Abstract: The power conversion machine has a piston which is adapted to effect a combined turning and rocking movement internally in a double-curved space. The piston is in drive connection with a rotary shaft via an eccentric disc which is obliquely disposed on the center axis of the rotary shaft. The center axis of the rotary shaft and the center axis of the eccentric disc cross each other in the center of the double-curved space. The double-curved space in defined within a ball shell and is divided into two opposing substantially ball-shaped spaces by means of a stationarily secured circular partition plate. The piston operates simultaneously in the two semi-spherical spaces, the piston passing through the partition plate via a diametrically extending slot. The piston comprises a disc-shaped main portion, and two oppositely directed roller portions which are received in respective semi-spherical spaces.