# No. 45, Frictional grooved gearing (Brown 1868): "a comparatively recent invention. The diagram to
# the right is an enlarged section, which can be more easily understood."
#
# Model (cm): two wheels whose rims are turned into V ridges and grooves (flanks at 30 deg to the
# radius, 0.8 apart): three ridges on the driver (pitch radius 6) wedge into the follower's grooves
# and four on the follower (pitch radius 9) into the driver's (batch7/gen045.py: each ridge a ring
# of convex segments, 331 on the driver and 503 on the follower, counts that cannot mesh like teeth). The follower's bearing is a carriage on a slide pulled towards the driver
# by a spring, so the ridges are wedged into the grooves: the flanks' normal force is the spring's
# divided by sin 30 deg, and the drive is by friction on the flanks alone (no teeth).
# Only the driver is motor-driven.
number: 45
slug: frictional-grooved-gearing
name: Frictional grooved gearing
brown: "Frictional grooved gearing\u2014a comparatively recent invention. The diagram to the right is an enlarged section, which can be more easily understood."
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: [0, 0, 0]
    density: 7800
    friction: 0.5
    color: "#e4d9bf"
    pieces:
      - {kind: disc, center: [0, 0], radius: 5.75, inner: 0.5, y: [-2.15, 2.15]}
      - {kind: rod, from: [0, -4.5, 0], to: [0, 4.5, 0], radius: 0.5, color: "#8f8a80"}
      - {kind: loft, a: [[5.7, -2.1732, 0.0], [6.25, -1.8557, 0.0], [6.25, -1.3443, 0.0], [5.7, -1.0268, 0.0]], b: [[5.699, -2.1732, 0.1082], [6.2489, -1.8557, 0.1186], [6.2489, -1.3443, 0.1186], [5.699, -1.0268, 0.1082]], collide: 1}
      - {kind: loft, a: [[5.699, -2.1732, 0.1082], [6.2489, -1.8557, 0.1186], [6.2489, -1.3443, 0.1186], [5.699, -1.0268, 0.1082]], b: [[5.6959, -2.1732, 0.2163], [6.2455, -1.8557, 0.2372], [6.2455, -1.3443, 0.2372], [5.6959, -1.0268, 0.2163]], collide: 1}
      - {kind: loft, a: [[5.6959, -2.1732, 0.2163], [6.2455, -1.8557, 0.2372], [6.2455, -1.3443, 0.2372], [5.6959, -1.0268, 0.2163]], b: [[5.6908, -2.1732, 0.3244], [6.2399, -1.8557, 0.3557], [6.2399, -1.3443, 0.3557], [5.6908, -1.0268, 0.3244]], collide: 1}
      - {kind: loft, a: [[5.6908, -2.1732, 0.3244], [6.2399, -1.8557, 0.3557], [6.2399, -1.3443, 0.3557], [5.6908, -1.0268, 0.3244]], b: [[5.6836, -2.1732, 0.4324], [6.232, -1.8557, 0.4741], [6.232, -1.3443, 0.4741], [5.6836, -1.0268, 0.4324]], collide: 1}
      - {kind: loft, a: [[5.6836, -2.1732, 0.4324], [6.232, -1.8557, 0.4741], [6.232, -1.3443, 0.4741], [5.6836, -1.0268, 0.4324]], b: [[5.6743, -2.1732, 0.5402], [6.2219, -1.8557, 0.5923], [6.2219, -1.3443, 0.5923], [5.6743, -1.0268, 0.5402]], collide: 1}
      - {kind: loft, a: [[5.6743, -2.1732, 0.5402], [6.2219, -1.8557, 0.5923], [6.2219, -1.3443, 0.5923], [5.6743, -1.0268, 0.5402]], b: [[5.6631, -2.1732, 0.6478], [6.2095, -1.8557, 0.7103], [6.2095, -1.3443, 0.7103], [5.6631, -1.0268, 0.6478]], collide: 1}
