507 Mechanical Movements

29

Spiral-thread disk and spur-gear

Transmission of rotary motion from one shaft at right angles to another. The spiral thread of the disk-wheel drives the spur-gear, moving it the distance of one tooth at every revolution.

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
a disk (r 14) with a raised 1.4-turn Archimedean thread on its face (radial pitch 1.5 cm) drives an 18-tooth spur gear (tooth pitch 1.5 cm) on a shaft at right angles, its back teeth caught between the coils like a rack
Measured
ω_gear/ω_disk = -0.0561 over 3 disk turns (Brown: one tooth per turn, 1/18 = 0.0556; frictionless -0.055)
Notes
Only the disk is motor-driven (20 rpm). Negative control: thread out of contact → the gear stands (0.0000). New: spur option `meets_parts` (its teeth also meet class-1 part pieces; no other movement's MJCF changes).

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

Figure 29 from Brown, 1868
Brown's figure 29 (1868)