A rotary machine for compression and decompression, comprising a disc-shaped rotor having a first rotation axis at right angles to the plane of the rotor and situated in a plane of orientation and a disc-shaped swing element having a second rotation axis. In the orientation plane, the second rotation axis makes an angle with the first rotation axis. Furthermore, a spherical housing is present surrounding the rotor and the swing element and in combination forming four (de-)compression chambers. A connecting body positions the rotor and the swing element in the housing. The rotary machine furthermore comprises a power drive and a mechanical connection delivering power to or taking off power from the rotary machine. In addition, the rotary machine is suitable for the seamless integration of generator components for generating or using electricity.