# Ideal rack and pinion, neglecting tooth friction
pinionRadius = 20 mm in 10..50
torque = 2 N*m in 0.5..10
rotation = 1 rad in 0.1..6
rackForce := torque / pinionRadius [N]
rackTravel := rotation * pinionRadius [mm]
check force budget: rackForce >= 50 N
scenario smaller pinion: pinionRadius = 12 mm


# Diagram dimensions are illustrative; teeth are schematic, not manufacturing profiles.
pinionTeeth = 20
module := 2*pinionRadius/pinionTeeth [mm]
check whole pinionTeeth: abs(pinionTeeth-round(pinionTeeth)) <= 0
check positive pinionTeeth: pinionTeeth >= 3