      - {kind: loft, a: [[5.6631, -2.1732, 0.6478], [6.2095, -1.8557, 0.7103], [6.2095, -1.3443, 0.7103], [5.6631, -1.0268, 0.6478]], b: [[5.6498, -2.1732, 0.7552], [6.1949, -1.8557, 0.828], [6.1949, -1.3443, 0.828], [5.6498, -1.0268, 0.7552]], collide: 1}
      - {kind: loft, a: [[5.6498, -2.1732, 0.7552], [6.1949, -1.8557, 0.828], [6.1949, -1.3443, 0.828], [5.6498, -1.0268, 0.7552]], b: [[5.6344, -2.1732, 0.8623], [6.1781, -1.8557, 0.9455], [6.1781, -1.3443, 0.9455], [5.6344, -1.0268, 0.8623]], collide: 1}
      - {kind: loft, a: [[5.6344, -2.1732, 0.8623], [6.1781, -1.8557, 0.9455], [6.1781, -1.3443, 0.9455], [5.6344, -1.0268, 0.8623]], b: [[5.617, -2.1732, 0.9691], [6.159, -1.8557, 1.0626], [6.159, -1.3443, 1.0626], [5.617, -1.0268, 0.9691]], collide: 1}
      - {kind: loft, a: [[5.617, -2.1732, 0.9691], [6.159, -1.8557, 1.0626], [6.159, -1.3443, 1.0626], [5.617, -1.0268, 0.9691]], b: [[5.5976, -2.1732, 1.0755], [6.1377, -1.8557, 1.1793], [6.1377, -1.3443, 1.1793], [5.5976, -1.0268, 1.0755]], collide: 1}
      - {kind: loft, a: [[5.5976, -2.1732, 1.0755], [6.1377, -1.8557, 1.1793], [6.1377, -1.3443, 1.1793], [5.5976, -1.0268, 1.0755]], b: [[5.5762, -2.1732, 1.1816], [6.1142, -1.8557, 1.2956], [6.1142, -1.3443, 1.2956], [5.5762, -1.0268, 1.1816]], collide: 1}
      - {kind: loft, a: [[5.5762, -2.1732, 1.1816], [6.1142, -1.8557, 1.2956], [6.1142, -1.3443, 1.2956], [5.5762, -1.0268, 1.1816]], b: [[5.5528, -2.1732, 1.2872], [6.0886, -1.8557, 1.4114], [6.0886, -1.3443, 1.4114], [5.5528, -1.0268, 1.2872]], collide: 1}
      - {kind: loft, a: [[5.5528, -2.1732, 1.2872], [6.0886, -1.8557, 1.4114], [6.0886, -1.3443, 1.4114], [5.5528, -1.0268, 1.2872]], b: [[5.5273, -2.1732, 1.3924], [6.0607, -1.8557, 1.5267], [6.0607, -1.3443, 1.5267], [5.5273, -1.0268, 1.3924]], collide: 1}
      - {kind: loft, a: [[5.5273, -2.1732, 1.3924], [6.0607, -1.8557, 1.5267], [6.0607, -1.3443, 1.5267], [5.5273, -1.0268, 1.3924]], b: [[5.4999, -2.1732, 1.497], [6.0306, -1.8557, 1.6415], [6.0306, -1.3443, 1.6415], [5.4999, -1.0268, 1.497]], collide: 1}
      - {kind: loft, a: [[5.4999, -2.1732, 1.497], [6.0306, -1.8557, 1.6415], [6.0306, -1.3443, 1.6415], [5.4999, -1.0268, 1.497]], b: [[5.4705, -2.1732, 1.6012], [5.9983, -1.8557, 1.7557], [5.9983, -1.3443, 1.7557], [5.4705, -1.0268, 1.6012]], collide: 1}
      - {kind: loft, a: [[5.4705, -2.1732, 1.6012], [5.9983, -1.8557, 1.7557], [5.9983, -1.3443, 1.7557], [5.4705, -1.0268, 1.6012]], b: [[5.4391, -2.1732, 1.7047], [5.9639, -1.8557, 1.8692], [5.9639, -1.3443, 1.8692], [5.4391, -1.0268, 1.7047]], collide: 1}
      - {kind: loft, a: [[5.4391, -2.1732, 1.7047], [5.9639, -1.8557, 1.8692], [5.9639, -1.3443, 1.8692], [5.4391, -1.0268, 1.7047]], b: [[5.4058, -2.1732, 1.8076], [5.9274, -1.8557, 1.9821], [5.9274, -1.3443, 1.9821], [5.4058, -1.0268, 1.8076]], collide: 1}
