507 Mechanical Movements

24

Spur-gears

Spur-gears.

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 involute spur gears (module 0.5 cm, 30 driving 40 teeth as counted on the plate, on parallel shafts 17.5 cm apart), every tooth its own convex hull (the spur-pair fixture's generator), the driven shaft turned by tooth contact alone
Measured
ω2/ω1 = -0.7500 (expect -0.75, slip 0.00 %), tooth penetration ≤ 0.003 mm
Notes
Only the driver (the 30-tooth shaft) is motor-driven. Negative control: the driven gear's tooth contact off → the driven shaft stays still (0.000 rad/s). Gear 2 phased half a tooth (pi/40): the teeth start clear.

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

Figure 24 from Brown, 1868
Brown's figure 24 (1868)