Abstract: Radial piston machine as a fluid pump or fluid motor comprising an inner valving trunnion, an outer cam ring and at least a cylinder block arranged therebetween and having reciprocating pistons, which tilt when the cylinder block rotates. The pistons have spherical heads and crowned piston rings along the biggest diameter or equator in order to create each an oblique sealing plane when the respective piston is tilted. Pressure in each chamber limited by said oblique sealing plane will give rise to a direct transformation of torque and fluid pressure. The valving trunnion has enlarged sealing fields to get a precompression of the fluid between high and low pressure fluid areas in order to avoid excitation of noise. The machine design can be for constant or variable displacement. In case of variable displacement, the sinusoidal curve of piston travel is adjusted for a variable preceeding angle (.epsilon.) by adding a constant eccentricity (c) so that the angle of the separation (.tau.