Fun with trochoids
x = major * sin (q) + minor
* sin (ratio*q-f)
y = major * cos (q) + minor * cos (ratio*q+f)
I think these things pretty much count as trochoids, being the trails left
by a point on a wheel as it rolls around another wheel.
Conventionally though trochoids are divided into two categories: Epitrochoids and hypotrochoids.
Epitrochoids are the trail from a wheel rolling around the outside of a fixed circle.
Hypotrochoids are those formed from a wheel rolling around the inside of a fixed circle.
These curves belong to a more general class, with the wheel being rolled around also turning.