# No. 151 (Brown 1868): "Continuous circular into continuous but much slower rectilinear motion. The worm on the upper shaft, acting on the toothed wheel on the screw-shaft, causes the right and left hand screw-threads to move the nuts, upon them toward or from each other according to the direction of rotation." # # Model (cm, no gravity): the worm (a right-hand single thread, 3 turns, as in No. 143) lies along x under the 18-tooth wheel (module 0.8) and turns it 0.0556 of a turn per turn of the worm. The wheel sits at the middle of a screw-shaft along y: right-handed thread (pitch 1.6 cm) on one side of it, its mirror (left-handed) on the other. # Each side carries a nut that can only slide along y; its thread is the ridge that fills the screw's groove. The worm is the one driven joint (180 turns a minute); at -180 the nuts approach (a nut moves 1.6 cm for each turn of the wheel): about 3.2 cm in 12 s. Generator: opencode-runs/batch10/gen151.py. number: 151 slug: worm-screw-nuts name: A worm and wheel moving two nuts on right and left screws brown: "Continuous circular into continuous but much slower rectilinear motion. The worm on the upper shaft, acting on the toothed wheel on the screw-shaft, causes the right and left hand screw-threads to move the nuts, upon them toward or from each other according to the direction of rotation." units: cm sim: timestep: 0.0002 integrator: implicitfast iterations: 100 solver: CG multiccd: true duration_s: 12.0 floor: false gravity: 0 bodies: - id: screw shape: part pos: [0, 0, 0] density: 7800 friction: 0.1 color: "#e8dec6" pieces: - {kind: rod, from: [0, -16.5, 0], to: [0, 16.5, 0], radius: 1.0, collide: 0, color: "#8f8a80"} - {kind: disc, center: [0, 0], radius: 6.15, inner: 0.9, y: [-0.6400000000000001, 0.6400000000000001]} - {kind: poly, points: [[-1.7, -1.7], [1.7, -1.7], [1.7, 1.7], [-1.7, 1.7]], y: [-0.9400000000000002, 0.9400000000000002], collide: 0, color: "#a89a7e"} - {kind: poly, points: [[-0.0715, -5.5795], [-0.0867, -6.7652], [-0.0725, -6.8888], [-0.0446, -7.0125], [-0.0074, -7.136], [0.0376, -7.2594], [0.0897, -7.3823], [0.1483, -7.5049], [0.213, -7.6268], [0.2837, -7.748], [0.36, -7.8683], [0.4419, -7.9878], [0.9519, -7.9432], [1.0118, -7.8113], [1.066, -7.6795], [1.1146, -7.5479], [1.1572, -7.4166], [1.1936, -7.2858], [1.2235, -7.1556], [1.2465, -7.0263], [1.2616, -6.8982], [1.2676, -6.7716], [1.2602, -6.6474], [1.0393, -5.4824]], y: [-0.6400000000000001, 0.6400000000000001], collide: 2} - 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{kind: loft, a: [[-0.5562, 11.23, -1.7119], [-0.5562, 9.81, -1.7119], [-0.3245, 10.185, -0.9986], [-0.3245, 10.855, -0.9986]], b: [[-1.058, 11.15, -1.4562], [-1.058, 9.73, -1.4562], [-0.6172, 10.105, -0.8495], [-0.6172, 10.775, -0.8495]], collide: 2} - {kind: loft, a: [[-1.058, 11.15, -1.4562], [-1.058, 9.73, -1.4562], [-0.6172, 