Work out rack and pinion travel instantly with clear inputs, formula shown and shareable results.
A pinion of module m with N teeth has pitch diameter m x N, so one revolution advances the rack by pi x m x N. That is also the resolution denominator: with a 2 mm module 20-tooth pinion, one motor revolution through a 10:1 gearbox moves 12.57 mm.
Rack and pinion
pitch diameter = module x teeth; travel per revolution = pi x pitch diameter
Unlimited stroke length and high speed. The trade is lower stiffness, more backlash and the need for a preloaded or twin-pinion arrangement for precision.
Use a smaller module or fewer pinion teeth, or increase the gearbox ratio — but all three reduce speed and increase reflected inertia.