Rosettes are cams. They are used to produce the rocking or pumping actions needed on rose engine lathes.
Typically, rosettes with the patterns on the edge (like those shown to the right) are used to produce rocking action, and rosettes with the patterns on the face (side) are used for pumping action.
Pat Miller made a very innovative device which uses the rosette designed to move the object in a rocking motion, and converts that motion into a pumping action. A YouTube video showing that device in operation is shown above in the pumping section.
Ornamental turners can make their own rosettes; however that requires :
This video is about the history, design, and production of rosettes. It was given by Jon Magill at the 2018 Ornamental Turners International Symposium. As you will probably note, this is not for the faint of heart. He lost me when he discussed Rectangular Lissajous Curves.
It is cheaper (and a whole lot faster) to buy pre-made rosettes than to learn how to design a rosette, and acquire a CNC milling machine. But, if you are seeking a reason to buy (and learn to use) a CNC milling machine, this is as good a reason as any. And, you can make rosettes that are very special-purpose in nature (Jon Magill made a rosette which produced shamrocks -- very cool!).
Theoretically, they could be 3D printed; though I have never seen nor heard of any made that way, and the people with whom I've spoken who tried it said it doesn't work well.
I purchased acrylic rosettes from Mandala Rose Works (for the rose engine lathe I made from a Delta Midi lathe -- and am abandoning). Jon Magill uses HDPE for his, and various other plastics, including Corian, are also used. Of course, the ornamental turner could always go old school and buy brass rosettes.
It is now common to see rosettes which have phasing holes pre-drilled in them, removing the need for an indexing plate to do phasing (the indexing plate is still useful for other operations). The benefits of this are :
This opens up a whole new set of artistic options for the ornamental turner, AND will give more abilities to stay out of your spouse's way when you retire !
This is the approach that Jon Magill has purposefully taken with the design of the MDF Rose Engine.
Alternatively, the artist/craftsman can position the cutter to cut on the far side of the object. This makes a pattern which is the inverse of the rosette. The difference is especially notable on the end of a piece, or when hollowing and the inside curves need to match the outside.