# No. 317 (Brown 1868): "Compound bar compensation pendulum. C is a compound bar of brass and iron or steel, brazed together with brass downward. As brass expands more than iron, the bar will bend upward as it gets warmer, and carry the weights, W, W, up with it, raising the center of the aggregate weight, M, W, to raise the center of oscillation as much as elongation of the pendulum-rod would let it down."
#
# Model (cm, gravity on). The clock is No. 303's dead-beat escapement (a 30-tooth wheel, the pallets on the arbor C); the pendulum's rod carries
# the bob M (104 g) at its end and, 17.47 below C, the compound bar C (10.3 long, 0.3 thick: brass below, steel above) clamped across it,
# with a weight W (40 g) on each end. Heat is not simulated: the bar's length is the one that compensates the rod (warmed a degree, the bar
# bends up with curvature 3.75e-05 per cm, lifting the weights 0.000497 cm, which lifts the centre of M, W, W as much as the rod's
# lengthening lets it down). Fully physical: the only input is a constant torque on the escape wheel (the clock's weight); the pendulum starts
# from rest, hanging straight, and the escapement starts itself. Generator: opencode-runs/batch12/gen317.py.
number: 317
slug: compound-bar-compensation-pendulum
name: Compound bar compensation pendulum
brown: "Compound bar compensation pendulum. C is a compound bar of brass and iron or steel, brazed together with brass downward. As brass expands more than iron, the bar will bend upward as it gets warmer, and carry the weights, W, W, up with it, raising the center of the aggregate weight, M, W, to raise the center of oscillation as much as elongation of the pendulum-rod would let it down."
units: cm
sim: {timestep: 0.0002, integrator: implicitfast, iterations: 50, duration_s: 10, floor: false}
bodies:
  # The escape wheel: brass, 30 teeth leaning forward (Graham), rim, four spokes, hub.
  - id: wheel
    shape: part
    pos: [0, 0, 0]
    density: 8500
    friction: 0.1
    color: "#e6d7b0"
    pieces:
      - kind: wheel
        center: [0, 0]
        teeth: 30
        # one tooth, polar (radius, angle from its tip) — the tip leads, the back is curved off
        tooth: [[5.0, 0], [4.45, 0.075], [3.9, 0.165], [3.9, 0.0756]]
        phase: 2.42601        # 139°: tooth 0 just short of D's impulse face
        root: 4.2
        rim: 3.6
        hub: 0.8
        spokes: 4
        spoke_width: 0.45
        y: [-0.25, 0.25]
        collide: 2
      - {kind: disc, center: [0, 0], radius: 0.25, y: [-0.7, 0.9], color: "#8f8a80"}   # arbor
  # The pallets (anchor) and the pendulum: one piece on the arbor C.
  - id: pendulum
    shape: part
    pos: [0, 0, 7.07107]
    density: 7800
    friction: 0.1
    color: "#d9cfba"
    pieces:
      - {kind: disc, center: [0, 7.07107], radius: 0.6, y: [-1.15, 0.35]}                       # 0 hub on the arbor
      - {kind: poly, points: [[-0.45183, 7.16247], [-4.23406, 4.21139], [-3.80346, 3.65951], [-0.02122, 6.61058]], y: [-0.3, 0.3]}  # 1
      - {kind: poly, points: [[0.02117, 6.61058], [3.73434, 3.71273], [4.16501, 4.26457], [0.45184, 7.16242]], y: [-0.3, 0.3]}  # 2
      # D (entry): locking face = outer arc r 5.2399 about C; impulse face down to r 4.8473 over 2.5° of lift
      - {kind: band, center: [0, 7.07107], r: [4.84731, 5.23989], a: [-2.57326, -2.36382], y: [-0.35, 0.35], collide: 1}  # 3
