An energy transfer machine, for example, a positive displacement internal combustion device, has a fixed outer housing, an internal rotating carrier and one or more inner rotors with rotational axes which are offset from the inner rotor carrier rotational axis. Projections from the fixed outer housing and rotor mesh with each other to define variable volume chambers. In another energy transfer machine, in which the outer housing may be fixed or rotating, projections of the rotor are expandable within cylinders defined by projections of the outer housing.