During the manufacture an aircraft, a tool-carrying rail is removably attached to a rail-side surface of the aircraft with a vacuum cup. The tool-carrying rail includes a longitudinal axis to mount a tool. The vacuum cup is stiffened along a first axis transverse to the longitudinal axis of the tool-carrying rail and the vacuum cup is stiffened along a second axis parallel to the rail-side surface of the aircraft. To removably attach the tool-carrying rail, a perimeter of the vacuum cup is removably sealed to the rail-side surface of the aircraft against vacuum loss and a point on the rail is rigidly positioned with respect to a point on the rail-side surface of the aircraft. In addition, a vacuum source is coupled to a spatial volume occupying all of a space between the vacuum cup and the rail-side surface of the aircraft and the tool is slidably positioned along the longitudinal axis of the tool-carrying rail.