Abstract: A rotary machine useful as a rotary compressor or engine having a cylindrical compressor rotor with a lobe outstanding from its cylindrical rolling surface geared to another cylindrical rotor with a recess, in its cylindrical rolling surface, the rotors being rotatable within respective parallel intersecting cylinders of a stator so that the lobe sweeps its stator cylinder and meshes with the recess as it moves past the other rotor.The lobe and recess are of such complementary shape that the lobe more than half fills the recess while still contiguous with its cylinder and the leading face of the lobe is contiguous with the leading surface of the recess after separation of the rolling surface so that the gases entrapped in the recess are of minimum quantity, and are released from the recess back into the cylinder but behind the trailing surface of the lobe.