# No. 191 (Brown 1868): "Scroll-gears for obtaining a gradually increasing speed."
#
# Model (cm): two equal scroll gears, each a logarithmic spiral of pitch r = 4 e^(0.2098 phi) over 300 degrees (radius 4 to 12),
# turning on shafts through their poles 16 apart. Two equal log spirals turned face to face roll on each other without slip at every angle
# (their radii in contact always sum to 16 and their arcs are equal), so the pitch curves carry 26 straight-flanked teeth (20 deg) on the driver and
# 27 on the driven at equal arc pitch 1.498, each its own convex piece square to the curve. The left gear is the one driven joint (10 turns a minute);
# the right one turns only by tooth contact, at -r1/r2 of its speed, which grows as the driver's radius in contact grows: from 0.36 to 2.62
# in 4.6 s, less than one turn, as scroll-gears can only work. Each gear carries a balance weight behind (a disc) that puts its centre of mass on its shaft. Generator: opencode-runs/batch11/gen191.py.
number: 191
slug: scroll-gears
name: Scroll-gears for a gradually increasing speed
brown: "Scroll-gears for obtaining a gradually increasing speed."
units: cm
sim:
  timestep: 0.0002
  integrator: implicitfast
  iterations: 100
  solver: CG
  multiccd: true
  duration_s: 4.6
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      - {kind: poly, points: [[8.0, 0.0], [10.8846, -6.4859], [10.3573, -6.8469]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [10.3573, -6.8469], [9.7894, -7.1668]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [9.7894, -7.1668], [9.1838, -7.4414]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [9.1838, -7.4414], [8.5441, -7.6667]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [8.5441, -7.6667], [7.874, -7.8387]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [7.874, -7.8387], [7.1777, -7.9538]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [7.1777, -7.9538], [6.4601, -8.009]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [6.4601, -8.009], [5.726, -8.0013]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [5.726, -8.0013], [4.9809, -7.9281]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [4.9809, -7.9281], [4.2303, -7.7876]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [4.2303, -7.7876], [3.4803, -7.5781]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [3.4803, -7.5781], [2.7369, -7.2986]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [2.7369, -7.2986], [2.0065, -6.9486]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [2.0065, -6.9486], [1.2956, -6.5281]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [1.2956, -6.5281], [0.6109, -6.0378]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [0.6109, -6.0378], [-0.0412, -5.4788]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [-0.0412, -5.4788], [-0.6539, -4.853]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [-0.6539, -4.853], [-1.2206, -4.1629]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [-1.2206, -4.1629], [-1.735, -3.4116]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [-1.735, -3.4116], [-2.1907, -2.6027]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [-2.1907, -2.6027], [-2.5817, -1.7406]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [-2.5817, -1.7406], [-2.9022, -0.8302]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [-2.9022, -0.8302], [-3.1468, 0.123]], y: [-0.3, 0.3], collide: 0}
      - {kind: poly, points: [[8.0, 0.0], [-3.1468, 0.123], [-3.3105, 1.1116]], y: [-0.3, 0.3], collide: 0}
      - {kind: disc, center: [8.0, 0], radius: 1.4, y: [-0.9, 0.9], collide: 0, color: "#8f8a80"}   # the hub
      - {kind: disc, center: [9.757, 2.4317], radius: 3.0, y: [0.65, 4.2891], collide: 0, color: "#6f6a60"}   # the balance weight, behind
