I have be researching what this is. It is from a Maryland estate. We remember it was used with hair.
The only place I found a lot of nice vintage hair items was on;http://www.taste-t-vintage.com/
Check them out if you are into hair vintage items!
I asked them what it was and they said a Jay pin curler.
I don't know if there are any other pieces or missing parts.
But check it out here: