An apparatus for performing machining operations on an object includes a carriage, a movable head configurable with an operating attachment to perform the machining operations on the object, and a position determination system operable to determine the spatial relationship of the carriage and the object and provide a first signal representative thereof. The position determination system periodically determines the spatial relationship of the head to the object during machining operations on the object and provides a second signal representative thereof. The second signal is used to re-position the head to a desired position during the machining operations.