That tool is annoying me ... really hate not knowing what something is.
I have been around long enough that there's not much I have not seen in old tools and machinery but am totally stumped.
I don't think the screw is designed to adjust it for clamping purposes, more to ensure the setting is consistent.
My guess so far is:
I once saw a program about restoring sailing ships and they were shaping the mast out of a chunk of tree, using of course all the old tools to replicate the times and the carpenter kept checking the diameter with something that looked very similar but I don't get the reason for the small hooked end.
That's probably 100% wrong but will do until I can think of something better.
Keep us informed if you find out, I am sure I have seen one somewhere and the majority of my past would suggest shipbuilding, farriers or farming, previous owner or other contents of the box not give you a clue?