Curves that are drawn when rolling on circles.
We have two boards with fixed circular gears. We also have a set of circular toothed pieces of different sizes.
When rolled inside you can see how the dots on the edge follow the drawn curves are called hypocycloids.
If they are rotated on the outside, epicicloids are obtained.
Some mathematical and historical aspects
Epicicloids, that is, the curves generated by a point in a circle that rotates without slipping on another circle, have played an important historical role: Aristotle and Ptolemy used them to describe the movement of planets within the geocentric model.
Despite the similarity, the curves drawn by the well-known "spirograph or spirograph " are not hypocycloides and epicicloids, the reason is that, in these devices, the point he draws is not located, as here, on the circumference if not somewhere inside the circle. The curves generated by the spirograph are called trocoids.