Abstract: This invention relates to power engineering, and more exactly, to engine building, and, in particular, to rotary internal combustion engines and pneumatic and hydraulic pump units. The invention helps to simplify the design of the rotary machine, reduce its material consumption rates, improve the manufacturing process thereof, and lower unit costs, all other conditions being equal, by using less complicated and less expensive manufacturing processes. The rotary machine comprises a housing in the form of two intersecting cylinder parts of different diameters having parallel axes; a rotor received in the housing coaxially with the smaller-diameter cylinder and comprising at least two segmental rotor parts provided with annular rotor covers. At least two pairs of annular elements are provided. Pivotal elements are interposed between the annular elements of each pair. A driving member is accommodated movably in the openings of the pivotal elements.