The invention relates to a device for converting a rotational displacement into a displacement back and forth. Said device comprises at least one control cam region, provided with a driven cam element, having an eccentric control surface, and a cam follower element that can be displaced or pivoted by the cam element. The cam element is rotatably mounted in a flexible encircling element which is displaceably connected to the cam follower element on a plane that is perpendicular to the rotational axis of the cam element. The encircling length of the flexible encircling element and the peripheral length of the control cam region are configured to correspond and can be modified.