Worm & bevel gears

Spur gears keep rotation in the same plane. To send power around a 90-degree corner, engineers reach for a worm and wheel, or a pair of bevel gears. A worm looks like a screw: each full turn advances the wheel by only one tooth per thread start, giving enormous reduction in a single mesh — and because the wheel usually cannot back-drive the worm, this pairing is naturally self-locking. Bevel gears are simply spur gears cut on a cone instead of a cylinder, letting two shafts meet at an angle while turning at ordinary gear ratios.

1. 1Spin the worm and watch how little the wheel moves per turn — that's the reduction ratio, set by the number of thread starts versus wheel teeth.
2. 2Try turning the wheel by hand in the diagram: on a real single-start worm, this direction usually cannot drive the worm backward. That's self-locking, useful for winches and hoists.
3. 3Switch to the bevel pair: the ratio math is identical to spur gears, but the shafts now meet at 90 degrees instead of staying parallel.