10.105, -0.8495], [-0.6172, 10.775, -0.8495]], b: [[-1.4562, 11.07, -1.058], [-1.4562, 9.65, -1.058], [-0.8495, 10.025, -0.6172], [-0.8495, 10.695, -0.6172]], collide: 2} - {kind: loft, a: [[-1.4562, 11.07, -1.058], [-1.4562, 9.65, -1.058], [-0.8495, 10.025, -0.6172], [-0.8495, 10.695, -0.6172]], b: [[-1.7119, 10.99, -0.5562], [-1.7119, 9.57, -0.5562], [-0.9986, 9.945, -0.3245], [-0.9986, 10.615, -0.3245]], collide: 2} - {kind: loft, a: [[-1.7119, 10.99, -0.5562], [-1.7119, 9.57, -0.5562], [-0.9986, 9.945, -0.3245], [-0.9986, 10.615, -0.3245]], b: [[-1.8, 10.91, -0.0], [-1.8, 9.49, -0.0], [-1.05, 9.865, -0.0], [-1.05, 10.535, -0.0]], collide: 2} - {kind: loft, a: [[-1.8, 10.91, -0.0], [-1.8, 9.49, -0.0], [-1.05, 9.865, -0.0], [-1.05, 10.535, -0.0]], b: [[-1.7119, 10.83, 0.5562], [-1.7119, 9.41, 0.5562], [-0.9986, 9.785, 0.3245], [-0.9986, 10.455, 0.3245]], collide: 2} - {kind: loft, a: [[-1.7119, 10.83, 0.5562], [-1.7119, 9.41, 0.5562], [-0.9986, 9.785, 0.3245], [-0.9986, 10.455, 0.3245]], b: [[-1.4562, 10.75, 1.058], [-1.4562, 9.33, 1.058], [-0.8495, 9.705, 0.6172], [-0.8495, 10.375, 0.6172]], collide: 2} - {kind: loft, a: [[-1.4562, 10.75, 1.058], [-1.4562, 9.33, 1.058], [-0.8495, 9.705, 0.6172], [-0.8495, 10.375, 0.6172]], b: [[-1.058, 10.67, 1.4562], [-1.058, 9.25, 1.4562], [-0.6172, 9.625, 0.8495], [-0.6172, 10.295, 0.8495]], collide: 2} - {kind: loft, a: [[-1.058, 10.67, 1.4562], [-1.058, 9.25, 1.4562], [-0.6172, 9.625, 0.8495], [-0.6172, 10.295, 0.8495]], b: [[-0.5562, 10.59, 1.7119], [-0.5562, 9.17, 1.7119], [-0.3245, 9.545, 0.9986], [-0.3245, 10.215, 0.9986]], collide: 2} - {kind: loft, a: [[-0.5562, 10.59, 1.7119], [-0.5562, 9.17, 1.7119], [-0.3245, 9.545, 0.9986], [-0.3245, 10.215, 0.9986]], b: [[-0.0, 10.51, 1.8], [-0.0, 9.09, 1.8], [-0.0, 9.465, 1.05], [-0.0, 10.135, 1.05]], collide: 2} - {kind: loft, a: [[-0.0, 10.51, 1.8], [-0.0, 9.09, 1.8], [-0.0, 9.465, 1.05], [-0.0, 10.135, 1.05]], b: [[0.5562, 10.43, 1.7119], [0.5562, 9.01, 1.7119], [0.3245, 9.385, 0.9986], [0.3245, 10.055, 0.9986]], collide: 2} - {kind: loft, a: [[0.5562, 10.43, 1.7119], [0.5562, 9.01, 1.7119], [0.3245, 9.385, 0.9986], [0.3245, 10.055, 0.9986]], b: [[1.058, 10.35, 1.4562], [1.058, 8.93, 1.4562], [0.6172, 9.305, 0.8495], [0.6172, 9.975, 0.8495]], collide: 2} - {kind: loft, a: [[1.058, 10.35, 1.4562], [1.058, 8.93, 1.4562], [0.6172, 9.305, 0.8495], [0.6172, 9.975, 0.8495]], b: [[1.4562, 10.27, 1.058], [1.4562, 8.85, 1.058], [0.8495, 9.225, 0.6172], [0.8495, 9.895, 0.6172]], collide: 2} - {kind: loft, a: [[1.4562, 10.27, 1.058], [1.4562, 8.85, 1.058], [0.8495, 9.225, 0.6172], [0.8495, 9.895, 0.6172]], b: [[1.7119, 10.19, 0.5562], [1.7119, 8.77, 0.5562], [0.9986, 9.145, 0.3245], [0.9986, 9.815, 0.3245]], collide: 2} - {kind: loft, a: [[1.7119, 10.19, 0.5562], [1.7119, 8.77, 0.5562], [0.9986, 9.145, 0.3245], [0.9986, 9.815, 0.3245]], b: [[1.8, 