number: 354
slug: crank-grooved-cross-head-uniform-velocity
name: Crank and cross-head with an endless groove
brown: "A modification of the crank and slotted cross-head, 93. The cross-head contains an endless groove in which the crank-wrist works, and which is formed to produce a uniform velocity of movement of the wrist or reciprocating-rod."
units: cm
sim: {timestep: 0.0002, integrator: implicitfast, iterations: 100, solver: PGS, duration_s: 8, floor: false, gravity: 0}
bodies:
  # the crank, its wrist working in the groove
  - id: crank
    shape: part
    pos: [0, 0, 0]
    density: 7800
    color: "#8f8a80"
    pieces:
      - {kind: disc, center: [0, 0], radius: 9.4, y: [0.2, 1.0]}
      - {kind: disc, center: [0, 8.0], radius: 0.5, y: [-1.8, 0.2], collide: 2, color: "#6f6a60"}
      - {kind: disc, center: [0, 0], radius: 1.0, y: [1.0, 3.0]}
  # the cross-head with its endless groove, and the reciprocating rod
  - id: head
    shape: part
    pos: [0, 0, 5.6]
    density: 2000
    color: "#b8ad97"
    pieces:
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      - {kind: rod, from: [0, -1.0, 10.5897], to: [0, -1.0, 24.5897], radius: 0.8}
      - {kind: rod, from: [0, -1.0, 0.6103], to: [0, -1.0, -13.3897], radius: 0.8}
  - id: frame
    shape: part
    pos: [0, 0, 0]
    fixed: true
    color: "#8f8a80"
    pieces:
      - {kind: poly, points: [[-3.5, 19.5897], [3.5, 19.5897], [3.5, 21.5897], [-3.5, 21.5897]], y: [-2.2, 0.2]}
      - {kind: poly, points: [[-3.5, -21.5897], [3.5, -21.5897], [3.5, -19.5897], [-3.5, -19.5897]], y: [-2.2, 0.2]}
      - {kind: poly, points: [[-16, -23.5897], [16, -23.5897], [16, 23.5897], [-16, 23.5897]], y: [3.0, 3.6], color: "#d8cfbb"}
joints:
  - {id: j_c, type: hinge, body: crank, axis: [0, 1, 0], damping: 0.01}   # the one driven joint; + : clockwise
  - {id: j_z, type: slide, body: head, axis: [0, 0, 1], damping: 0.05, range: [-13.2, 2]}   # the rod in its guides; + : up
contact: {solref: [0.002, 1.0], solimp: [0.95, 0.99, 0.0005], margin: 0}
driver: {joint: j_c, kind: velocity, rpm: 30, kv: 20, max_torque: 40}
checks:
  # while the wrist goes from 0.6 rad past the top to 0.6 rad short of the bottom, the rod falls at a uniform rate ...
  - {type: follow, out: j_z, in: j_c, expect: -0.03966, tol: 0.00119, min_r2: 0.998, settle_s: 2.191, window_s: 0.618}
  # ... and rises at the same rate on the other half turn
  - {type: follow, out: j_z, in: j_c, expect: 0.03966, tol: 0.00119, min_r2: 0.998, settle_s: 3.191, window_s: 0.618}
  # the stroke is twice A, once each turn
  - {type: position, joint: j_z, min: -11.5, max: 0.3, settle_s: 0.5, window_s: 7}
  - {type: penetration, max: 0.0005, settle_s: 0.5}
camera: {target: [0, 0, -5], position: [0, -121, -5], fov: 30}
display:
  output: j_z
  labels: {j_c: "Crank (driver)", j_z: "Cross-head and rod"}