      - {kind: loft, a: [[5.4058, -2.1732, 1.8076], [5.9274, -1.8557, 1.9821], [5.9274, -1.3443, 1.9821], [5.4058, -1.0268, 1.8076]], b: [[5.3705, -2.1732, 1.9099], [5.8887, -1.8557, 2.0942], [5.8887, -1.3443, 2.0942], [5.3705, -1.0268, 1.9099]], collide: 1}
      - {kind: loft, a: [[5.3705, -2.1732, 1.9099], [5.8887, -1.8557, 2.0942], [5.8887, -1.3443, 2.0942], [5.3705, -1.0268, 1.9099]], b: [[5.3333, -2.1732, 2.0115], [5.8479, -1.8557, 2.2056], [5.8479, -1.3443, 2.2056], [5.3333, -1.0268, 2.0115]], collide: 1}
      - {kind: loft, a: [[5.3333, -2.1732, 2.0115], [5.8479, -1.8557, 2.2056], [5.8479, -1.3443, 2.2056], [5.3333, -1.0268, 2.0115]], b: [[5.2941, -2.1732, 2.1124], [5.805, -1.8557, 2.3162], [5.805, -1.3443, 2.3162], [5.2941, -1.0268, 2.1124]], collide: 1}
      - {kind: loft, a: [[5.2941, -2.1732, 2.1124], [5.805, -1.8557, 2.3162], [5.805, -1.3443, 2.3162], [5.2941, -1.0268, 2.1124]], b: [[5.2531, -2.1732, 2.2125], [5.76, -1.8557, 2.426], [5.76, -1.3443, 2.426], [5.2531, -1.0268, 2.2125]], collide: 1}
      - {kind: loft, a: [[5.2531, -2.1732, 2.2125], [5.76, -1.8557, 2.426], [5.76, -1.3443, 2.426], [5.2531, -1.0268, 2.2125]], b: [[5.2101, -2.1732, 2.3118], [5.7129, -1.8557, 2.5349], [5.7129, -1.3443, 2.5349], [5.2101, -1.0268, 2.3118]], collide: 1}
      - {kind: loft, a: [[5.2101, -2.1732, 2.3118], [5.7129, -1.8557, 2.5349], [5.7129, -1.3443, 2.5349], [5.2101, -1.0268, 2.3118]], b: [[5.1653, -2.1732, 2.4103], [5.6637, -1.8557, 2.6429], [5.6637, -1.3443, 2.6429], [5.1653, -1.0268, 2.4103]], collide: 1}
      - {kind: loft, a: [[5.1653, -2.1732, 2.4103], [5.6637, -1.8557, 2.6429], [5.6637, -1.3443, 2.6429], [5.1653, -1.0268, 2.4103]], b: [[5.1186, -2.1732, 2.5079], [5.6125, -1.8557, 2.7499], [5.6125, -1.3443, 2.7499], [5.1186, -1.0268, 2.5079]], collide: 1}
      - {kind: loft, a: [[5.1186, -2.1732, 2.5079], [5.6125, -1.8557, 2.7499], [5.6125, -1.3443, 2.7499], [5.1186, -1.0268, 2.5079]], b: [[5.0701, -2.1732, 2.6046], [5.5593, -1.8557, 2.8559], [5.5593, -1.3443, 2.8559], [5.0701, -1.0268, 2.6046]], collide: 1}
      - {kind: loft, a: [[5.0701, -2.1732, 2.6046], [5.5593, -1.8557, 2.8559], [5.5593, -1.3443, 2.8559], [5.0701, -1.0268, 2.6046]], b: [[5.0198, -2.1732, 2.7004], [5.5041, -1.8557, 2.9609], [5.5041, -1.3443, 2.9609], [5.0198, -1.0268, 2.7004]], collide: 1}
      - {kind: loft, a: [[5.0198, -2.1732, 2.7004], [5.5041, -1.8557, 2.9609], [5.5041, -1.3443, 2.9609], [5.0198, -1.0268, 2.7004]], b: [[4.9676, -2.1732, 2.7952], [5.4469, -1.8557, 3.0649], [5.4469, -1.3443, 3.0649], [4.9676, -1.0268, 2.7952]], collide: 1}
      - {kind: loft, a: [[4.9676, -2.1732, 2.7952], [5.4469, -1.8557, 3.0649], [5.4469, -1.3443, 3.0649], [4.9676, -1.0268, 2.7952]], b: [[4.9136, -2.1732, 2.889], [5.3878, -1.8557, 3.1677], [5.3878, -1.3443, 3.1677], [4.9136, -1.0268, 2.889]], collide: 1}
