Different arrangements of pulleys
19, 20, 21 and 22. Are different arrangements of pulleys. The following rule applies to these pulleys:—In a system of pulleys where each pulley is embraced by a cord attached at one end to a fixed point and at the other to the center of the movable pulley, the effect of the whole will be = the number 2, multiplied by itself as many times as there are movable pulleys in the system.
Only the input is driven; every other part of this model moves by physics (MuJoCo), and its ratios are measured. Run it live, change its parameters, or switch the friction off to see the output stop.
- Modelled as
- three cords of links (friction on the sheaves), each from its own eye in the ceiling, under a movable pulley and up to the next block's seizing eye; the third over the fixed pulley F to the hand
- Measured
- weight/hand 0.127 (2 × 2 × 2 = 8: Brown's rule, 0.125), P2 0.252, P3 0.502, sheaves P1 −1.70, P2 −3.38, P3 −6.74, F 13.45 rad/m (strand speeds: −1.689, −3.378, −6.757, 13.51), pull 33.9 N against T3 less the hand's weight 33.5 N, pen ≤ 0.04 mm
- Notes
- Only the hand is driven (a slide in a plumb guide on the hand rope, 2 cm/s). Shared plate 19–22. The plate draws each cord seized at the next block's centre; here each block carries a seizing eye out to the strand's plumb line. Negative control: all three cords' contact switched off → the weight does not rise (0.000; it drops to its stop while the hand still hauls; run at dt 1e-5, since at 1e-4 the freed cords whip and go unstable).
Film (MP4) · GIF · Still (PNG) · Spec (YAML) · Model (MJCF)
