Abstract: On a testing or processing machine the axis of a second bracket is to be ctly aligned relative to the axis of a first bracket. For this purpose a laser is mounted on the first bracket which directs a beam onto the reflector surface of a disc mounted on the second bracket. The reflected beam produces a dot of light on the perforated disc, which is arranged about the exit aperture of the light source. By adjusting the second bracket the dot of light is directed onto the aperture. Once this is done the two brackets are in exact alignment. To align brackets arranged at an angle to each other a beam deflecting device can be arranged in the path of the beam. All the auxiliary devices needed for measurement can likewise be exactly adjusted in accordance with the method.