The Eccentric Cutting Frame is a variation of the fly cutter, but the cutter's body is held in a drilling frame. The cutter is spinning along the same axis as the drilling frame, but eccentrically from it (like the eccentric chuck).
It is used with a fly cutter which should be ground with a wide cutting angle. The typical fly cutter is ground with a 60° angle (see also, Sharpening a Rose Engine Fly Cutter, Round Rod). However, jewelers have shown that the angle needs to be >90° for the cut so that the light is reflected back to the viewer. Otherwise, it simply looks like a set of thick dark lines. 120° is not uncommon.
Spacing of the cuts is something where planning is needed. It is commonly noted that the circles should touch, especially when the cuts are on the edge of a piece, or on a spherical surface. BarleyCorn is the term typically used for this, and Bill Ooms put together a spreadsheet for making the calculations. This and more are available on his web site.
Spacing of the cuts can also give great artistic effects. When they are close together, the artist can skip the making of a cut every so often (e.g., every 5th one) to give a nice effect. This is called an interrupted pattern.
John Edwards' web site, OrnamentalTurning.co.uk, has really great information about the setup and use of these devices. There is a lot of great information on John's web site, and it is worth reading. Understanding the history behind the devices we use really helps make one far better at understanding and using today's rose engines. And, as I noted elsewhere on this site, the newer designs for devices like a spherical slide still draw much from what was done more than a hundred years ago. And this is why so many books that were written up to 200 years ago are referenced in the section, How to Get More Information.
There is also a hand-operated version of this tool, which is called by some a Pearling Tool.
The JaHo Ornamental Turning Device from Drechselbedarf can be used on a traditional lathe to add ornamentation to work. The video below shows one in use with an eccentric cutting frame.
Balancing the eccentric cutting frame is very important, and the video below shows Jon Spencer's design for that. (Jon is a great resource for cutting tools.)