      - {kind: loft, a: [[4.9136, -2.1732, 2.889], [5.3878, -1.8557, 3.1677], [5.3878, -1.3443, 3.1677], [4.9136, -1.0268, 2.889]], b: [[4.8579, -2.1732, 2.9817], [5.3267, -1.8557, 3.2694], [5.3267, -1.3443, 3.2694], [4.8579, -1.0268, 2.9817]], collide: 1}
      - {kind: loft, a: [[4.8579, -2.1732, 2.9817], [5.3267, -1.8557, 3.2694], [5.3267, -1.3443, 3.2694], [4.8579, -1.0268, 2.9817]], b: [[4.8005, -2.1732, 3.0734], [5.2637, -1.8557, 3.3699], [5.2637, -1.3443, 3.3699], [4.8005, -1.0268, 3.0734]], collide: 1}
      - {kind: loft, a: [[4.8005, -2.1732, 3.0734], [5.2637, -1.8557, 3.3699], [5.2637, -1.3443, 3.3699], [4.8005, -1.0268, 3.0734]], b: [[4.7413, -2.1732, 3.1639], [5.1987, -1.8557, 3.4692], [5.1987, -1.3443, 3.4692], [4.7413, -1.0268, 3.1639]], collide: 1}
      - {kind: loft, a: [[4.7413, -2.1732, 3.1639], [5.1987, -1.8557, 3.4692], [5.1987, -1.3443, 3.4692], [4.7413, -1.0268, 3.1639]], b: [[4.6803, -2.1732, 3.2534], [5.132, -1.8557, 3.5673], [5.132, -1.3443, 3.5673], [4.6803, -1.0268, 3.2534]], collide: 1}
      - {kind: loft, a: [[4.6803, -2.1732, 3.2534], [5.132, -1.8557, 3.5673], [5.132, -1.3443, 3.5673], [4.6803, -1.0268, 3.2534]], b: [[4.6177, -2.1732, 3.3416], [5.0633, -1.8557, 3.6641], [5.0633, -1.3443, 3.6641], [4.6177, -1.0268, 3.3416]], collide: 1}
      - {kind: loft, a: [[4.6177, -2.1732, 3.3416], [5.0633, -1.8557, 3.6641], [5.0633, -1.3443, 3.6641], [4.6177, -1.0268, 3.3416]], b: [[4.5535, -2.1732, 3.4287], [4.9929, -1.8557, 3.7595], [4.9929, -1.3443, 3.7595], [4.5535, -1.0268, 3.4287]], collide: 1}
      - {kind: loft, a: [[4.5535, -2.1732, 3.4287], [4.9929, -1.8557, 3.7595], [4.9929, -1.3443, 3.7595], [4.5535, -1.0268, 3.4287]], b: [[4.4876, -2.1732, 3.5145], [4.9206, -1.8557, 3.8536], [4.9206, -1.3443, 3.8536], [4.4876, -1.0268, 3.5145]], collide: 1}
      - {kind: loft, a: [[4.4876, -2.1732, 3.5145], [4.9206, -1.8557, 3.8536], [4.9206, -1.3443, 3.8536], [4.4876, -1.0268, 3.5145]], b: [[4.4201, -2.1732, 3.599], [4.8466, -1.8557, 3.9463], [4.8466, -1.3443, 3.9463], [4.4201, -1.0268, 3.599]], collide: 1}
      - {kind: loft, a: [[4.4201, -2.1732, 3.599], [4.8466, -1.8557, 3.9463], [4.8466, -1.3443, 3.9463], [4.4201, -1.0268, 3.599]], b: [[4.351, -2.1732, 3.6823], [4.7708, -1.8557, 4.0376], [4.7708, -1.3443, 4.0376], [4.351, -1.0268, 3.6823]], collide: 1}
      - {kind: loft, a: [[4.351, -2.1732, 3.6823], [4.7708, -1.8557, 4.0376], [4.7708, -1.3443, 4.0376], [4.351, -1.0268, 3.6823]], b: [[4.2803, -2.1732, 3.7642], [4.6933, -1.8557, 4.1274], [4.6933, -1.3443, 4.1274], [4.2803, -1.0268, 3.7642]], collide: 1}
      - {kind: loft, a: [[4.2803, -2.1732, 3.7642], [4.6933, -1.8557, 4.1274], [4.6933, -1.3443, 4.1274], [4.2803, -1.0268, 3.7642]], b: [[4.2081, -2.1732, 3.8448], [4.6141, -1.8557, 4.2158], [4.6141, -1.3443, 4.2158], [4.2081, -1.0268, 3.8448]], collide: 1}
