Abstract: Continuously variable speed ratio transmissions (CVT) for an in-wheel application use one or more magnetorheological (MR) or oil-shear clutch assemblies, each of which can have a unique speed ratio, to transmit torque between an input shaft and an output shaft. The clutch assemblies comprise an input drive element, input idler assemblies, a number of clutch assemblies output idler assemblies, and an output shaft assembly. Preferably, the CVT can be structured and arranged to occupy a volume between about 10- and 11-inches in diameter and between about 4 and 5 inches in axial length. The MR clutch assembly includes a rotateable input cylinder and a rotateable output cylinder that are coaxial about a stationary shaft. The input cylinder and output cylinder are separated by a gap that is filled with an MR fluid. A multitude of coil windings are disposed on the stator of each of the MR clutch assemblies. When current flows through the coil windings, a magnetic flux field is produced in the MR fluid.