I seem to remember seeing a bunch of clamps like those hanging on a wall in a neighbors farm shed. Thinking back, the old guy did make his own baskets for tomatoes back in the day, maybe they had something to do with building the baskets? A clamp to hole the bottom disc as they stapled the sides together?
Other than that, maybe some sort of assembly tool, something to hold a spring compressed or something?
What ever the disc part holds, it likely doesn't have to hold it very tight since its only got a wing nut to tighten it up, this makes me think its more a of an assembly fixture than a clamp. It looks like its mean to hold something of the side of a bench while its being assembled or worked on.