Disclosed are rotary positive displacement machines capable of acting as an engine and as a pump, serving to improve the profile of working members of helical rotary engines, compressors and pumps. An actuator is comprised of a pair of rotors having engaged helical teeth. The rotors are disposed in chambers which encircle both. The working areas of the profiles of the teeth in an engaged pair are delineated in cross-section by portions of a cycloidal curve for one rotor and by arcs of circumferences which are eccentrically offset from the axis of the second rotor. Such a profile of teeth produces an eccentrically cycloidal engagement capable to work efficiently at very high rotor rotation speeds. The presence of power contact and low sensitivity to gearwheel skews allow for working with nonhomogeneous media, including those containing solid inclusions.