An apparatus for use in orienting an object at a reference angle includes a pin gauge having at least two projections located at an end of the body of the apparatus. The projections are located at certain X Y coordinates of an X, Y Z Cartesian coordinate system. A horizontal support supports the body so as to be movable horizontally in the longitudinal direction of the projections. A mechanical drive member is operable to move the body mechanically in the horizontal direction. The apparatus may also include a vertical support and vertical drive member. The pin gauge is mechanically moved into contact with a surface of an object to provide a reference angle for the object. Then the object is pivoted, if necessary, to bring the surface into point contact with all of the projections of the pin gauge, whereupon the object is oriented at the reference angle. Process errors in aligning the object using the reference angle are reduced because the orienting of the object at the reference angle is accomplished using mechanical elements.