A rotary pump has a chamber with a cross section defined by a pair of intersecting arcs which create a pair of cusps; a sun rotor (32) sweeps the cusps and has a pair of arcuate recesses (40) in the circumference which accommodate a pair of planet rotors (18, 20). The assembly is driven by an epicyclic gear train. The gears have adjustment to advance or retard the drive in order to fill and empty the working spaces (42) of the pump efficiently. The planet rotor shape is adapted for sealing in the cusp zone. The pump parts are reduced in volume so as to give a working space which is 60-70 % of the chamber volume. Versions with 2 and 3 planet rotors are described. Use as a hydraulic motor.
