Abstract: The center of a collet having a plurality of individual gripper members resiliently spaced apart in an annular array and operated on by a frustoconical surface can be adjusted by displacing some of the gripper members more than others of said gripper members parallel to the axis with which both the annular array and the frustoconical surface are nominally concentric. This causes the frustoconical surface to produce greater radial displacement of some of the gripper members, thereby shifting the center of the collet transverse to the above-mentioned axis.