# No. 41, Rotary converted into rotary motion: spur-gears with double-oblique (V) teeth (Brown 1868).
#
# "The teeth of these gears, being oblique, give a more continuous bearing than ordinary spur-gears."
# Plate 40-41: the model of No. 40 has the teeth oblique one way across the whole face; No. 41 is modelled
# with each tooth oblique both ways from the middle of the face (a V, 25 deg each side), the other
# form of oblique teeth, whose two halves' end thrusts balance.
#
# Model (cm): as No. 40, a 24-tooth driver (pitch radius 6) and a 36-tooth follower (pitch radius 9)
# on parallel shafts 15 apart, face 3 wide; each tooth eight straight-flanked (20 deg) segments, each
# the convex hull of its two end sections, bent at the middle of the face (batch7/gen040.py vee).
# Only the driver is motor-driven; the follower turns only through the teeth (ratio -24/36).
number: 41
slug: double-oblique-tooth-spur-gears
name: Double-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: [[-0.5824, -1.5, 0.8059], [0.276, -1.5, 1.3888], [0.1825, -1.5, 1.7589], [-0.8497, -1.5, 1.8642]], b: [[-0.5612, -1.125, 0.6477], [0.3138, -1.125, 1.2053], [0.2311, -1.125, 1.578], [-0.7976, -1.125, 1.7133]], collide: 1}
      - {kind: loft, a: [[-0.5612, -1.125, 0.6477], [0.3138, -1.125, 1.2053], [0.2311, -1.125, 1.578], [-0.7976, -1.125, 1.7133]], 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: [[-0.5327, -0.375, 0.3297], [0.3733, -0.375, 0.8354], [0.3125, -0.375, 1.2123], [-0.7066, -0.375, 1.4073]], collide: 1}
      - {kind: loft, a: [[-0.5327, -0.375, 0.3297], [0.3733, -0.375, 0.8354], [0.3125, -0.375, 1.2123], [-0.7066, -0.375, 1.4073]], b: [[-0.5254, 0.0, 0.1703], [0.3949, 0.0, 0.6494], [0.3451, 0.0, 1.0279], [-0.6679, 0.0, 1.2525]], collide: 1}
      - {kind: loft, a: [[-0.5254, 0.0, 0.1703], [0.3949, 0.0, 0.6494], [0.3451, 0.0, 1.0279], [-0.6679, 0.0, 1.2525]], b: [[-0.5327, 0.375, 0.3297], [0.3733, 0.375, 0.8354], [0.3125, 0.375, 1.2123], [-0.7066, 0.375, 1.4073]], collide: 1}
      - {kind: loft, a: [[-0.5327, 0.375, 0.3297], [0.3733, 0.375, 0.8354], [0.3125, 0.375, 1.2123], [-0.7066, 0.375, 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, 1.125, 0.6477], [0.3138, 1.125, 1.2053], [0.2311, 1.125, 1.578], [-0.7976, 1.125, 1.7133]], collide: 1}
      - {kind: loft, a: [[-0.5612, 1.125, 0.6477], [0.3138, 1.125, 1.2053], [0.2311, 1.125, 1.578], [-0.7976, 1.125, 1.7133]], b: [[-0.5824, 1.5, 0.8059], [0.276, 1.5, 1.3888], [0.1825, 1.5, 1.7589], [-0.8497, 1.5, 1.8642]], collide: 1}
      - {kind: loft, a: [[-0.9755, -1.5, 2.1806], [-0.2973, -1.5, 2.9658], [-0.4834, -1.5, 3.2991], [-1.5077, -1.5, 3.1336]], b: [[-0.9141, -1.125, 2.0333], [-0.2133, -1.125, 2.7984], [-0.3896, -1.125, 3.137], [-1.4183, -1.125, 3.0014]], collide: 1}
      - {kind: loft, a: [[-0.9141, -1.125, 2.0333], [-0.2133, -1.125, 2.7984], [-0.3896, -1.125, 3.137], [-1.4183, -1.125, 3.0014]], 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: [[-0.8043, -0.375, 1.7335], [-0.0601, -0.375, 2.4565], [-0.2164, -0.375, 2.8048], [-1.2512, -0.375, 2.7294]], collide: 1}
