Epitrochoids are curves generated by a point selected on a circle of smaller radius rolling around the outside
of a fixed circle of larger radius, and that selected point can be
chosen at some distance from the center of the smaller circle. These are
then 3-parametric curves. They can be helpful in creating decorative designs and other art applications, and can serve also as pastime and recreation for children. Since 1965 there is available a toy (geometric drawing device) known as spirograph, combining mathematics and art. It allows producing physically numerous curve designs based exactly on epitrochoid and hypotrochoid parametric equations.
However, nowadays the epitrochoids (as well as hypotrochoids - see another post at https://draft.blogger.com/blog/post/edit/3323809043368251287/9189797010242374274?hl=en-GB) can be generated quite easily in Excel by using VBA
macro like the one provided at the end of this post.
Here are some examples of charts showing epitrochoid curves generated with the macro. Some of them present combined double curves.