Abstract: The machine comprises two plate-like supports (9, 12) each provided with a crown of displacement blades (10), respectively displacement chambers (11), engaged into each other, and displaceable into a relative circular translation motion. The drive is implemented by a gear (7-9) at the center of the supports (9, 12), which exerts a force (F.sub.N) on one of the supports (9) at a radially displaceable position, said force presenting a radial component (F.sub.R) and a tangential component (F.sub.T). The direction of the force and the arrangement of the chambers (11) are so selected as to provide for a predetermined static position of the blades (10) in the chambers (11) independently of the wear. Optimum operation conditions are thus obtained with simple design and fabrication. For producing said pump, the plate-like supports are lapped pair-wise when they are in the state of blanks in conditions similar to the operation conditions and are then mounted in the machine.