So the U-clamp/shaft slides back & forth, allowing the 4 oblique-angled levers to move from a smaller diameter to a larger diameter, or 'vise'-versa? And the delta-diameter of the four fingers is relatively-limited, due to the narrow slots in-which they move?
Seems like some-sort of an assembly tool for inserting some type of seal into a flange, like for a very-large diameter pipe, where you are placing grommets into large machined holes or onto shafts.