Dear Tom,
The tool is a FREEWHEEL remover for the old style freewheels (such as Regina) with the dreadful "two-notch" design.
The "wings" are placed betwixt two adjacent cogs in order to try and keep the male part of the remover in tighter contact with the (soon-to-be-stripped) freewheel body. Can you tell how much I admire the old-style Regina /Everest/ etc. design of freewheel bodies ?
What makes the tool seem so confusing for you is that there is an entire piece missing from your tool that attaches to the threaded piece in the center. I have that old tool complete and I'll send you a picture of what the whole unit actually looks like.
I believe these things were made in Italy originally, sometime in the fifties to the 1960's or so. They are quite hefty and function well as conversation pieces and doorstops . . . but don't get rid of your chainwhips and pipewrench - you'll still need them to get the stubborn freewheels off after the removal notches inevitably strip out.
Mike Fabian
San Francisco, CA