The incremental very accurate positioning device is operable to control accurate positioning of a movable member such as a tool. The apparatus comprises a base with a mounting bar spaced from the base for mounting the member. The bar is movable along its elongate axis by a drive force applied to the proximal end thereof for moving the distal end forwardly and rearwardly along the axis. The bar is mounted on two parallel spaced elongated flat springs that extend transversely of the bar. The springs are fixed to the bar for maintaining an axial force on the bar and are mounted at each end to a block which is pivotally mounted on the base.
