Scroll-gears for obtaining a gradually increasing speed

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

Two equal logarithmic-spiral gears (r = 4 e^(0.2098 phi) over 300 deg, radius 4 to 12) on shafts through their poles 16 apart; equal log spirals roll on each other without slip, so straight-flanked teeth (26 and 27) sit at equal arc pitch 1.498 square to the pitch curve. The left gear is driven at 10 rpm; the right turns by tooth contact only, at -r1/r2, which grows from 0.43 to about 2.6 in 4.6 s (less than a turn). Each gear has a balance weight behind so gravity does not turn it. gen191.py.

Measured

Mean ratio -0.911 over 0.6-4.2 s (kinematic -0.923, 1.3%); slice means of the speed ratio grow from -0.445 to -1.753; no run-back; penetration 0.02 mm.

Notes

Scroll-gears work for less than one turn; the run stops before the ends of the spirals. Tooth thickness 0.40 of the pitch to clear the oblique mesh.

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