At first I thought it might be a nut cracker, since those are sometimes made like a press, but you could probably put a small coconut in that.
It might be a cider press (possibly incomplete, a cider press should have some sort of vessel to contain liquid, or some means of moving liquid into a bigger vat)
Too small for a caliper press. Looked more carefully, no stampings or numbers. But, has a label on it! Hadn't seen it before, it's on the inside:
It's very stout. Welch Scientific makes classroom physics and chemistry equipment. I'm sure it's a press of some kind. A search of their website for "press" and for "clamp" didn't turn up a match. Does this info help job anybody's memory?