# No. 152 (Brown 1868): "An ellipsograph. The traverse bar (shown in an oblique position) carries two studs which slide in the grooves of the cross-piece. By turning the traverse bar an attached pencil is made to describe an ellipse by the rectilinear movement of the studs in the grooves."
#
# Model (cm, no gravity; a plan): the stud A runs in the groove along x (j_x) and the stud B in the groove along z (j_z), 8 cm apart on the traverse bar. The bar turns on the stud A (the one driven joint, 20 turns a minute, + : clockwise); the stud B is pinned to the
# bar and held in its own groove, so the bar can only go round with A drawn out and in. The pencil is fixed on the bar at 1.5 times the way from A to B (12 cm from A), and so describes an ellipse of semi-axes 4 and 12 cm.
# Generator: opencode-runs/batch10/gen152.py.
number: 152
slug: ellipsograph
name: An ellipsograph
brown: "An ellipsograph. The traverse bar (shown in an oblique position) carries two studs which slide in the grooves of the cross-piece. By turning the traverse bar an attached pencil is made to describe an ellipse by the rectilinear movement of the studs in the grooves."
units: cm
sim:
  timestep: 0.0005
  integrator: implicitfast
  iterations: 100
  solver: PGS
  duration_s: 9.0
  floor: false
  gravity: 0
bodies:
  - id: frame
    shape: part
    pos: [0, 0, 0]
    fixed: true
    color: "#cfc6b4"
    pieces:
      - {kind: poly, points: [[-11.2, -14.6], [11.2, -14.6], [11.2, 14.6], [-11.2, 14.6]], y: [0.2, 1.4], collide: 0, color: "#cfc6b4"}
      - {kind: poly, points: [[-9.0, 0.7], [9.0, 0.7], [9.0, -0.7], [-9.0, -0.7]], y: [-0.1, 0.2], collide: 0, color: "#4a4338"}
      - {kind: poly, points: [[-0.7, -9.0], [-0.7, 9.0], [0.7, 9.0], [0.7, -9.0]], y: [-0.1, 0.2], collide: 0, color: "#4a4338"}
      - {kind: poly, points: [[3.9, -0.0015], [3.8848, 1.0444], [4.0848, 1.0473], [4.1, 0.0015]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
      - {kind: poly, points: [[3.8849, 1.0415], [3.8393, 2.0794], [4.0391, 2.0882], [4.0847, 1.0503]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
      - {kind: poly, points: [[3.8395, 2.0764], [3.764, 3.0985], [3.9634, 3.1132], [4.039, 2.0911]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
      - {kind: poly, points: [[3.7643, 3.0954], [3.6593, 4.0938], [3.8582, 4.1147], [3.9632, 3.1163]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
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      - {kind: poly, points: [[3.5267, 5.0543], [3.3656, 5.9829], [3.5626, 6.0171], [3.7238, 5.0885]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
      - {kind: poly, points: [[3.3663, 5.9792], [3.1788, 6.8621], [3.3744, 6.9037], [3.5619, 6.0208]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
      - {kind: poly, points: [[3.1797, 6.8581], [2.9673, 7.6887], [3.1611, 7.7382], [3.3735, 6.9077]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
      - {kind: poly, points: [[2.9685, 7.6842], [2.7328, 8.4561], [2.9241, 8.5145], [3.1598, 7.7427]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
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      - {kind: poly, points: [[-3.9, 0.0015], [-3.8848, -1.0444], [-4.0848, -1.0473], [-4.1, -0.0015]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
