MANY of the automotive differentials that have been developed since the first one was built in 1827 are described here.
The ideal differential would distribute torque equally to the two driven wheels being differentiated, under any condition of relative motion as dictated by ground speed. At the same time it would never permit torque to be applied to any one wheel in excess of the available traction without causing both wheels to slip simultaneously.
The complete answer to this problem has not yet been found and, the authors admit, may be what we are looking for is a mechanical or electronic brain to do the job.