]], collide: 1}
      - {kind: loft, a: [[-2.8686, 0.375, 4.4939], [-2.7036, 0.375, 5.5182], [-3.037, 0.375, 5.7042], [-3.8219, 0.375, 5.0256]], b: [[-3.0009, 0.75, 4.5832], [-2.8658, 0.75, 5.6119], [-3.2045, 0.75, 5.7881], [-3.9693, 0.75, 5.0869]], collide: 1}
      - {kind: loft, a: [[-3.0009, 0.75, 4.5832], [-2.8658, 0.75, 5.6119], [-3.2045, 0.75, 5.7881], [-3.9693, 0.75, 5.0869]], b: [[-3.1357, 1.125, 4.6687], [-3.0307, 1.125, 5.7009], [-3.3744, 1.125, 5.8671], [-4.1183, 1.125, 5.1439]], collide: 1}
      - {kind: loft, a: [[-3.1357, 1.125, 4.6687], [-3.0307, 1.125, 5.7009], [-3.3744, 1.125, 5.8671], [-4.1183, 1.125, 5.1439]], b: [[-3.273, 1.5, 4.7501], [-3.1981, 1.5, 5.785], [-3.5464, 1.5, 5.9411], [-4.269, 1.5, 5.1966]], collide: 1}
      - {kind: loft, a: [[-3.4102, -1.5, 4.8263], [-3.3649, -1.5, 5.8629], [-3.7176, -1.5, 6.009], [-4.4186, -1.5, 5.244]], b: [[-3.5519, -1.125, 4.8997], [-3.5369, -1.125, 5.9372], [-3.8937, -1.125, 6.0729], [-4.5721, -1.125, 5.2879]], collide: 1}
      - {kind: loft, a: [[-3.5519, -1.125, 4.8997], [-3.5369, -1.125, 5.9372], [-3.8937, -1.125, 6.0729], [-4.5721, -1.125, 5.2879]], b: [[-3.6957, -0.75, 4.969], [-3.7109, -0.75, 6.0064], [-4.0715, -0.75, 6.1317], [-4.7268, -0.75, 5.3272]], collide: 1}
      - {kind: loft, a: [[-3.6957, -0.75, 4.969], [-3.7109, -0.75, 6.0064], [-4.0715, -0.75, 6.1317], [-4.7268, -0.75, 5.3272]], b: [[-3.8415, -0.375, 5.034], [-3.8869, -0.375, 6.0706], [-4.251, -0.375, 6.1853], [-4.8825, -0.375, 5.3621]], collide: 1}
      - {kind: loft, a: [[-3.8415, -0.375, 5.034], [-3.8869, -0.375, 6.0706], [-4.251, -0.375, 6.1853], [-4.8825, -0.375, 5.3621]], b: [[-3.9891, 0.0, 5.0948], [-4.0647, 0.0, 6.1296], [-4.432, 0.0, 6.2337], [-5.0393, 0.0, 5.3923]], collide: 1}
      - {kind: loft, a: [[-3.9891, 0.0, 5.0948], [-4.0647, 0.0, 6.1296], [-4.432, 0.0, 6.2337], [-5.0393, 0.0, 5.3923]], b: [[-4.1384, 0.375, 5.1512], [-4.2442, 0.375, 6.1834], [-4.6143, 0.375, 6.2767], [-5.1968, 0.375, 5.418]], collide: 1}
      - {kind: loft, a: [[-4.1384, 0.375, 5.1512], [-4.2442, 0.375, 6.1834], [-4.6143, 0.375, 6.2767], [-5.1968, 0.375, 5.418]], b: [[-4.2893, 0.75, 5.2033], [-4.4251, 0.75, 6.2319], [-4.7978, 0.75, 6.3144], [-5.355, 0.75, 5.4392]], collide: 1}
      - {kind: loft, a: [[-4.2893, 0.75, 5.2033], [-4.4251, 0.75, 6.2319], [-4.7978, 0.75, 6.3144], [-5.355, 0.75, 5.4392]], b: [[-4.4417, 1.125, 5.2509], [-4.6074, 1.125, 6.2752], [-4.9824, 1.125, 6.3468], [-5.5138, 1.125, 5.4556]], collide: 1}
      - {kind: loft, a: [[-4.4417, 1.125, 5.2509], [-4.6074, 1.125, 6.2752], [-4.9824, 1.125, 6.3468], [-5.5138, 1.125, 5.4556]], b: [[-4.5953, 1.5, 5.2941], [-4.7908, 1.5, 6.3131], [-5.1677, 1.5, 6.3737], [-5.673, 1.5, 5.4675]], collide: 1}
      - {kind: loft, a: [[-4.7475, -1.5, 5.3321], [-4.9721, -1.5, 6.3451], [-5.3506, -1.5, 6.3949], [-5.8297, -1.5, 5.4746]], b: [[-4.9035, -1.125, 5.3664], [-5.1574, -1.125, 6.3724], [-5.5372, -1.125, 6.4112], [-5.9893, -1.125, 5.4772]], collide: 1}
      - {kind: loft, a: [[-4.9035, -1.125, 5.3664], [-5.1574, -1.125, 6.3724], [-5.5372, -1.125, 6.4112], [-5.9893, -1.125, 5.4772]], b: [[-5.0603, -0.75, 5.396], [-5.3435, -0.75, 6.3942], [-5.7243, -0.75, 6.4219], [-6.1489, -0.75, 5.4752]], collide: 1}
      - {kind: loft, a: [[-5.0603, -0.75, 5.396], [-5.3435, -0.75, 6.3942], [-5.7243, -0.75, 6.4219], [-6.1489, -0.75, 5.4752]], b: [[-5.2179, -0.375, 5.4211], [-5.5301, -0.375, 6.4106], [-5.9115, -0.375, 6.4272], [-6.3084, -0.375, 5.4686]], collide: 1}
      - {kind: loft, a: [[-5.2179, -0.375, 5.4211], [-5.5301, -0.375, 6.4106], [-5.9115, -0.375, 6.4272], [-6.3084, -0.375, 5.4686]], b: [[-5.3762, 0.0, 5.4416], [-5.7171, 0.0, 6.4216], [-6.0988, 0.0, 6.4271], [-6.4676, 0.0, 5.4573]], collide: 1}
