The way that sort of lock works is the outer ring rotates the small cylindrical pin so that it rolls up the flat ramp. As the pin moves up the ramp, it forces the gap in the inner ramp ring to close, constricting it around the anvil shaft. The inner ring is keyed, there is a raised area where it engages to the body, so it shouldn't rotate and when it grips the inner shaft everything should lock. That gap in the inner ramp ring needs to be clean, swarf in there will prevent it from closing. The little pin needs to be round and large enough to engage easily with the outer ring when in the rest position, and the ramp surface needs to be smooth and flat.
That pin and ramp both look a little worn from use. Lapping the flat ramp area, and finding a small hardened pin to replace the existing one, assuming it is as bad as it looks from your picture, should restore the functionality. Starrett is good about supplying replacement parts, so you may still be able to get OEM stuff if it needs replacing.