Abstract: A positioning device for positioning an element, such as an optical element used to direct a radiation beam with respect to tracks on a carrier, with respect to translation along three mutually perpendicular axes and pivoting about two of those axes. Two sets of coils are disposed one at each end of a permanent magnet structure, each set having at least three coils having axes generally parallel to the structure axis, and arranged to co-act with the external return field of the magnet structure such that selective electrically energizing of two or more of the coils will produce a reaction force in the structure for positioning the structure in one or more of the selected degrees of freedom.