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      - {kind: poly, points: [[3.6593, -4.0938], [3.7643, -3.0954], [3.9632, -3.1163], [3.8582, -4.1147]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
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      - {kind: poly, points: [[3.8848, -1.0444], [3.9, 0.0015], [4.1, -0.0015], [4.0848, -1.0473]], y: [-0.12, 0.2], collide: 0, color: "#a23b2a"}
  - id: stud_a
    shape: part
    pos: [5.1423, 0, 0.0]
    mass: 0.3
    color: "#8f8a80"
    pieces:
      - {kind: rod, from: [5.1423, 0.2, 0.0], to: [5.1423, -2.6, 0.0], radius: 0.48, collide: 0, color: "#8f8a80"}
  - id: stud_b
    shape: part
    pos: [0.0, 0, 6.1284]
    mass: 0.3
    color: "#8f8a80"
    pieces:
      - {kind: rod, from: [0.0, 0.2, 6.1284], to: [0.0, -2.6, 6.1284], radius: 0.48, collide: 0, color: "#8f8a80"}
  - id: bar
    shape: part
    pos: [5.1423, 0, 0.0]
    mount: stud_a
    mass: 0.5
    color: "#b8ad97"
    pieces:
      - {kind: poly, points: [[5.2229, -1.1073], [-3.6476, 9.4642], [-2.6517, 10.2998], [6.2187, -0.2716]], y: [-2.4, -1.6], collide: 0, color: "#b8ad97"}
      - {kind: disc, center: [5.1423, 0.0], radius: 0.85, y: [-2.9, -2.4], color: "#8f8a80"}
      - {kind: disc, center: [0.0, 6.1284], radius: 0.85, y: [-2.9, -2.4], color: "#8f8a80"}
      - {kind: rod, from: [-2.5712, -1.6, 9.1925], to: [-2.5712, 0.2, 9.1925], radius: 0.22, collide: 0, color: "#a23b2a"}
      - {kind: disc, center: [-2.5712, 9.1925], radius: 0.6, y: [-2.9, -2.4], color: "#a23b2a"}
joints:
  - {id: j_x, type: slide, body: stud_a, axis: [1, 0, 0], damping: 0.02}   # the stud A in its groove; + : to the right
  - {id: j_z, type: slide, body: stud_b, axis: [0, 0, 1], damping: 0.02}   # the stud B in its groove; + : up
  - {id: j_b, type: hinge, body: bar, axis: [0, 1, 0], damping: 0.002}   # the traverse bar on the stud A, the one driven joint; + : clockwise
pins:
  - {id: pin_b, a: bar, b: stud_b, at: [0.0, 0, 6.1284]}
contact: {solref: [0.002, 1.0], solimp: [0.95, 0.99, 0.0005], margin: 0}
driver: {joint: j_b, kind: velocity, rpm: 20, kv: 5.0, max_torque: 5}
checks:
  - {type: follow, out: j_z, in: j_b, expect: 0.0784, tol: 0.0047, min_r2: 0.99, settle_s: 5.495, window_s: 0.4167}
  - {type: follow, out: j_x, in: j_b, expect: -0.0784, tol: 0.0047, min_r2: 0.99, settle_s: 3.245, window_s: 0.4167}
  - {type: follow, out: j_z, in: j_b, expect: -0.0784, tol: 0.0047, min_r2: 0.99, settle_s: 3.995, window_s: 0.4167}
  - {type: follow, out: j_x, in: j_b, expect: 0.0784, tol: 0.0047, min_r2: 0.99, settle_s: 4.745, window_s: 0.4167}
  - {type: follow, out: j_z, in: j_b, expect: 0.0784, tol: 0.0047, min_r2: 0.99, settle_s: 5.495, window_s: 0.4167}
  - {type: follow, out: j_x, in: j_b, expect: -0.0784, tol: 0.0047, min_r2: 0.99, settle_s: 6.245, window_s: 0.4167}
  - {type: position, joint: j_x, min: -13.3423, max: 3.0577, settle_s: 0.0, window_s: 8.5}
  - {type: position, joint: j_z, min: -14.3284, max: 2.0716, settle_s: 0.0, window_s: 8.5}
camera: {target: [0, 0, -1.0], position: [-14.0, -72.0, 8.0], fov: 34}
display:
  output: j_z
  labels: {j_b: "Traverse bar (driver)", j_x: "Stud A", j_z: "Stud B"}
  proof: {label: "Stud B unpinned", sub: "the bar turns but its other stud stays put"}