Abstract: According to the exemplary embodiment shown, the machine comprises a housing having a chamber formed therewithin which is circumscribed by a plurality of spiralled, parallel and arcuate lands with intervening, narrow grooves, and a rotor journalled therewithin, the rotor having a plurality of spiralled, parallel and arcuate grooves with intervening, narrow ribs. The rotor has a ring-type gear mounted therewithin, and the latter meshes with a gear centrally mounted on a rotor-traversing shaft. The arcuate grooves and ribs are one less in number than the arcuate lands and narrow grooves, and the journalling of the rotor and mesh of the gears causes the rotor to describe an epicyclic rotation relative to the housing. The depicted embodiment comprises an internal combustion engine, however the machine is useful as an expander, fluid motor, and the like.