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Classic sources on gears:

- "Spinning Levers", a Jam Handy film.[1] This is a good basic intro to what gears really do.

- "Gearology" from Boston Gear.[2] This is what you need to know to buy gears.

The original article talks a lot about involute gears, but doesn't explain a key motivation for that tooth form. An involute gear will mesh with a straight-sided rack, which can be thought of as an infinite-radius gear. All gears which will mesh with the same rack will mesh with each other. So you only need N gear sizes, not N^2.

This only works for spur gears. Worm gears and helical gears are matched pairs.

[1] https://archive.org/details/0762_Spinning_Levers_04_45_20_00

[2] https://web.archive.org/web/20100602093101/https://www.bosto...




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