Elliptical Cutting Frames (sometimes called Ellipse Cutting Frames) are another variation of the fly cutter. They add additional functionality to the eccentric cutting frame by adding gears. These gears allow the cutter to follow an elliptical path instead of a circular one.
Elliptical cutting frames are often used with for adding designs to the end of an object, especially with guilloché type of work. The trained user of the elliptical cutting frame can change the gearing and produce other, highly intricate designs including multiple four-leaf clovers.
The best reference for these is Turning and Mechanical Manipulation, vol. 5 - The Principles and Practice of Ornamental or Complex Turning (1884).