I should know what this is, but I don't.  My guess is to measure RPM.  Anyone know for sure???

 Rpm is the right answer.

Yup, rpm. It is really just a counter tho, it counts how many times a shaft goes around. To measure speed, you also need a watch to time how long it took to go around that many times...

I have 3 of them, but none have the needed rubber ends to allow them touch the shaft with. What brand is yours?

Wayne

Most of them have a friction "cluch" , the early starrets didn't (pre 1905?) You line up the "dimples" and hold down on the top one. apply to speeding shaft, when ready release pressure and time for one minute. Whala! you should have your shaft speed?
Graeme

>the needed rubber ends

Pencil eraser : )

This one is a Starrett.  It does look like it has a pencil eraser retrofit, at least the metal crimp that holds the eraser.  The end that touches the shaft is black rubber.
Jim