Abstract: A piston mechanism assembly includes a piston group that includes two annulus-shaped undulant-surface pistons that axially mate each other and movable relative to each other. Each undulant-surface piston includes an axial through hole and has an end forming a continuous undulant surface. Each undulant surface includes at least two crest portions and two trough portions to mate another undulant surface. Two outer rings surround an outer circumference of the piston group and are respectively movable in synchronization with each piston and have outer ring gates corresponding to the undulant surfaces. Two inner rings are respectively received in the axial through holes of each undulant-surface piston to be movable therewith and have inner ring gates corresponding to the continuous undulant surfaces. While the two pistons rotate relative to each other, an axial reciprocal motion is induced by the undulant surfaces on the pistons to cause volume variation of chambers therebetween.