Abstract: A grinding tool with a cylindrical sleeve, having several longitudinally extending slots penetrated by radially shiftable wedge-shaped bars with abrasive outer faces, is provided with a mandrel received in the sleeve and axially displaceable therein for shifting the bars radially outward and inward. The mandrel has longitudinal guide grooves with sloping bottoms, engaged by the correspondingly sloping inner faces of respective bars, and a shallower annular groove of frustoconical bottom intersecting these guide grooves; segments of a frustoconical ring, lodged in the annular groove and projecting into the intersecting guide grooves, engage in mortises of adjacent flanks of respective bars sliding in the guide grooves for positively shifting the bars when the mandrel is displaced in one of the other axial direction.