10.11, 0.0], [1.8, 8.69, 0.0], [1.05, 9.065, 0.0], [1.05, 9.735, 0.0]], collide: 2} - {kind: loft, a: [[1.8, 10.11, 0.0], [1.8, 8.69, 0.0], [1.05, 9.065, 0.0], [1.05, 9.735, 0.0]], b: [[1.7119, 10.03, -0.5562], [1.7119, 8.61, -0.5562], [0.9986, 8.985, -0.3245], [0.9986, 9.655, -0.3245]], collide: 2} - {kind: loft, a: [[1.7119, 10.03, -0.5562], [1.7119, 8.61, -0.5562], [0.9986, 8.985, -0.3245], [0.9986, 9.655, -0.3245]], b: [[1.4562, 9.95, -1.058], [1.4562, 8.53, -1.058], [0.8495, 8.905, -0.6172], [0.8495, 9.575, -0.6172]], collide: 2} - {kind: loft, a: [[1.4562, 9.95, -1.058], [1.4562, 8.53, -1.058], [0.8495, 8.905, -0.6172], [0.8495, 9.575, -0.6172]], b: [[1.058, 9.87, -1.4562], [1.058, 8.45, -1.4562], [0.6172, 8.825, -0.8495], [0.6172, 9.495, -0.8495]], collide: 2} - {kind: loft, a: [[1.058, 9.87, -1.4562], [1.058, 8.45, -1.4562], [0.6172, 8.825, -0.8495], [0.6172, 9.495, -0.8495]], b: [[0.5562, 9.79, -1.7119], [0.5562, 8.37, -1.7119], [0.3245, 8.745, -0.9986], [0.3245, 9.415, -0.9986]], collide: 2} - {kind: loft, a: [[0.5562, 9.79, -1.7119], [0.5562, 8.37, -1.7119], [0.3245, 8.745, -0.9986], [0.3245, 9.415, -0.9986]], b: [[0.0, 9.71, -1.8], [0.0, 8.29, -1.8], [0.0, 8.665, -1.05], [0.0, 9.335, -1.05]], collide: 2} - {kind: loft, a: [[0.0, 9.71, -1.8], [0.0, 8.29, -1.8], [0.0, 8.665, -1.05], [0.0, 9.335, -1.05]], b: [[-0.5562, 9.63, -1.7119], [-0.5562, 8.21, -1.7119], [-0.3245, 8.585, -0.9986], [-0.3245, 9.255, -0.9986]], collide: 2} - {kind: loft, a: [[-0.5562, 9.63, -1.7119], [-0.5562, 8.21, -1.7119], [-0.3245, 8.585, -0.9986], [-0.3245, 9.255, -0.9986]], b: [[-1.058, 9.55, -1.4562], [-1.058, 8.13, -1.4562], [-0.6172, 8.505, -0.8495], [-0.6172, 9.175, -0.8495]], collide: 2} - {kind: loft, a: [[-1.058, 9.55, -1.4562], [-1.058, 8.13, -1.4562], [-0.6172, 8.505, -0.8495], [-0.6172, 9.175, -0.8495]], b: [[-1.4562, 9.47, -1.058], [-1.4562, 8.05, -1.058], [-0.8495, 8.425, -0.6172], [-0.8495, 9.095, -0.6172]], collide: 2} - {kind: loft, a: [[-1.4562, 9.47, -1.058], [-1.4562, 8.05, -1.058], [-0.8495, 8.425, -0.6172], [-0.8495, 9.095, -0.6172]], b: [[-1.7119, 9.39, -0.5562], [-1.7119, 7.97, -0.5562], [-0.9986, 8.345, -0.3245], [-0.9986, 9.015, -0.3245]], collide: 2} - {kind: loft, a: [[-1.7119, 9.39, -0.5562], [-1.7119, 7.97, -0.5562], [-0.9986, 8.345, -0.3245], [-0.9986, 9.015, -0.3245]], b: [[-1.8, 9.31, -0.0], [-1.8, 7.89, -0.0], [-1.05, 8.265, -0.0], [-1.05, 8.935, -0.0]], collide: 2} - id: frame shape: part pos: [0, 0, 0] fixed: true color: "#cfc6b4" pieces: - {kind: poly, points: [[-10, -16.06], [10, -16.06], [10, -15.26], [-10, -15.26]], y: [-17.5, 17.5], color: "#b9b09c"} - {kind: poly, points: [[-1.8, -15.26], [1.8, -15.26], [1.4, -1.2], [-1.4, -1.2]], y: [15.4, 16.6], color: "#cfc6b4"} - {kind: poly, points: [[-1.8, -15.26], [1.8, -15.26], [1.4, -1.2], [-1.4, -1.2]], y: [-16.6, -15.4], color: "#cfc6b4"} - {kind: poly, points: [[-1.0, -15.26], [1.0, -15.26], [1.0, -4.6], [-1.0, -4.6]], y: [14.8, 16.0], collide: 0, color: "#cfc6b4"} - {kind: poly, points: [[-1.0, -15.26], [1.0, -15.26], [1.0, -4.6], [-1.0, -4.6]], y: [-16.0, -14.8], collide: 0, color: "#cfc6b4"} - {kind: rod, from: [-8.8, 0, -9.76], to: [-6.6, 0, -9.76], radius: 1.0, color: "#8f8a80"} - {kind: rod, from: [6.6, 0, -9.76], to: [8.8, 0, -9.76], radius: 1.0, color: "#8f8a80"} - {kind: poly, points: [[-8.8, -15.26], [-6.6, -15.26], [-6.6, -7.96], [-8.8, -7.96]], y: [-1.2, 1.2], color: "#cfc6b4"} - {kind: poly, points: [[6.6, -15.26], [8.8, -15.26], [8.8, -7.96], [6.6, -7.96]], y: [-1.2, 1.2], color: "#cfc6b4"} - {kind: poly, points: [[-1.2, -5.4], [1.2, -5.4], [1.2, -4.6], [-1.2, -4.6]], y: [-16.0, 16.0], collide: 0, color: "#a89a7e"} joints: - {id: j_wh, type: hinge, body: screw, axis: [0, 1, 0], damping: 0.01} # the toothed wheel and screw-shaft; + : clockwise seen along y - {id: j_wo, type: hinge, body: worm, axis: [1, 0, 0], damping: 0.001} # the one driven joint: the worm on its shaft - {id: j_n1, type: slide, body: nut_r, axis: [0, 1, 0], range: [-6.29, 6.29], damping: 0.05} # the nut on the right-hand thread (y < 0); + : toward the wheel - {id: j_n2, type: slide, body: nut_l, axis: [0, 1, 0], range: [-6.29, 6.29], damping: 0.05} # the nut on the left-hand thread (y > 0); + : away from the wheel (so it travels in the minus sense when the nuts approach) contact: {solref: [0.002, 1.0], solimp: [0.98, 0.99, 0.0002], margin: 0} driver: {joint: j_wo, kind: velocity, rpm: -180.0, kv: 2.0, max_torque: 1.0} checks: - {type: ratio, out: j_wh, in: j_wo, expect: 0.0556, tol: 0.002, settle_s: 1, window_s: 10.0} - {type: follow, out: j_n1, in: j_wh, expect: -0.002546, tol: 0.000102, min_r2: 0.99, settle_s: 1.5, window_s: 3.0} - {type: follow, out: j_n1, in: j_wh, expect: -0.002546, tol: 0.000102, min_r2: 0.99, settle_s: 5.5, window_s: 3.0} - {type: follow, out: j_n1, in: j_wh, expect: -0.002546, tol: 0.000102, min_r2: 0.99, settle_s: 9.0, window_s: 2.5} - {type: follow, out: j_n2, in: j_wh, expect: 0.002546, tol: 0.000102, min_r2: 0.99, settle_s: 1.5, window_s: 3.0} - {type: follow, out: j_n2, in: j_wh, expect: 0.002546, tol: 0.000102, min_r2: 0.99, settle_s: 5.5, window_s: 3.0} - {type: follow, out: j_n2, in: j_wh, expect: 0.002546, tol: 0.000102, min_r2: 0.99, settle_s: 9.0, window_s: 2.5} - {type: position, joint: j_n1, min: -0.05, max: 3.7, settle_s: 0.0, window_s: 11.5} - {type: position, joint: j_n2, min: -3.7, max: 0.05, settle_s: 0.0, window_s: 11.5} - {type: penetration, max: 0.001, settle_s: 0.5} camera: {target: [0, 0, -9.0], position: [-60.0, -68.0, 20.0], fov: 34} display: output: j_n1 labels: {j_wo: "Worm (driver)", j_n1: "Nut, right-hand thread", j_n2: "Nut, left-hand thread"} proof: {label: "Thread out of contact", sub: "the worm turns alone: the wheel, screw and nuts stand"}