507 Mechanical Movements

44

Stepped gearing

A kind of gearing used to transmit great force and give a continuous bearing to the teeth. Each wheel is composed of two, three, or more distinct spur-gears. The teeth, instead of being in line, are arranged in steps to give a continuous bearing. This system is sometimes used for driving screw propellers, and sometimes, with a rack of similar character, to drive the beds of large iron-planing machines.

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
each wheel three 1-wide spur gears side by side on one shaft, each a third of a pitch on from the last: a 20-tooth driver (r 5) and a 30-tooth follower (r 7.5)
Measured
−0.6667 (ideal −20/30); slices of 1/24 s within −0.693..−0.640
Notes
Only the driver is motor-driven. Steps checked: the middle gear set the wrong way round interferes by 4.7 mm at rest. Robust in 6 perturbed runs. Negative control: the driver's three gears out of contact → the follower stands (0.0000).

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

Figure 44 from Brown, 1868
Brown's figure 44 (1868)