A workpart chuck is provided with a centering member that is movable toward the axis of rotation of the chuck as the chuck rotates the workpart in an eccentric non-centered position. As the centering member moves the workpart, a sensing device senses the extent of changing eccentric movement of the workpart and generates an electrical signal that is indicative of the extent of such eccentric movement. The workpart is moved toward the chuck axis until the signal reaches a predetermined value indicative that the workpart is rotating about its axis; i.e., the workpart axis and chuck axis are substantially coaxial. The centering member is offset slightly relative to the chuck axis of rotation to assure that excessive movement of the centering member placing the workpart center beyond the chuck axis of rotation will not result in the workpart being driven to an extremely eccentric position and possibly even off the face of the chuck. The sensing device will detect a sudden shift of the workpart position relative to the centering member indicative of such movement beyond center, whereupon the control system will cause the centering member to retract a small distance and advance in a new attempt to center the workpart.