The inventive volume expansion rotary piston machine includes a body (1) with a circular working cavity which is provided with and intake and exhaust channels (18, 19) and in which bladed pistons (5, 6) are disposed on two coaxial shafts (2, 3). Said shafts have arms (4) which are connected, by means of connecting rods (10), to crankshafts with planet toothed wheels which are fastened to said crankshafts and are engaged with a fixed central toothed wheel (12). The volume expansion rotary piston machine comprises an output shaft (7) with an eccentric (8) on which a planet wheel (11) with a carrier (9) are rigidly connected and mounted, and which planet wheel is kinematically connected to the arms (4) of the two shafts (2, 3) by means of the connecting rods (10).