Unknown tool / transfer tool gauge

I need help identifying this tools purpose. This is made of steel with a brass locking screw and nut. It also has three hardened points (see first photo for details), they are aso of different lengths to make up for the difference in heights of each segment. Closed it is three inches long, opened to a full radius, it covers a circle of about four inches . There are no manufacturers markings anywhere on this item. My thoughts are that it is some kind transfer gauge. What does our combined knowledge think?