I think that the middle part is a support shaft for a large cutter radius attachment for a Cincinnati Monoset cuttergrinder.
I found an image for one for a new Monaset clone.
Features CMI’s MONASET Tool Grinder precisely grinds, sharpens, and reconditions parts with complex shapes… We looked at our successful MONASET grinder very closely before we came up with the engineering refinements which, when combined with its field proven concepts, make it an even better tool...
cinmac.com
I don't have the one for my original Monoset but do have the ofset bracket that fits on the end .
The holes in the bracket are 3/4" dia. so that should correspond to the left hand end of of your part if it is for a Monoset.
The tapered end if it fits a Monoset should be the same as a #40 Milling machine taper .
The cap nut on the Monoset spindle would hold it in .
you can see the original Monoset collet and other tool holder setup here on page 25
I couldn't find an image of this part in there .
I have attached some pictures from my old machine.
I don't have the part like yours but have never needed it but maybe some other monoset owners could use it if in fact that is what you have there.