The hippopede is historically famous because Eudoxus used its properties in the first mathematical model of planetary motion. He nested concentric spheres rotating at different inclinations to each other, and had the motion transfer from outer ones inward, the planet was attached to the equator of the innermost sphere. With three or more spheres he achieved trajectories with backward loops ("retrogradations") similar to those observed for the planets.
But with just two (see animations here and here) the trajectory is the figure eight shaped curve obtained by intersecting a sphere with a cylinder touching it from the inside (see interactive graphic illustrating that it really is the same curve).
Clearly, under any composition of rotations a moving point has to stay on a sphere, but why is it also confined to an off-centered cylinder?