NOVELTY - The machine has multiple rotor cranks provided with rotor crank arms extending away from a rotor rotational axis. Each rotor crank arm comprises a rotor crankpin at a distal end laterally spaced from the rotor rotational axis. A synchronizing plate is rotatably coupled to the rotor crankpins for non-rotative epicyclic oscillation with respect to rotor shafts and helical rotors. A driver crank is rotatably coupled to a central bearing in a geometric center of the plate. A driveshaft (30) is fixedly coupled to the driver crank and located coaxial with a central axis of the machine.    USE - Planetary rotor machine e.g. 3-rotor planetary rotor machine and 4-rotor planetary rotor machine, for geothermal power generation application. Can also be used for geopressure power production application, waste heat application, solar thermal and solar pond application, biomass application, natural gas wellhead pressure letdown application, grid sub-station pressure let-down application, oil and gas producing well application, off-shore oil platform application, biomass refinement let-down application and biomass pumping application.    ADVANTAGE - The machine can eliminate backlash risks associated with the gears or pulley/belt assemblies by a synchronizing mechanism to facilitate a level of synchronized precision over duty cycles at high speeds such as 3600 RPM or higher for planetary rotor machines. The machine reduces forces experienced by the rotor crank bearings for extending life of the bearings and allowing the use of smaller bearings in a given application. The machine utilizes the rotor crank arms with angled portions such that crank throw length can be increased while maintaining high structural integrity of the rotor crank arm as compared to an arm with a single-angled portion that creates a similar crank throw.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for the following:    (1) a 4-rotor synchronizing mechanism for a 4-rotor planetary rotor machine    (2) a 3-rotor synchronizing mechanism for a 3-rotor planetary rotor machine.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of a planetary rotor machine during geothermal power generation.    Planetary rotor expander (10)    Intake valve (20)    Driveshaft (30)    Synchronizing mechanism (40)    Generator (50)