create an interactive spirograph to explain how it works
Worked for 1m 12s

Drag the radii and pen distance to see how the rolling circle turns into the traced curve.

curve closes after 12 turnsratio 93:36
Pen point: x=(R−r)cos(t)+d cos((R−r)/r)t, y=(R−r)sin(t)−d sin((R−r)/r)t.
traced pen pathfixed ringrolling circle
4:39 PM