507 Mechanical Movements

42

Bevel-gears for oblique shafts

42 and 43. Different kinds of gears for transmitting rotary motion from one shaft to another arranged obliquely thereto.

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 20-tooth bevel on an upright shaft drives a 30-tooth bevel on a shaft leaning 60° from it; pitch cones on a common apex, half-angles 23.41° and 36.59° (tan γ1 = sin 60°/(30/20 + cos 60°)), cone distance 10.07
Measured
−0.6666 (ideal −20/30; negative because both joint axes point away from the apex)
Notes
shared plate 42–43. Only the upright shaft is motor-driven. Robust in 6 perturbed runs. Negative control: the 30-tooth gear's teeth out of contact → the oblique shaft stands (0.0000).

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

Figure 42 from Brown, 1868
Brown's figure 42 (1868)