A Geometric Chuck (sometimes called an Epicycloidal Chuck) is used for cutting patterns made up of rolling centres.
Newer Geometric Chuck
|5 Stage Geometric Chuck by Plant|
This is a YouTube video from Chuck Bommarito (aka, outsidescrewball) showing a Leinhard Rose Geometric Chuck in use. The video is a bit long, but does show the chuck well, as well as a piece made on it.
This video shows an Ibbetson Geometric Chuck on a Holtzapffel rose engine lathe.
Basically, it is achieved by rolling one object around another, forming a composite of two perfectly circular motions (see also the graphic below of a planet in epicyclic motion).
That pictures shows one stage, now imagine that multiple 2, 3, or even 5 times.
The geometric mathematics behind this chuck's movement are explained by Dr. Frank Farris in his 1996 paper, "Wheels on Wheels on Wheels-Surprising Symmetry". There is also a nice article on this at Wolfram MathWorld.