Worm or endless screw and worm-wheel. Modification of 31, used when steadiness or great power is required.
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
As in the plate, a 40-tooth worm-wheel (module 0.5, pitch radius 10) stands face-on over a worm on a horizontal shaft, the only driven joint (60 rpm). The worm is an hour-glass: its thread is curved round the wheel's pitch circle and spans +-20.6 deg of the rim (about 4.6 teeth), instead of No. 31's straight screw that holds one or two. Pitch radius 1.6 at the throat, 2.21 at the ends. The thread is 110 loft segments; at worm angle t its section is the wheel's tooth space set on the wheel's radius at angle (t - 90 deg)/40.
Measured
Over 1-5 s the wheel turns 0.0252 times the worm (1/40 = 0.025), with 0.85% slip from backlash. Max penetration 0.01 mm.
Notes
The wheel's teeth are No. 31's straight spur teeth rather than throated ones. The bearings are drawn only.