Epicycloidal Cutting Frames (sometimes called a Geometric Cutting Frame) are ridiculously complex cutting frames that are basically the merger of an Eccentric Cutting Frame with a Geometric Chuck, taking them to a new level.
Epicycloidal cutting frames are typically used with for adding designs to the end of an object, especially with guilloché type of work. Also, miniature cutting heads can be used in place of the fly cutter to allow for deeper cuts (Fred Armbruster developed one).
The best reference for these is Turning and Mechanical Manipulation, vol. 5 - The Principles and Practice of Ornamental or Complex Turning (1884), but Holtzapffel also wrote this document : Notes on the Epicycloidal Cutting Frame.
peterwgilroy has a great snippet of one of these in action on this Instagram posting.