Actually Cobbler came closest.
The wing nut adjustment is to allow the sticks to be lined up with the pen lines:
And then its function is obvious:
It's a center finder for circles.
I found this the other day tucked into a nook under my workbench. Clearly I made it at some point, but I don't remember doing it, or why I needed it. It took me a couple of minutes even to figure out what it was.