      - {kind: loft, a: [[-0.8043, -0.375, 1.7335], [-0.0601, -0.375, 2.4565], [-0.2164, -0.375, 2.8048], [-1.2512, -0.375, 2.7294]], b: [[-0.756, 0.0, 1.5814], [0.009, 0.0, 2.2824], [-0.1371, 0.0, 2.6351], [-1.1737, 0.0, 2.5898]], collide: 1}
      - {kind: loft, a: [[-0.756, 0.0, 1.5814], [0.009, 0.0, 2.2824], [-0.1371, 0.0, 2.6351], [-1.1737, 0.0, 2.5898]], b: [[-0.8043, 0.375, 1.7335], [-0.0601, 0.375, 2.4565], [-0.2164, 0.375, 2.8048], [-1.2512, 0.375, 2.7294]], collide: 1}
      - {kind: loft, a: [[-0.8043, 0.375, 1.7335], [-0.0601, 0.375, 2.4565], [-0.2164, 0.375, 2.8048], [-1.2512, 0.375, 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, 1.125, 2.0333], [-0.2133, 1.125, 2.7984], [-0.3896, 1.125, 3.137], [-1.4183, 1.125, 3.0014]], collide: 1}
      - {kind: loft, a: [[-0.9141, 1.125, 2.0333], [-0.2133, 1.125, 2.7984], [-0.3896, 1.125, 3.137], [-1.4183, 1.125, 3.0014]], b: [[-0.9755, 1.5, 2.1806], [-0.2973, 1.5, 2.9658], [-0.4834, 1.5, 3.2991], [-1.5077, 1.5, 3.1336]], collide: 1}
      - {kind: loft, a: [[-1.7111, -1.5, 3.4067], [-1.2592, -1.5, 4.3407], [-1.5253, -1.5, 4.6145], [-2.4718, -1.5, 4.1895]], b: [[-1.6137, -1.125, 3.2803], [-1.1347, -1.125, 4.2007], [-1.3927, -1.125, 4.4822], [-2.3512, -1.125, 4.0849]], collide: 1}
      - {kind: loft, a: [[-1.6137, -1.125, 3.2803], [-1.1347, -1.125, 4.2007], [-1.3927, -1.125, 4.4822], [-2.3512, -1.125, 4.0849]], 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: [[-1.43, -0.375, 3.0192], [-0.8983, -0.375, 3.9102], [-1.1394, -0.375, 4.2062], [-2.1195, -0.375, 3.8655]], collide: 1}
      - {kind: loft, a: [[-1.43, -0.375, 3.0192], [-0.8983, -0.375, 3.9102], [-1.1394, -0.375, 4.2062], [-2.1195, -0.375, 3.8655]], b: [[-1.344, 0.0, 2.8848], [-0.7865, 0.0, 3.7599], [-1.0189, 0.0, 4.0627], [-2.0085, 0.0, 3.7507]], collide: 1}
      - {kind: loft, a: [[-1.344, 0.0, 2.8848], [-0.7865, 0.0, 3.7599], [-1.0189, 0.0, 4.0627], [-2.0085, 0.0, 3.7507]], b: [[-1.43, 0.375, 3.0192], [-0.8983, 0.375, 3.9102], [-1.1394, 0.375, 4.2062], [-2.1195, 0.375, 3.8655]], collide: 1}
      - {kind: loft, a: [[-1.43, 0.375, 3.0192], [-0.8983, 0.375, 3.9102], [-1.1394, 0.375, 4.2062], [-2.1195, 0.375, 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, 1.125, 3.2803], [-1.1347, 1.125, 4.2007], [-1.3927, 1.125, 4.4822], [-2.3512, 1.125, 4.0849]], collide: 1}
      - {kind: loft, a: [[-1.6137, 1.125, 3.2803], [-1.1347, 1.125, 4.2007], [-1.3927, 1.125, 4.4822], [-2.3512, 1.125, 4.0849]], b: [[-1.7111, 1.5, 3.4067], [-1.2592, 1.5, 4.3407], [-1.5253, 1.5, 4.6145], [-2.4718, 1.5, 4.1895]], collide: 1}
      - {kind: loft, a: [[-2.739, -1.5, 4.4007], [-2.5442, -1.5, 5.4198], [-2.8721, -1.5, 5.6154], [-3.6764, -1.5, 4.9599]], b: [[-2.6121, -1.125, 4.3038], [-2.3877, -1.125, 5.3168], [-2.7098, -1.125, 5.5219], [-3.5328, -1.125, 4.8901]], collide: 1}
