A method is provided for aligning an articulated beam delivery device, such as a robot, by utilizing an electronic, high resolution television camera as a transducer for measuring small beam deviations at relatively short distances. A display monitor coupled to the camera is located in view of an operator of the robot to provide direct visual feedback for use during the aligning method. The aligning method includes the step of transmitting a collimated optical beam so that the beam travels along a first base path and is deflected by an adjustable mirror supported on an arm assembly having first and second axes of the robot for rotation therewith about the first axis and thence along a second beam path. The beam is also deflected by at least one other mirror supported within a wrist mechanism of the robot to travel along a third beam path to a beam exit end of the robot. The camera is mounted on a tool support member rotatable about a third axis of the wrist mechanism to sense the beam and to thereby generate a video image containing a beam point related to the beam. The beam point is then displayed on the video display device. In order to adjust the first mirror, the operator causes the arm assembly and, consequently, the camera to rotate about the first axis so that the beam point on the display device traces a curve, every point of which is substantially equidistant from a fixed center point.