Abstract: This engine is substantially free from any vibration and noise, small in friction loss, improved in mechanical efficiency to a considerable extent, compact and lightweight, and applicable to a reciprocating piston engine. The engine comprises: curved cylinders each assuming a circular shape in cross section; curved pistons (1, 1a) each fitting and reciprocating within the cylinder; a rotor (2) carrying the pistons (1, 1a) to keep them in balance and to have them be rockable about the center of the rotor (2), wherein the rotor (2) is provided with connecting rods (6, 6a) to impart half a rocking power of the rotor (2) to each of crank shafts (10, 10a) each of which converts the half of the rocking power to a piece of torque on its axis of rotation; a gear mechanism for receiving the pieces of torque to combine them into an output power; and, an output shaft connected with the gear mechanism for receiving and out-putting the output power.