Pin down a ring or bar, roll a gear along its teeth with a pen in one of the holes, and see what it draws.
Roll the gear
Round gears (teeth)
Shapes
Pen color
The British engineer Denys Fisher invented the Spirograph toy, which went on sale in 1965, but the curves are much older. A circle rolling inside another circle traces a hypotrochoid, and one rolling outside traces an epitrochoid. Astronomers used circles riding on circles, called epicycles, to describe the paths of the planets for well over a thousand years before Kepler.
The shaped pieces roll the same way as the gears: at every moment, the length of edge that has touched the track equals the length of track it has covered, because no teeth can slip.