This mechanism for driving motions of a surface of spherical, ellipsoidal, plane, or other shape comprises a pair of drive wheels mounted on a freely pivoting frame, each wheel being driven by its own bidirectional motor. The motors and the active electronics of an angle encoder are mounted in an associated fixed frame, so no slip rings or other rotating connections are needed for motor power and control, or for determining the rotation angle of the pivoting frame. Control of the motors provides differential rotation of the two wheels to effect controlled rotation of the pivoting frame, and therefore of wheel direction. This avoids the use of a separate motor for changing the direction of motion of the surface.