Wow, you guys are good! Thanks fellas, I was pretty sure it had something to do with cloth or leather, but beyond that I was stumped.
Hmm, looking through the examples in the links, they all have some sort of rotating brass barrel (with different length shoes) for the blade and punch to come up against. Mine must have worked differently somehow, before it's brass shoe went missing. Ah well, at least I know what it is now.