Described is a planetary harmonic differential transmission, comprised of a rigid externally-toothed inner sprocket, a rigid internally-toothed outer sprocket, a deformable belt that is toothed on both its internal and external faces, and a set of free-rotating planetary sprockets that are mounted on a rotating carrier cage and cause the belt to progressively engage and disengage from successive portions of the rigid sprockets. The input to the transmission is the relative motion between the carrier cage and the inner sprocket, and the output is the relative motion between the outer sprocket and the inner sprocket, resulting in a differential transmission.