A free-piston Stirling machine drivingly coupled to at least one rotary electromagnetic transducer. At least one pulley is oriented in a plane of a reciprocating piston connecting rod. At least one motion translating drive link connects the connecting rod to the pulley by at least two straps so that the pulley moves in rotationally oscillating motion. The two straps extend along an arcuate surface of the pulley into connection to the piston rod at two spaced locations. The pulley is linked to a rotary electromagnetic transducer so that both move in rotationally oscillating motion. Preferably a piston spring resonates the piston at an operating frequency of the Stirling machine and a torsion spring resonates the pulley in rotational oscillation at the operating frequency of the Stirling machine.