Is there a name /any references for the curve traced out by point $C$ in the following gif?
Specifically, let $r$ and $R$ denote the radius of the inner and outer circles. Let $P$ denote the center of the inner circle, and $d = R - r$ denote the distance from the origin to center of the smaller circle.
Suppose the center of the smaller circle $P$ moves along the following curve parametrized by $t$, \begin{equation} P(t) = ( d \cos(t), \; d \sin(t) ) \end{equation}
Then, I'm interested in the curve traced out by $C$ for the -y direction, then reflected along the x axis for the +y direction.
This looks like the purple curve in the image below.
Is there a name for this curve / any references for this? Thanks!