Some sort of stretcher seems like a good possibility. The teeth are angled down and toward the center so as to grab when pushed. Might be too small for a carpet stretcher, but maybe a web stretcher. Also, one of my ancestors was a cobbler, we still have his cobblers bench, forms and tools. These were not stored with them, but could be related to that?
The end definately is 2 pieces. Looks like the 2 pieces could be adjusted about 1/8 of an inch apart.
I've only got the one here, but all three appear to be the same size.
Fantastic feedback, I think we are on the right track.