Rose Cutting Frames are a really interesting fly cutter where the cutter's holder rides along a rosette for it's movement (whilst also spinning). They are typically used with for adding wonderful 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).
John Jacob Holtzapffel came to the idea of making a device which would make designs like a rose engine lathe, but would be usable on a lathe with a fixed headstock (as he recorded in 1884 in Turning and Mechanical Manipulation, vol. 5, pg. 328).
The well known undulating lines of rose engine turning are usually obtained by giving a variously controlled vibratory motion to the revolving mandrel carying the work, while the tool, stationary during every cut, is moved from point to point between them by the travers of the sliderest. It appeared to the author of these pages that if the conditions were reversed, viz., the tool to rotate and vibrate and the work to stand still, that a large proportion of surface rose engine turning could be executed in the ordinate lathe; ...
And, as these were apparently invented by John Jacob Holtzapffel, the best reference for these is Turning and Mechanical Manipulation, vol. 5 - The Principles and Practice of Ornamental or Complex Turning.
Incidentally, the only reference to rosettes in this book is in relation to the use of them on this cutting frame.
GPhilPoirier has a snippet of one of these in action on this Instagram posting.