A crankgear-free rotary piston motor or machine is comprised of at least one oval stationary element (1) and at least one rotary ring with a toothed outer contour in the shape of a broken spherical triangle (2), wherein the oval stationary element (1) is positioned in a rounded spherical triangle shaped working cavity (13), the said working cavity (13) being located inside the rotary ring with the toothed outer contour in the shape of a broken spherical triangle (2), while the assembly of the said oval stationary element (1) and rotary ring with the toothed outer contour in the shape of a broken spherical triangle (2) is cinematically linked by at least two pinions (11) that mate with the outer toothing (12) of the said rotary ring (2).
