Abstract: A hot gas engine operating with a Stirling cycle includes a hot chamber, displacer piston, regenerator, cold chamber, and power piston. A displacer piston is associated with a kinematic transmission train employing non-circular gears so as to convert rotary motion of a mainshaft into longitudinal piston movement and vice-versa. A power piston is associated with a kinematic transmission train employing non-circular gears so as to convert rotary motion of a mainshaft into longitudinal piston motion and vice-versa. The displacer piston and power piston relate to each other so that the engine working gas operates in close accordance with the theoretical four strokes comprising the Stirling cycle.