Rosettes are cams, and they are used to produce the rocking or pumping actions needed on rose engine lathes. The rosette is truly what makes the magic happen.
Typically, rosettes with the patterns on the edge (like those shown below on the left) 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 on the pumping entry in this dictionary.
One of the really cool things about rosettes is that the piece can be made very differently using the various options with the given rosette on the rose engine lathe. For example:
This is very evident with the plain-sided rosettes, which get rounded when the cut radius is larger than designed, and collapse in the middle when smaller. If that is not what the artist wishes to do, an amplitude adjuster can be used to compensate for this.
Holtzapffel was probably the first to put a structure in place for how rosettes are named, and the Holtzapffel company made a machine for making them (today, most manufacturers use CNC-driven milling machines).
There is a good web site, Traduction de l'Aide du logiciel CornLathe3, which has this convention outlined well, so I won't repeat it here. The page is partly in French, and partly in English, but you should be able to get the general idea. (By the way, a number of the earliest books on ornamental turning are in French, and there is a great school which teaches OT in southern France. So learning French could be a useful skill for OT, and for impressing your spouse!)
The overarching idea in the rosette numbering scheme is that the number represents a multiple of a base shape. Sometimes, the multiple doesn't really work well to produce a pleasing outcome. Using the F-1 as an example,
Final note: Not all rosette manufacturers follow the Holtzapffel scheme in labelling what they make, but they follow a similar scheme. And, there have been rosette shapes made since that time that follow their own naming convention.
My recommendation is to start with one of each of these rosettes,
John Tarpley wrote this article about rosettes in 2012 (starting on pg. 3) for users of the Lindow-White Rose Engine Lathe. It is a good read.
It is now common to see rosettes which have phasing holes pre-drilled in them, removing the need for a crossing wheel. The advantage noted for using the phrasing holes in the rosette is that it takes a lot of the math out of the process as you don't have to calculate how much to move the crossing wheel to achieve the phasing you want.
Additionally, you are provided phasing outcomes which would be difficult to do otherwise (i.e., phasing a 7-lobed rosetted by half a lobe is difficult when 25.7° of rotation is needed.
Lastly, each rosette can be phased relative to another rosette, not just the object.
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.
Note: an indexing wheel could also be used to phase the rosettes, and that is how I made my first rose engine lathe. But an indexing wheel this small usually only has 5° increments, and that is cumbersome for rosettes with lobes that are not increments of 5°. And even when the increments are divisible by 5, the actual use of this approach is tedious and mistakes are easy to make ("Did I advance it 4 holes or 5?"). This is why machinists typically use an indexing wheel with stops so that each advance is equal.
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 designed a rosette which produces 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. Maybe as that technology continues to mature and become more affordable, it will be the wave of the future.
I purchased acrylic rosettes from Mandala Rose Works (for the rose engine lathe I made from a Delta Midi lathe). Jon Magill uses HDPE for his. Various other plastics, including Corian, are also used. Of course, the ornamental turner could always go old school and buy brass rosettes.
Wes Pilley describes in this video how he turns the petals on a tudor rose on his Lindow rose engine lathe.
This video shows the beauty of rosettes in motion..
Al Collins is one of the current day masters on the rose engine lathe, and this is a video of his machine, showing rose engine turning with a ridiculously complicated, 3D rosette!
I am pretty sure there are less than 10 people in the world who can make something like this, and only a handful more who know how to use it.