Rex

Rex Driving wheel.

 

This looks like a treadle wheel for a lathe, maybe for a watchmakers lathe.

Source; Melhuish catalogue 1925.

Looking on the net has not uncovered any information about Rex.

This firm is known for sewing machines.

They made several motor bike's under the name Rex Acme, and also where a grinding/polishing wheel manufacturer.
 

One more little piece they made,

This is a Rex roller remover, for watches?