We are exploring how to generate non-circular gears for fdm printing.
This will be our first major video. We are submitting it for the Summer of
Math Exposition contest.
So far, we have worked out how to computationally define the geometry and motion of arbitrary non-circular pitch curve pairs.
What is a pitch curve?
Without getting too technical, you can think of the pitch curve of a gear
as its "base shape" before you add the teeth
Here is Captain Campea's draft write-up proof thing for the generation method: View draft (PDF)
Here is a demo in html canvas by Captain Isaac:
(but Isaac uses a slightly different generation method lol)