      - {kind: loft, a: [[4.2081, -2.1732, 3.8448], [4.6141, -1.8557, 4.2158], [4.6141, -1.3443, 4.2158], [4.2081, -1.0268, 3.8448]], b: [[4.1343, -2.1732, 3.9239], [4.5332, -1.8557, 4.3026], [4.5332, -1.3443, 4.3026], [4.1343, -1.0268, 3.9239]], collide: 1}
      - {kind: loft, a: [[4.1343, -2.1732, 3.9239], [4.5332, -1.8557, 4.3026], [4.5332, -1.3443, 4.3026], [4.1343, -1.0268, 3.9239]], b: [[4.0591, -2.1732, 4.0017], [4.4508, -1.8557, 4.3878], [4.4508, -1.3443, 4.3878], [4.0591, -1.0268, 4.0017]], collide: 1}
      - {kind: loft, a: [[4.0591, -2.1732, 4.0017], [4.4508, -1.8557, 4.3878], [4.4508, -1.3443, 4.3878], [4.0591, -1.0268, 4.0017]], b: [[3.9824, -2.1732, 4.078], [4.3667, -1.8557, 4.4715], [4.3667, -1.3443, 4.4715], [3.9824, -1.0268, 4.078]], collide: 1}
      - {kind: loft, a: [[3.9824, -2.1732, 4.078], [4.3667, -1.8557, 4.4715], [4.3667, -1.3443, 4.4715], [3.9824, -1.0268, 4.078]], b: [[3.9043, -2.1732, 4.1529], [4.281, -1.8557, 4.5536], [4.281, -1.3443, 4.5536], [3.9043, -1.0268, 4.1529]], collide: 1}
      - {kind: loft, a: [[3.9043, -2.1732, 4.1529], [4.281, -1.8557, 4.5536], [4.281, -1.3443, 4.5536], [3.9043, -1.0268, 4.1529]], b: [[3.8248, -2.1732, 4.2263], [4.1938, -1.8557, 4.6341], [4.1938, -1.3443, 4.6341], [3.8248, -1.0268, 4.2263]], collide: 1}
      - {kind: loft, a: [[3.8248, -2.1732, 4.2263], [4.1938, -1.8557, 4.6341], [4.1938, -1.3443, 4.6341], [3.8248, -1.0268, 4.2263]], b: [[3.7438, -2.1732, 4.2981], [4.1051, -1.8557, 4.7128], [4.1051, -1.3443, 4.7128], [3.7438, -1.0268, 4.2981]], collide: 1}
      - {kind: loft, a: [[3.7438, -2.1732, 4.2981], [4.1051, -1.8557, 4.7128], [4.1051, -1.3443, 4.7128], [3.7438, -1.0268, 4.2981]], b: [[3.6616, -2.1732, 4.3684], [4.0149, -1.8557, 4.7899], [4.0149, -1.3443, 4.7899], [3.6616, -1.0268, 4.3684]], collide: 1}
      - {kind: loft, a: [[3.6616, -2.1732, 4.3684], [4.0149, -1.8557, 4.7899], [4.0149, -1.3443, 4.7899], [3.6616, -1.0268, 4.3684]], b: [[3.578, -2.1732, 4.4371], [3.9233, -1.8557, 4.8652], [3.9233, -1.3443, 4.8652], [3.578, -1.0268, 4.4371]], collide: 1}
      - {kind: loft, a: [[3.578, -2.1732, 4.4371], [3.9233, -1.8557, 4.8652], [3.9233, -1.3443, 4.8652], [3.578, -1.0268, 4.4371]], b: [[3.4931, -2.1732, 4.5042], [3.8302, -1.8557, 4.9388], [3.8302, -1.3443, 4.9388], [3.4931, -1.0268, 4.5042]], collide: 1}
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  - id: carriage
    shape: part
    pos: [15.05, 0, 0]
    density: 2500
    color: "#b8ad97"
    pieces:
      - {kind: poly, points: [[12.5, -1.2], [17.6, -1.2], [17.6, 1.2], [12.5, 1.2]], y: [4.2, 5.2]}
      - {kind: rod, from: [15.05, 3.6, 0], to: [15.05, 5.2, 0], radius: 0.8}
  - id: gb
    shape: part
    pos: [15.05, 0, 0]
    mount: carriage
    density: 7800
    friction: 0.5
    color: "#e8dec6"
    pieces:
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      - {kind: disc, center: [15.05, 0], radius: 1.6, inner: 0.5, y: [-3.5, 3.5]}
