An apparatus for aligning a machine tool with a target location on a structure. A machine plate positionable on the structure has a plate bushing providing a hole through the plate. The apparatus also includes a nosepiece for guiding a distal end of the tool through the plate bushing to the target location. The nosepiece has a collet configured to be moved at least partly through and sideward in the plate bushing to center the nosepiece on an element projecting from the structure at the target location. The nosepiece can be attached to the plate bushing to establish normality of the tool relative to the projecting element.