[Mooser]

I've got 3 of these in different sizes, came with some machinist tools someone I know gave me, he wasn't sure where they came from, probably his dads old stuff
Anyway, I have no idea what they are and haven't come up with a use for them is several years so it's not something in my line and yet somehow looks familiar
No part numbers or anything, might be "home made" but I don't see the purpose

Here's a picture of the larger one
Steel, doesn't seem hardened and will surface rust fairly easy
Edges are all pretty sharp but maybe not "sharpened"
The internal thread is tapered, the set screw stops before bottoming out and I can see the thread get shallower, might just be from a starting tap shape though
No slits or anything so not an expanding mandrel (unless they were un-finished?) and the internal square is pointless if they were
The set screw is short and the hex for the key goes right through
Corners on the inside square are pretty small/sharp, not sure if it was wire-cut or broached

Look familiar to anyone?

[peteeng]

a

[Mooser]

Set screw appears to be straight thread, goes in equally deep if flipped over, doesn't actually seem to have a top or bottom
M