      - {kind: rod, from: [15.05, -4.5, 0], to: [15.05, 4.0, 0], radius: 0.5, color: "#8f8a80"}
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      - {kind: loft, a: [[23.6173, 1.8268, -1.5137], [24.1589, 2.1443, -1.6094], [24.1589, 2.6557, -1.6094], [23.6173, 2.9732, -1.5137]], b: [[23.6355, 1.8268, -1.4066], [24.1783, 2.1443, -1.4955], [24.1783, 2.6557, -1.4955], [23.6355, 2.9732, -1.4066]], collide: 2}
      - {kind: loft, a: [[23.6355, 1.8268, -1.4066], [24.1783, 2.1443, -1.4955], [24.1783, 2.6557, -1.4955], [23.6355, 2.9732, -1.4066]], b: [[23.6524, 1.8268, -1.2992], [24.1963, 2.1443, -1.3814], [24.1963, 2.6557, -1.3814], [23.6524, 2.9732, -1.2992]], collide: 2}
      - {kind: loft, a: [[23.6524, 1.8268, -1.2992], [24.1963, 2.1443, -1.3814], [24.1963, 2.6557, -1.3814], [23.6524, 2.9732, -1.2992]], b: [[23.668, 1.8268, -1.1917], [24.2128, 2.1443, -1.267], [24.2128, 2.6557, -1.267], [23.668, 2.9732, -1.1917]], collide: 2}
      - {kind: loft, a: [[23.668, 1.8268, -1.1917], [24.2128, 2.1443, -1.267], [24.2128, 2.6557, -1.267], [23.668, 2.9732, -1.1917]], b: [[23.6822, 1.8268, -1.0839], [24.2279, 2.1443, -1.1525], [24.2279, 2.6557, -1.1525], [23.6822, 2.9732, -1.0839]], collide: 2}
      - {kind: loft, a: [[23.6822, 1.8268, -1.0839], [24.2279, 2.1443, -1.1525], [24.2279, 2.6557, -1.1525], [23.6822, 2.9732, -1.0839]], b: [[23.6951, 1.8268, -0.976], [24.2416, 2.1443, -1.0377], [24.2416, 2.6557, -1.0377], [23.6951, 2.9732, -0.976]], collide: 2}
      - {kind: loft, a: [[23.6951, 1.8268, -0.976], [24.2416, 2.1443, -1.0377], [24.2416, 2.6557, -1.0377], [23.6951, 2.9732, -0.976]], b: [[23.7066, 1.8268, -0.868], [24.2539, 2.1443, -0.9228], [24.2539, 2.6557, -0.9228], [23.7066, 2.9732, -0.868]], collide: 2}
      - {kind: loft, a: [[23.7066, 1.8268, -0.868], [24.2539, 2.1443, -0.9228], [24.2539, 2.6557, -0.9228], [23.7066, 2.9732, -0.868]], b: [[23.7168, 1.8268, -0.7598], [24.2647, 2.1443, -0.8078], [24.2647, 2.6557, -0.8078], [23.7168, 2.9732, -0.7598]], collide: 2}
      - {kind: loft, a: [[23.7168, 1.8268, -0.7598], [24.2647, 2.1443, -0.8078], [24.2647, 2.6557, -0.8078], [23.7168, 2.9732, -0.7598]], b: [[23.7256, 1.8268, -0.6514], [24.274, 2.1443, -0.6926], [24.274, 2.6557, -0.6926], [23.7256, 2.9732, -0.6514]], collide: 2}
      - {kind: loft, a: [[23.7256, 1.8268, -0.6514], [24.274, 2.1443, -0.6926], [24.274, 2.6557, -0.6926], [23.7256, 2.9732, -0.6514]], b: [[23.733, 1.8268, -0.543], [24.282, 2.1443, -0.5774], [24.282, 2.6557, -0.5774], [23.733, 2.9732, -0.543]], collide: 2}
      - {kind: loft, a: [[23.733, 1.8268, -0.543], [24.282, 2.1443, -0.5774], [24.282, 2.6557, -0.5774], [23.733, 2.9732, -0.543]], b: [[23.7391, 1.8268, -0.4345], [24.2885, 2.1443, -0.462], [24.2885, 2.6557, -0.462], [23.7391, 2.9732, -0.4345]], collide: 2}
