A volume-expansion rotor machine comprises a casing (1) in the spherical cavity of which is mounted a rotor. The rotor has a spherical form and consists of a disk-shaped partition (2) hingedly connected, on its opposite sides, with blades (3, 4). The blades (3, 4) are connected with the partition (2) along its diameter, are mutually perpendicular and are connected with power take-off shafts (5, 5') oriented at an angle to each other. The hinged connection of the partition (2) to each blade (3, 4) consists of a cylindrical protrusion (9, 9') provided on the partition (2), engaging with a reciprocal groove (10, 10') on the end-face part of the blade (3, 4). Axes (a, b) of the protrusions (9, 9') of the partition (2) are mutually perpendicular and are located in one and the same plane.