A linear electrical machine including a frame with a level reference plane, an array of electromagnets connected to the frame and coupled to an alternating current power source energizing each electromagnet, at least one reaction platen of paramagnetic, diamagnetic, or non-magnetic conductive material disposed to cooperate with the electromagnets of the array of electromagnets so that excitation of the electromagnets with alternating current generates levitation and propulsion forces against the reaction platen that controllably levitate and propel the reaction platen along at least one drive line, in a controlled attitude relative to the drive plane, and a controller operably coupled to the array of electromagnets and the alternating current power source and configured so as to sequentially excite the electromagnets with multiphase alternating current with a predetermined excitation characteristic so that each reaction platen is levitated and propelled with up to six degrees of freedom.