Here's my implementation, also inspired by these videos

It was made in 1kb for the JS1K demo competition: https://js1k.com/2018-coins/demo/3124

Detailed source code: https://github.com/xem/epicycles/blob/gh-pages/index.html

Controls:

- Arrow keys: up / down to change the number of gears, left to toggle intermediate paths, right to clear the scene.

- Mouse: click to add points to the path