Watchmaker's lathes often have a specialised chuck that look like a faceplate with three slots; in those slots are mounted three (one each slot) little vises. These are used, I assume, for holding thin flat things that you want to do lathe tricks with.
In all of the pictures of these that I have seen the slots are one straight radial, and the other two are curved. Why?
Here's an example: ebay #130098743586