The subject of the invention is a variable-volume rotary device with a housing (1) comprising an inner spherical cavity, inlet and exhaust ports and a bypass flow path. Within the housing (1) a rotary displacement member with spherical outer configurations capable of revolving around the center point of the spherical inner surface of the housing is mounted. Said rotary displacement member is equipped with a centrally disposed, disc-shaped partition (6) that forms a mutually isolated division in the spherical inner cavity of the housing (1) and has two pivot vanes (7, 8), splitting the housing cavity further into four isolated quadrants, the volume of which vary during gyration. Vanes (7, 8) are similar in shape to orange segments. Vanes (7, 8) are connected to opposing sides of and along the diameters of the central disc (6), and extend in mutually perpendicular planes, allowing for rotary movement. Inlet- and exhaust ports are arranged on the housing (1) so that, when the rotary displacement member is in motion, the inlet port connects only to a quadrant represented by the smaller spherical projection of the disc (6) within the inner spherical cavity of the housing (1), whereas the exhaust port only meets a quadrant indicated by the larger spherical projection of the disc (6) within the inner spherical cavity of the housing (1).