      - {kind: loft, a: [[-2.6121, -1.125, 4.3038], [-2.3877, -1.125, 5.3168], [-2.7098, -1.125, 5.5219], [-3.5328, -1.125, 4.8901]], 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: [[-2.3672, -0.375, 4.0991], [-2.0841, -0.375, 5.0974], [-2.3937, -0.375, 5.3208], [-3.2521, -0.375, 4.7381]], collide: 1}
      - {kind: loft, a: [[-2.3672, -0.375, 4.0991], [-2.0841, -0.375, 5.0974], [-2.3937, -0.375, 5.3208], [-3.2521, -0.375, 4.7381]], b: [[-2.2493, 0.0, 3.9915], [-1.9373, 0.0, 4.9811], [-2.2401, 0.0, 5.2135], [-3.1152, 0.0, 4.656]], collide: 1}
      - {kind: loft, a: [[-2.2493, 0.0, 3.9915], [-1.9373, 0.0, 4.9811], [-2.2401, 0.0, 5.2135], [-3.1152, 0.0, 4.656]], b: [[-2.3672, 0.375, 4.0991], [-2.0841, 0.375, 5.0974], [-2.3937, 0.375, 5.3208], [-3.2521, 0.375, 4.7381]], collide: 1}
      - {kind: loft, a: [[-2.3672, 0.375, 4.0991], [-2.0841, 0.375, 5.0974], [-2.3937, 0.375, 5.3208], [-3.2521, 0.375, 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, 1.125, 4.3038], [-2.3877, 1.125, 5.3168], [-2.7098, 1.125, 5.5219], [-3.5328, 1.125, 4.8901]], collide: 1}
      - {kind: loft, a: [[-2.6121, 1.125, 4.3038], [-2.3877, 1.125, 5.3168], [-2.7098, 1.125, 5.5219], [-3.5328, 1.125, 4.8901]], b: [[-2.739, 1.5, 4.4007], [-2.5442, 1.5, 5.4198], [-2.8721, 1.5, 5.6154], [-3.6764, 1.5, 4.9599]], collide: 1}
      - {kind: loft, a: [[-3.9891, -1.5, 5.0948], [-4.0647, -1.5, 6.1296], [-4.432, -1.5, 6.2337], [-5.0393, -1.5, 5.3923]], b: [[-3.8415, -1.125, 5.034], [-3.8869, -1.125, 6.0706], [-4.251, -1.125, 6.1853], [-4.8825, -1.125, 5.3621]], collide: 1}
      - {kind: loft, a: [[-3.8415, -1.125, 5.034], [-3.8869, -1.125, 6.0706], [-4.251, -1.125, 6.1853], [-4.8825, -1.125, 5.3621]], 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: [[-3.5519, -0.375, 4.8997], [-3.5369, -0.375, 5.9372], [-3.8937, -0.375, 6.0729], [-4.5721, -0.375, 5.2879]], collide: 1}
      - {kind: loft, a: [[-3.5519, -0.375, 4.8997], [-3.5369, -0.375, 5.9372], [-3.8937, -0.375, 6.0729], [-4.5721, -0.375, 5.2879]], b: [[-3.4102, 0.0, 4.8263], [-3.3649, 0.0, 5.8629], [-3.7176, 0.0, 6.009], [-4.4186, 0.0, 5.244]], collide: 1}
      - {kind: loft, a: [[-3.4102, 0.0, 4.8263], [-3.3649, 0.0, 5.8629], [-3.7176, 0.0, 6.009], [-4.4186, 0.0, 5.244]], b: [[-3.5519, 0.375, 4.8997], [-3.5369, 0.375, 5.9372], [-3.8937, 0.375, 6.0729], [-4.5721, 0.375, 5.2879]], collide: 1}
      - {kind: loft, a: [[-3.5519, 0.375, 4.8997], [-3.5369, 0.375, 5.9372], [-3.8937, 0.375, 6.0729], [-4.5721, 0.375, 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, 1.125, 5.034], [-3.8869, 1.125, 6.0706], [-4.251, 1.125, 6.1853], [-4.8825, 1.125, 5.3621]], collide: 1}
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      - {kind: loft, a: [[-5.3762, -1.5, 5.4416], [-5.7171, -1.5, 6.4216], [-6.0988, -1.5, 6.4271], [-6.4676, -1.5, 5.4573]], b: [[-5.2179, -1.125, 5.4211], [-5.5301, -1.125, 6.4106], [-5.9115, -1.125, 6.4272], [-6.3084, -1.125, 5.4686]], collide: 1}
