"part of a zig-zag rule" is too obvious, so I won't say it
It could be something like the simple clamps guitarmakers use when gluing the purfling on a guitar/other instrument. Stewart MacDonald's current versions look like this:
but they were traditionally made by the craftsman, looking more like this:
I've seen some discussions of making your own that refer to hole saws for cutting out the "jaws." I imagine, before power tools, that the jaw shapes were more varied, chosen by the fastest manufacturing method; as the Stewart MacDonald picture shows, you need a lot of them.