A device for converting rotary motion into translational motion comprises a first component and a second component, with the second component being arranged to be able to turn around an axis of rotation relative to the first component and to move in the axial direction. Each component is provided with at least one track in which are arranged roll bodies. To produce a relatively high axial force with relatively small dimensions of the device, the tracks are arranged at opposing faces of the two components, with the tracks extending in a circle around the axis of rotation and in a spiral manner with a given pitch over the periphery of the components.