Feed-motion of Woodworth’s planing machine, a smooth supporting…
Feed-motion of Woodworth’s planing machine, a smooth supporting roller, and a toothed top roller.
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
Gravity on. A board 3 cm thick lies on a smooth supporting roller (radius 7, free on its axis). Over it the toothed top roller (body radius 6, 20 pointed teeth 1.3 cm high, each a real colliding prism) is driven at 10 rpm (the only driven joint) and bears on the board by its weighted bearings (8 kg), free to rise on a vertical guide. The board is free to rise and fall and to slide along; only the teeth's grip on it (friction 0.9) feeds it.
Measured
The board is fed at the teeth's points' speed: 0.0726 m per radian of the top roller (expected 0.073, within 6%). The board in its turn turns the smooth roller at -1.038 times the top roller's speed (expected -1.043). Deepest penetration 0.12 cm.
Notes
Brown gives no sizes; the model keeps his end view (toothed roller above, smooth roller below, the board between). The teeth do not bite into the board; their grip is friction at their points. The top roller's guide is drawn behind.