A rotary machine which can be either a pump or an internal combustion engine has a housing enclosing a plurality of rotor spindles lying on the surface of an imaginary cone for driving an output shaft positioned at the vertex of the imaginary cone. The spindles have a beveled gear on one end and engaging an output shaft and a conical bearing on the other end. Angled eccentric rotors are mounted to each spindle shaped to maintain tangential sliding contact with two adjacent rotors to form a compression or combustion chamber. A spherical version of a compressor or an engine uses a plurality of rotary pistons each of which is eccentrically mounted and forms a spherical segment. Each rotary piston is mounted for tangential sliding contact with at least two other rotary pistons to form a displacement chamber therebetween. The rotary pistons use a generally “tear drop” shape. A rotary pump has a housing having a manifold for distributing intake and exhaust air. The pump has a plurality of lobe shafts, each having an eccentrically mounted rotor attached thereto mounted in the housing to form a compression chamber in the middle of the rotor when the rotors are all in contact with each other during rotation.