      - {kind: loft, a: [[23.7391, 1.8268, -0.4345], [24.2885, 2.1443, -0.462], [24.2885, 2.6557, -0.462], [23.7391, 2.9732, -0.4345]], b: [[23.7439, 1.8268, -0.3259], [24.2935, 2.1443, -0.3466], [24.2935, 2.6557, -0.3466], [23.7439, 2.9732, -0.3259]], collide: 2}
      - {kind: loft, a: [[23.7439, 1.8268, -0.3259], [24.2935, 2.1443, -0.3466], [24.2935, 2.6557, -0.3466], [23.7439, 2.9732, -0.3259]], b: [[23.7473, 1.8268, -0.2173], [24.2971, 2.1443, -0.2311], [24.2971, 2.6557, -0.2311], [23.7473, 2.9732, -0.2173]], collide: 2}
      - {kind: loft, a: [[23.7473, 1.8268, -0.2173], [24.2971, 2.1443, -0.2311], [24.2971, 2.6557, -0.2311], [23.7473, 2.9732, -0.2173]], b: [[23.7493, 1.8268, -0.1087], [24.2993, 2.1443, -0.1155], [24.2993, 2.6557, -0.1155], [23.7493, 2.9732, -0.1087]], collide: 2}
      - {kind: loft, a: [[23.7493, 1.8268, -0.1087], [24.2993, 2.1443, -0.1155], [24.2993, 2.6557, -0.1155], [23.7493, 2.9732, -0.1087]], b: [[23.75, 1.8268, -0.0], [24.3, 2.1443, -0.0], [24.3, 2.6557, -0.0], [23.75, 2.9732, -0.0]], collide: 2}
  - id: frame
    shape: part
    pos: [0, 0, 0]
    fixed: true
    color: "#cfc6b4"
    pieces:
      - {kind: poly, points: [[-1.5, -12], [1.5, -12], [0.9, 0], [-0.9, 0]], y: [4.5, 5.5]}
      - {kind: disc, center: [0, 0], radius: 1.2, y: [4.5, 5.5]}
      - {kind: poly, points: [[10, -1.6], [22, -1.6], [22, -1.2], [10, -1.2]], y: [4.0, 5.4]}
      - {kind: poly, points: [[10, 1.2], [22, 1.2], [22, 1.6], [10, 1.6]], y: [4.0, 5.4]}
      - {kind: poly, points: [[20.8, -12], [22, -12], [22, 1.6], [20.8, 1.6]], y: [4.0, 5.4]}
      - {kind: poly, points: [[-8, -13], [26, -13], [26, -12], [-8, -12]], y: [3, 7], color: "#b9b09c"}
joints:
  - {id: j_a, type: hinge, body: ga, axis: [0, -1, 0], damping: 0.001}
  - {id: j_press, type: slide, body: carriage, axis: [1, 0, 0], range: [-1, 1], stiffness: 4000, springref: -0.15, damping: 200}
  - {id: j_b, type: hinge, body: gb, axis: [0, -1, 0], damping: 0.002}
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:
  # By friction alone. The ridges bear on the flanks at their tips and roots (half the load each), where
  # they would roll at 6.25/8.75 = 0.714 and 5.75/9.25 = 0.622: the two fight, the flanks rub (the
  # known fault of grooved gearing), and the follower creeps to about -0.61 (pitch-line ratio -0.667).
  - {type: ratio, out: j_b, in: j_a, expect: -0.61, tol: 0.03, settle_s: 1, window_s: 5}
  # the spring holds the ridges home in the grooves
  - {type: position, joint: j_press, min: -0.07, max: -0.03, settle_s: 1, window_s: 5}
  - {type: penetration, max: 0.001, settle_s: 0.5}
camera: {target: [7.5, 0, -2], position: [14, -56, 24], fov: 30}
display:
  output: j_b
  labels: {j_a: "Driver (grooved, r 6)", j_b: "Follower (grooved, r 9)", j_press: "Sprung bearing"}
  expect: {default: -0.6667}
  proof: {label: "Flanks made frictionless", sub: "the ridges still wedge into the grooves, but nothing grips: the follower stands"}