A smooth-surface V-grooved pulley for a round band

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

Front view, shafts level, gravity on. Two pulleys, each with a smooth V-groove (flanks 20 degrees either side of the radial plane) turned in its face. The larger (pitch radius 7.4 cm) is on the driving shaft, turned at 40 rpm (the one driven joint). The smaller (pitch radius 4.9 cm), 26 cm away, carries a load (a damper). A tensioned round band (0.8 cm cord) of links on real contact lies wedged between the flanks, its centre 1.17 cm above the V's bottom, which it never reaches, and drives the smaller by friction on the flanks.

Measured

The small pulley turns at 1.4938 times the large one's speed against 1.5102 from the pitch radii (slip 1.1%), over 1 to 5.5 s. The band stays in the grooves (radial deviation 0.31 cm, the wedge letting it sink a little into the V; lateral 0.07 cm). The deepest contact after 1 s is 1.17 mm, inside the cord's soft contact.

Notes

Brown gives no sizes. The faces are solids of revolution of the V's section, built as frusta with rings of 48 points, fine enough that a band cannot catch on their corners (at 12 points a frictionless band was carried at 12.9%).

Film (MP4) · Still (PNG) · Spec (YAML) · Model (MJCF)