      - {kind: poly, points: [[6.2427, 2.864], [7.0534, 3.4727], [6.145, 4.0648], [5.9274, 3.9014]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[7.316, 3.6016], [8.2872, 3.8924], [7.6397, 4.7621], [7.379, 4.6841]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[8.5902, 3.9281], [9.6034, 3.8896], [9.2714, 4.9219], [8.9995, 4.9322]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[9.9133, 3.8269], [10.8672, 3.4836], [10.8633, 4.5679], [10.6073, 4.66]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[11.1538, 3.3282], [11.9703, 2.7273], [12.2756, 3.7677], [12.0564, 3.929]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[12.2091, 2.4928], [12.8338, 1.6943], [13.4077, 2.6142], [13.2401, 2.8285]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[13.0069, 1.3988], [13.4076, 0.4674], [14.197, 1.2107], [14.0895, 1.4607]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[13.504, 0.1314], [13.6673, -0.8692], [14.6132, -0.339], [14.5693, -0.0705]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[13.6821, -1.2248], [13.6104, -2.2361], [14.653, -1.9382], [14.6722, -1.6667]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[13.5438, -2.5916], [13.2515, -3.5624], [14.334, -3.5011], [14.4125, -3.2405]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[13.108, -3.9002], [12.6181, -4.7878], [13.6893, -4.9555], [13.8208, -4.7173]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[12.4054, -5.093], [11.7467, -5.8637], [12.7623, -6.2437], [12.9391, -6.0369]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[11.4749, -6.124], [10.6796, -6.7528], [11.6025, -7.322], [11.816, -7.1532]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[10.3599, -6.9592], [9.4617, -7.4293], [10.2627, -8.1601], [10.5038, -8.0339]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[9.1062, -7.5754], [8.1383, -7.8772], [8.7956, -8.7395], [9.0554, -8.6585]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[7.7592, -7.9594], [6.7538, -8.0898], [7.2525, -9.0526], [7.5224, -9.0176]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[6.3629, -8.1068], [5.3498, -8.0679], [5.6814, -9.1003], [5.9533, -9.1107]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[4.9583, -8.0204], [3.9647, -7.8191], [4.1258, -8.8914], [4.3926, -8.9454]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[3.5829, -7.7095], [2.6327, -7.356], [2.625, -8.4402], [2.88, -8.5351]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[2.2697, -7.188], [1.3836, -6.6953], [1.2126, -7.7661], [1.4504, -7.8983]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[1.0474, -6.474], [0.2429, -5.8571], [-0.0828, -6.8914], [0.1331, -7.0569]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[-0.0598, -5.5881], [-0.7687, -4.8634], [-1.2378, -5.841], [-1.0475, -6.0355]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[-1.0323, -4.553], [-1.6347, -3.7376], [-2.2339, -4.6413], [-2.0722, -4.8601]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[-1.8549, -3.3925], [-2.3427, -2.5037], [-3.0575, -3.3191], [-2.9265, -3.5576]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[-2.5163, -2.1308], [-2.8842, -1.1861], [-3.6991, -1.9014], [-3.6003, -2.155]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[-3.009, -0.7921], [-3.2542, 0.1916], [-4.1532, -0.4146], [-4.0874, -0.6787]], y: [-0.6, 0.6], collide: 2}
      - {kind: poly, points: [[-3.3291, 0.5999], [-3.451, 1.6064], [-4.4179, 1.1158], [-4.3852, 0.8456]], y: [-0.6, 0.6], collide: 2}
  - id: frame
    shape: part
    pos: [0, 0, 0]
    fixed: true
    density: 7800
    color: "#cfc6b4"
    pieces:
      - {kind: disc, center: [-8.0, 0], radius: 0.6, y: [0.9, 4.6], collide: 0, color: "#6f6a60"}   # the shaft of the driver
      - {kind: disc, center: [8.0, 0], radius: 0.6, y: [0.9, 2.6], collide: 0, color: "#6f6a60"}   # and of the driven
      - {kind: poly, points: [[-10.0, -1.6], [10.0, -1.6], [10.0, 1.6], [-10.0, 1.6]], y: [4.6, 5.4], collide: 0}   # the frame behind
joints:
  - {id: j_a, type: hinge, body: ga, axis: [0, -1, 0], damping: 0.001}   # the one driven joint: the driver; + : counter-clockwise
  - {id: j_b, type: hinge, body: gb, axis: [0, -1, 0], damping: 0.01}   # the driven scroll; turns clockwise
contact: {solref: [0.002, 1.0], solimp: [0.95, 0.99, 0.0005], margin: 0}
driver: {joint: j_a, kind: velocity, rpm: 10.0, kv: 6, max_torque: 8}
checks:
  - {type: ratio, out: j_b, in: j_a, expect: -0.9230, tol: 0.0369, settle_s: 0.6, window_s: 3.6}   # mean of -r1/r2 over the window
  - {type: ratio_range, out: j_b, in: j_a, min: -2.459, max: -0.344, min_swing: 0.922, settle_s: 0.6, window_s: 3.6, slices: 12}   # the speed grows
  - {type: monotonic, joint: j_b, direction: -1, max_back: 0.02, settle_s: 0.3, window_s: 4.2}
  - {type: penetration, max: 0.001, settle_s: 0.5}
camera: {target: [0, 0, 0], position: [0, -62, 1.5], fov: 34}
display:
  output: j_b
  labels: {j_a: "Driver scroll (left)", j_b: "Driven scroll (right)"}