Hypotrochoid positive-displacement machine

A displacement device comprising:

• a housing;
• an inner rotor with an outer surface defining an inner rotor projection number of outward-facing projections, the inner rotor being fixed for rotation relative to the housing about a first axis;
• and
• an outer rotor with an inner surface defining an outer rotor projection number of inward-facing projections, the outer rotor being fixed for rotation relative to the housing about a second axis parallel to and offset from the first axis;
• the inward-facing projections of the outer rotor having inward-most tips defining, during rotation of the inner and outer rotors, hypotrochoid paths relative to the inner rotor;
• the outer surface of the inner rotor comprising tip sealing zones at tips of the outward-facing projections, the tip sealing zones being arranged to seal against the inward-most tips of the projections of the outer rotor as the inward-most tips trace the hypotrochoid paths;
• the inward-facing projections of the outer rotor intermeshing with the outward-facing projections of the inner rotor, and driving surfaces of the outward-facing projections of the inner rotor contacting corresponding driven surfaces of the inward-facing projections of the outer rotor as the inward-facing projections and the outward-facing projections intermesh to fix a relative ratio of rotation speeds defined by a ratio of the inner rotor projection number to the outer rotor projection number, the inward-facing projections defining respective slots extending from the inner surface of the outer rotor and axially spanning the inward-facing projections to cause respective driven surface flexible zones, of the inner surface at the inward-facing projections and defined by the respective slots, to flex under contact between the inner and outer rotors and the corresponding driven surfaces being formed at least in part on the respective driven surface flexible zones;
• in which, in use of the displacement device, contact between the driving surfaces and corresponding driven surfaces moves radially outward from a point of initial contact relative to a direction of rotation of the inner and outer rotors in which the driving surfaces drive the driven surfaces.