A rotary machine employing a heterodyne transmission includes: a central axle; a planetary gear set comprising a sun gear journaling the central axle and a plurality of planet gears surrounding and intermeshed with the sun gear; and a plurality of rotating clusters, each of the rotating clusters comprising a rotating central body and a plurality of rotating eccentric bodies surrounding and intermeshed with the rotating central body, wherein the rotating central body is coupled to a respective one of the planet gears, and wherein each of the rotating eccentric bodies has a center of mass off-axis with respect to its axis of rotation.