An actuator comprising a primary part having primary part windings adapted to be energized, having the primary part in the radial direction and arranged rotatably around an axis of rotation , and having a hollow body surrounding the rotor in the radial direction, wherein the rotor and the hollow body are magnetically coupled to one another in such a manner that the rotor moves upon rotation along a helix extending around the axis of rotation , and wherein the rotor can be motion-coupled to an actuator in such a manner that upon rotation around the helix the actuator is translationally displaced, characterized in that the rotor extending parallel or obliquely to the axis of rotation is formed in a single piece and has a uniform magnetic polarization and has rotor segments arranged adjacent to one another along the circumference, wherein adjacently arranged rotor segments are magnetically polarized differently, and wherein the individual rotor segments each have, on the upper side facing the hollow body , a plurality of raised active portions which interact with the hollow body , that the hollow body has hollow body segments extending parallel or oblique to the axis of rotation and arranged adjacent to one another along the circumference, wherein adjacently arranged hollow body segments are differently magnetically polarized, and wherein the hollow body segments each have on the inner side facing the rotor a plurality of raised counter portions interacting with the active portions , and that the active portions , which are equally magnetically polarized, and the counter portions , which are equally magnetically polarized, are each arranged along a helix extending around the axis of rotation . primary part in the radial direction and arranged rotatably around an axis of rotation , and having a hollow body surrounding the rotor in the radial direction, wherein the rotor and the hollow body are magnetically coupled to one another in such a manner that the rotor moves upon rotation along a helix extending around the axis of rotation , and wherein the rotor can be motion-coupled to an actuator in such a manner that upon rotation around the helix the actuator is translationally displaced, characterized in that the rotor extending parallel or obliquely to the axis of rotation is formed in a single piece and has a uniform magnetic polarization and has rotor segments arranged adjacent to one another along the circumference, wherein adjacently arranged rotor segments are magnetically polarized differently, and wherein the individual rotor segments each have, on the upper side facing the hollow body , a plurality of raised active portions which interact with the hollow body , that the hollow body has hollow body segments extending parallel or oblique to the axis of rotation and arranged adjacent to one another along the circumference, wherein adjacently arranged hollow body segments are differently magnetically polarized, and wherein the hollow body segments each have on the inner side facing the rotor a plurality of raised counter portions interacting with the active portions , and that the active portions , which are equally magnetically polarized, and the counter portions , which are equally magnetically polarized, are each arranged along a helix extending around the axis of rotation . <EOS>