      - {kind: poly, points: [[-3.77162, 3.43357], [-3.73332, 3.39427], [-3.30196, 3.52234], [-3.48904, 3.7061]], y: [-0.35, 0.35], collide: 1}  # 4
      # E (exit): locking face = inner arc r 4.7601 about C; impulse face out to r 5.1527
      - {kind: band, center: [0, 7.07107], r: [4.76011, 5.15269], a: [-0.77788, -0.56844], y: [-0.35, 0.35], collide: 1}  # 5
      - {kind: poly, points: [[3.42591, 3.76625], [3.39111, 3.73056], [3.50957, 3.29838], [3.70845, 3.49369]], y: [-0.35, 0.35], collide: 1}  # 6
      - {kind: rod, from: [0, -1.0, 7.07107], to: [0, -1.0, -12.92893], radius: 0.15, color: "#8f8a80"}   # 7 the pendulum-rod (steel)
      - {kind: disc, center: [0, -12.92893], radius: 1.8, y: [-1.6, -0.4], density: 8500, color: "#e6d7b0"}   # 8 the bob M (brass, 104 g)
      - {kind: poly, points: [[-5.15, -10.55], [5.15, -10.55], [5.15, -10.4], [-5.15, -10.4]], y: [-1.5, -0.5], density: 8500, color: "#d8b25a"}   # 9 the compound bar C: brass, downward
      - {kind: poly, points: [[-5.15, -10.4], [5.15, -10.4], [5.15, -10.25], [-5.15, -10.25]], y: [-1.5, -0.5], density: 7800, color: "#8f8a80"}   # 10 and steel above it
      - {kind: disc, center: [0, -10.4], radius: 0.45, y: [-1.7, -0.3], density: 7800, color: "#8f8a80"}   # 11 the bar's clamp on the rod
      - {kind: disc, center: [-5.15, -9.13], radius: 1.12, y: [-1.6, -0.4], density: 8500, color: "#e6d7b0"}   # 12 a weight W (40 g)
      - {kind: disc, center: [5.15, -9.13], radius: 1.12, y: [-1.6, -0.4], density: 8500, color: "#e6d7b0"}   # 13 a weight W
  # The cock that carries C (frame, drawn only).
  - id: cock
    shape: part
    pos: [0, 0, 7.07107]
    fixed: true
    color: "#cfc6b4"
    pieces:
      - {kind: poly, points: [[-1.3, 8.6], [1.3, 8.6], [0.75, 6.75], [-0.75, 6.75]], y: [0.4, 1.0]}
      - {kind: disc, center: [0, 7.07107], radius: 0.18, y: [-1.3, 1.0], color: "#8f8a80"}
joints:
  - {id: j_wheel, type: hinge, body: wheel, axis: [0, 1, 0], damping: 0.00002}
  - {id: j_pend, type: hinge, body: pendulum, axis: [0, 1, 0], damping: 0.0015}   # air and pivot losses
contact: {solref: [0.002, 1], solimp: [0.95, 0.99, 0.0005], margin: 0}
# The clock's weight: a constant torque on the escape wheel, clockwise (+y). Nothing else is driven.
driver: {joint: j_wheel, kind: torque, torque: 0.008, max_torque: 0.05}
checks:
  # the pendulum keeps time: its period against the compound pendulum's 2π√(I/(m g d)) from the model
  - {type: period, joint: j_pend, tol: 0.03, settle_s: 4, window_s: 4}
  # half a tooth (2π/30 / 2) per beat: one tooth per two beats
  - {type: advance, joint: j_wheel, beat: j_pend, expect: 0.10472, tol: 0.03, settle_s: 4, window_s: 4}
  # dead beat: the wheel never turns back while locked (recoil) beyond contact compliance
  - {type: monotonic, joint: j_wheel, direction: 1, max_back: 0.004, settle_s: 2, window_s: 6}
  # the impulse keeps the swing going against the damping
  - {type: amplitude, joint: j_pend, min: 0.05, max: 0.2, sustain: 0.9, settle_s: 4, window_s: 4}
  - {type: penetration, max: 0.0005, settle_s: 1}
camera: {target: [0, 0, -8.6], position: [11, -80.0, -3.6], fov: 30}
display:
  output: j_pend
  swing: j_pend
  labels: {j_wheel: Escape wheel (weight), j_pend: Compensated pendulum and pallets}
  brake: Extra air drag on the pendulum
  proof: {label: Pallets out of contact, sub: "the teeth no longer touch the pallets: nothing makes good the pendulum's losses, so its swing dies away, and the weight spins the wheel freely"}