A driving unit for use with a rolling vehicle is provided containing a first and second motor mechanically coupled to two wheels via a transmission unit which is pivotable about the steering axis of the driving unit and adapted to establish a driving relationship between the first motor and one wheel of the unit and for establishing a driving relationship between the second motor and a second wheel of the unit. The coupling between the first motor and second motor and the transmission unit allows the transmission unit to pivot about the steering axis without causing a corresponding pivotal movement of the platform on which the first motor and the second motor are fixedly mounted, while allowing the first motor and the second motor to transmit power to their respective wheels. Various transmission units for use in these driving units are provided as well as rolling vehicles containing such units.