If points traced are located on the rolling circle itself then, in this particular case, the resulting curves are called cycloids. We won't differentiate between the two families. In all cases, points participate in two simultaneous motions of which one is a rotation of the small circle around its center. In the beginning it's set to 1 which means that the circle rolls with no slipping. Slipping will grow along with the speed.
Hypocycloids possess some unexpected properties .
For example, adjust the radius of the small circle to be half that of the big one. The points then trace either straight segments or ellipses. They only have effect when pressed or immediately after pressing the Reset button. The radius of the small circle can also be changed by dragging its center. There are two ways to simulate tracing cycloids.