A linear unit has a substantially rigid housing unit having an engagement slot, a rotor that is received in said housing unit so as to be movable back and forth in a travel direction, the rotor having at least one engagement device which engages the engagement slot in said housing unit in an engagement direction extending substantially orthogonally to the travel direction, the at least one engagement device including not only a contact unit associated with the rotor, but also a strip unit, and means for compensating a position of the strip units relative to the contact unit.