Indexing wheels (also known as an division plates or a indexing plates) get used for a number of operations on the rose engine.
Basket Weave Pattern (on the side of the box)
As with traditional lathes, indexing wheels are used for cuts which need to be at set angles around the circle : say, every 15°.
A common use for indexing wheels in ornamental turning is for phasing. Phasing is changing the relationship between the rosette and the object being turned.
For example, to make a basket weave pattern
the ornamental turner cuts a pattern on the object, one complete revolution.
the ornamental turner then rotates the object some pre-determined direction and number of degrees (say, 15° clockwise)
the ornamental turner repositions the cutting head a pre-determined distance (say, 0.050 inch towards the lathe headstock)
the ornamental turner then cuts the same pattern on the object, one complete revolution.
Steps 2-4 are repeated until the object is completed.
Indexing wheels like the yellow one shown can be made with 3D printers, or they be purchased. I purchased an aluminium one from Alisam Engineering.
Jon Magill authored an article titled, "Phasing Fundamentals" that describes phasing in better details. That article was published in the AAW's magazine, "American Woodturner" in Summer 2008, pages 62-63.
Spiral Fluting an Ornament on a Rose Engine
This video shows a number of things, including the use of an Alisam index wheel (around 2:35 into the video).
Disclaimer : eMail comments to me at OTBookOfKnowledge @ Gmail.com. The process of woodturning involves the use of tools, machinery and materials which could cause injury or be a health hazard unless proper precautions are taken, including the wearing of appropriate protective equipment.