An engine, called rotary piston engine, comprising: - a shape of revolution with respect to an axis (delta), and movable in rotation about said axis (delta) relative to an enclosure, - n cells (A_i) which consist of shapes of revolution with an axis (β_i), distributed on the periphery of the shape of revolution, - in each cell (A_i) is housed a roller (G_i) which rotates about the axis (β_i), and has at least two faces, (G_i_1) and (G_i_2), the first of these faces (G_i_1) being capable of ensuring sealing with the cell (A_i) at certain moments of the cycle of the system when this face is inside the cell (A_i) and whose section by a plane perpendicular to (β_i), is a circular arc centered on the axis (β_i), with a center angle, - a mechanical means which makes the rotation of each roller (G_i) about the axis (β_i) proportional to the relative rotation of the axis (delta) of the shape of revolution with respect to the enclosure, - the enclosure being the enclosure generated by the rollers (G_i) in their rotational movement about the axes (β_i) themselves driven by the shape of revolution, and the relative rotation of the axis (delta) of the shape of revolution with respect to the enclosure, - the face (G_i_2) of the roller (G_i) is the enclosure generated by the enclosure at the level of the roller (G_i) and thus ensures sealing between the roller (G_i) and the enclosure, the assembly is made in such a way that, if we consider a section by a plane perpendicular to the axis (delta), the enclosure, the shape of revolution and one end of the circular arc of the face (G_i_1) of the roller (G_i), are in contact, in one place, at a particular moment of the cycle, - side walls or flanges (J1,J2) on which the shape of revolution, the rollers (G_i), and the enclosure bear, - the shape of revolution, the rollers (G_i), the enclosure, the flanges (J1, J2), delimiting closed and variable volumes at different moments of the cycle of the relative rotation of the shape of revolution with respect to the enclosure, the engine being characterized in that at least two cells (A_i) and (A_i+1) are contiguous, and in that, between at least two consecutive cells (A_i) and (A_i+1), a passage is arranged such that, when one end of the enclosure is between these two cells, the fluid compressed by one of the faces of the end of the enclosure, can pass onto the other face. - a shape of revolution with respect to an axis (delta), and movable in rotation about said axis (delta) relative to an enclosure, - n cells (A_i) which consist of shapes of revolution with an axis (β_i), distributed on the periphery of the shape of revolution, - in each cell (A_i) is housed a roller (G_i) which rotates about the axis (β_i), and has at least two faces, (G_i_1) and (G_i_2), the first of these faces (G_i_1) being capable of ensuring sealing with the cell (A_i) at certain moments of the cycle of the system when this face is inside the cell (A_i) and whose section by a plane perpendicular to (β_i), is a circular arc centered on the axis (β_i), with a center angle, - a mechanical means which makes the rotation of each roller (G_i) about the axis (β_i) proportional to the relative rotation of the axis (delta) of the shape of revolution with respect to the enclosure, - the enclosure being the enclosure generated by the rollers (G_i) in their rotational movement about the axes (β_i) themselves driven by the shape of revolution, and the relative rotation of the axis (delta) of the shape of revolution with respect to the enclosure, - the face (G_i_2) of the roller (G_i) is the enclosure generated by the enclosure at the level of the roller (G_i) and thus ensures sealing between the roller (G_i) and the enclosure, the assembly is made in such a way that, if we consider a section by a plane perpendicular to the axis (delta), the enclosure, the shape of revolution and one end of the circular arc of the face (G_i_1) of the roller (G_i), are in contact, in one place, at a particular moment of the cycle, - side walls or flanges (J1,J2) on which the shape of revolution, the rollers (G_i), and the enclosure bear, - the shape of revolution, the rollers (G_i), the enclosure, the flanges (J1, J2), delimiting closed and variable volumes at different moments of the cycle of the relative rotation of the shape of revolution with respect to the enclosure,