      - {kind: loft, a: [[-5.2179, -1.125, 5.4211], [-5.5301, -1.125, 6.4106], [-5.9115, -1.125, 6.4272], [-6.3084, -1.125, 5.4686]], 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: [[-4.9035, -0.375, 5.3664], [-5.1574, -0.375, 6.3724], [-5.5372, -0.375, 6.4112], [-5.9893, -0.375, 5.4772]], collide: 1}
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      - {kind: loft, a: [[-4.7475, 0.0, 5.3321], [-4.9721, 0.0, 6.3451], [-5.3506, 0.0, 6.3949], [-5.8297, 0.0, 5.4746]], b: [[-4.9035, 0.375, 5.3664], [-5.1574, 0.375, 6.3724], [-5.5372, 0.375, 6.4112], [-5.9893, 0.375, 5.4772]], collide: 1}
      - {kind: loft, a: [[-4.9035, 0.375, 5.3664], [-5.1574, 0.375, 6.3724], [-5.5372, 0.375, 6.4112], [-5.9893, 0.375, 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, 1.125, 5.4211], [-5.5301, 1.125, 6.4106], [-5.9115, 1.125, 6.4272], [-6.3084, 1.125, 5.4686]], collide: 1}
      - {kind: loft, a: [[-5.2179, 1.125, 5.4211], [-5.5301, 1.125, 6.4106], [-5.9115, 1.125, 6.4272], [-6.3084, 1.125, 5.4686]], b: [[-5.3762, 1.5, 5.4416], [-5.7171, 1.5, 6.4216], [-6.0988, 1.5, 6.4271], [-6.4676, 1.5, 5.4573]], collide: 1}
      - {kind: loft, a: [[-6.8059, -1.5, 5.4176], [-7.3888, -1.5, 6.276], [-7.7589, -1.5, 6.1825], [-7.8642, -1.5, 5.1503]], b: [[-6.6477, -1.125, 5.4388], [-7.2053, -1.125, 6.3138], [-7.578, -1.125, 6.2311], [-7.7133, -1.125, 5.2024]], collide: 1}
      - {kind: loft, a: [[-6.6477, -1.125, 5.4388], [-7.2053, -1.125, 6.3138], [-7.578, -1.125, 6.2311], [-7.7133, -1.125, 5.2024]], 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: [[-6.3297, -0.375, 5.4673], [-6.8354, -0.375, 6.3733], [-7.2123, -0.375, 6.3125], [-7.4073, -0.375, 5.2934]], 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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      - {kind: loft, a: [[0.8572, 0.75, 2.3229], [-0.1708, 0.75, 2.1825], [-0.2516, 0.75, 1.8094], [0.6261, 0.75, 1.2561]], b: [[0.9039, 1.125, 2.4806], [-0.1267, 1.125, 2.3603], [-0.2147, 1.125, 1.9888], [0.6521, 1.125, 1.4186]], collide: 2}
      - {kind: loft, a: [[0.9039, 1.125, 2.4806], [-0.1267, 1.125, 2.3603], [-0.2147, 1.125, 1.9888], [0.6521, 1.125, 1.4186]], b: [[0.9536, 1.5, 2.6375], [-0.0791, 1.5, 2.5372], [-0.1744, 1.5, 2.1675], [0.6812, 1.5, 1.5805]], collide: 2}
  - id: stand
    shape: part
    pos: [0, 0, 0]
    fixed: true
    color: "#cfc6b4"
    pieces:
      - {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: 1, 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;
  # a little more ripple than No. 40's, from the bend at the middle of each tooth)
  - {type: ratio_range, out: j_b, in: j_a, min: -0.70, max: -0.635, 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: 0.1798}
    - {id: light, label: Light, links: [], timestep: 0.0008, integrator: discrete, ms: 0.354}
  output: j_b
  labels: {j_a: "Driver (24 V teeth)", j_b: "Follower (36 V teeth)"}
  expect: {default: -0.6667}
  proof: {label: "Teeth out of contact", sub: "the driver turns alone: the follower stops"}