A converter for use in a high speed rotationally oscillating surgical burring device comprises an output shaft, and a rotationally oscillating secondary drive rotor coupled to the output shaft. The secondary drive rotor is arranged and configured with a size and mass to minimize its angular momentum. A unidirectionally rotating primary drive rotor is provided. A linearly reciprocating transmission converts unidirectional rotation to bidirectional rotational oscillation coupling the primary and secondary drive rotors. The transmission is arranged and configured with a size and mass to minimize its linear momentum. An input shaft is coupled to the rotating primary drive rotor to which a unidirectional rotational force is applied.