      - {kind: loft, a: [[-5.3762, 0.0, 5.4416], [-5.7171, 0.0, 6.4216], [-6.0988, 0.0, 6.4271], [-6.4676, 0.0, 5.4573]], b: [[-5.5351, 0.375, 5.4575], [-5.9044, 0.375, 6.4271], [-6.2861, 0.375, 6.4215], [-6.6265, 0.375, 5.4413]], collide: 1}
      - {kind: loft, a: [[-5.5351, 0.375, 5.4575], [-5.9044, 0.375, 6.4271], [-6.2861, 0.375, 6.4215], [-6.6265, 0.375, 5.4413]], b: [[-5.6943, 0.75, 5.4687], [-6.0917, 0.75, 6.4272], [-6.4731, 0.75, 6.4104], [-6.7848, 0.75, 5.4207]], collide: 1}
      - {kind: loft, a: [[-5.6943, 0.75, 5.4687], [-6.0917, 0.75, 6.4272], [-6.4731, 0.75, 6.4104], [-6.7848, 0.75, 5.4207]], b: [[-5.8538, 1.125, 5.4753], [-6.2789, 1.125, 6.4218], [-6.6597, 1.125, 6.3939], [-6.9424, 1.125, 5.3956]], collide: 1}
      - {kind: loft, a: [[-5.8538, 1.125, 5.4753], [-6.2789, 1.125, 6.4218], [-6.6597, 1.125, 6.3939], [-6.9424, 1.125, 5.3956]], b: [[-6.0134, 1.5, 5.4772], [-6.4659, 1.5, 6.4109], [-6.8457, 1.5, 6.372], [-7.0992, 1.5, 5.3658]], collide: 1}
      - {kind: loft, a: [[-6.1703, -1.5, 5.4746], [-6.6494, -1.5, 6.3949], [-7.0279, -1.5, 6.3451], [-7.2525, -1.5, 5.3321]], b: [[-6.3297, -1.125, 5.4673], [-6.8354, -1.125, 6.3733], [-7.2123, -1.125, 6.3125], [-7.4073, -1.125, 5.2934]], collide: 1}
      - {kind: loft, a: [[-6.3297, -1.125, 5.4673], [-6.8354, -1.125, 6.3733], [-7.2123, -1.125, 6.3125], [-7.4073, -1.125, 5.2934]], b: [[-6.4889, -0.75, 5.4554], [-7.0208, -0.75, 6.3463], [-7.3958, -0.75, 6.2745], [-7.561, -0.75, 5.2501]], collide: 1}
      - {kind: loft, a: [[-6.4889, -0.75, 5.4554], [-7.0208, -0.75, 6.3463], [-7.3958, -0.75, 6.2745], [-7.561, -0.75, 5.2501]], b: [[-6.6477, -0.375, 5.4388], [-7.2053, -0.375, 6.3138], [-7.578, -0.375, 6.2311], [-7.7133, -0.375, 5.2024]], collide: 1}
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  - id: gb
    shape: part
    pos: [9, 0, 0]
    density: 7800
    friction: 0.1
    color: "#e8dec6"
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    shape: part
    pos: [0, 0, 0]
    fixed: true
    color: "#cfc6b4"
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      - {kind: poly, points: [[-8, -13], [-4, -13], [-5.3, 0], [-6.7, 0]], y: [4.5, 5.5]}
      - {kind: disc, center: [-6, 0], radius: 1.3, y: [4.5, 5.5]}
      - {kind: poly, points: [[7, -13], [11, -13], [9.7, 0], [8.3, 0]], y: [4.5, 5.5]}
      - {kind: disc, center: [9, 0], radius: 1.3, y: [4.5, 5.5]}
      - {kind: poly, points: [[-12, -14], [18, -14], [18, -13], [-12, -13]], y: [3.5, 6.5], color: "#b9b09c"}
joints:
  - {id: j_a, type: hinge, body: ga, axis: [0, -1, 0], damping: 0.001}
  - {id: j_b, type: hinge, body: gb, axis: [0, -1, 0], damping: 0.02}
contact: {solref: [0.002, 1], solimp: [0.95, 0.99, 0.0005], margin: 0}
driver: {joint: j_a, kind: velocity, rpm: 30, kv: 4, max_torque: 8}
checks:
  - {type: ratio, out: j_b, in: j_a, expect: -0.66667, tol: 0.003, settle_s: 1, window_s: 5}
  # the continuous bearing: the follower's speed stays even through every tooth (slices of 1/24 s)
  - {type: ratio_range, out: j_b, in: j_a, min: -0.69, max: -0.645, settle_s: 1, window_s: 5, slices: 120}
  - {type: penetration, max: 0.001, settle_s: 0.5}
camera: {target: [1.5, 0, -4], position: [8, -56, 26], fov: 30}
display:
  tiers:
    - {id: full, label: Full, ms: 0.1758}
    - {id: light, label: Light, links: [], timestep: 0.0008, integrator: discrete, ms: 0.2704}
  output: j_b
  labels: {j_a: "Driver (24 oblique teeth)", j_b: "Follower (36 oblique teeth)"}
  expect: {default: -0.6667}
  proof: {label: "Teeth out of contact", sub: "the driver turns alone: the follower stops"}