Positive displacement machine with planetary motion and hypertrochoidal geometry

A positive displacement machine including a cylindrical mechanism, essentially constituted by a cylindrical piston (male device) having an integral order of symmetry s.sub.P with respect to its axis, a cylindrical enclosure that surrounds it (female device), having an integral order of symmetry s.sub.C with respect to its axis, and a third device physically embodying two axes, parallel to those of the cylindrical surfaces defining the shape of the piston and enclosure, this third device being in rotoidal connection about its axes with the piston and the enclosure, respectively, the orders of symmetry s.sub.P and s.sub.C differing from each other by one and the geometries of the piston and enclosure being defined so that these devices are in direct contact, characterized in that one of the devices, male or female, has a directrix D.sub.1 which is identified with a curve that is uniformly distant (the uniform distance optionally being zero) from a closed hypertrochoid, excluding hypertrochoids degenerated into hypotrochoids, peritrochoids and epitrochoids or with curves uniformly distant from these hypotrochoids, peritrochoids and epitrochoids, this hypertrochoid having neither a double point nor a retrogressive point, the other device having a directrix D.sub.2 which is the envelope of D.sub.1 in a relative planetary motion defined by two circles C.sub.1 and C.sub.2, having respective centers and radii (O.sub.1, R.sub.1 and (O.sub.2, R.sub.2), which are respectively solid with the directrixes D.sub.1 and D.sub.2 and roll on one another without slipping, by internal contact, .vertline.O.sub.1 O.sub.2 .vertline. specifying the center distance between the axes of the third device.