Imagine you had a robot, consisting of series of arms. They would be of same length, and each one would be attached to the end of the previous one, so it could rotate in the same 2d plane. If each joint were given some angular speed, what would the curve traced by the end-most point look like?
Well, here are several examples. The ellipse is expected, and boring, but some other curves are beatiful, and complicated. Some look like they were traced with a spirograph.
Some of these curves are epitrochoids, but I’m not sure what their general classification would be.