and the first right angle prism 40 this derotator 30 rotates the first leg of the beam so that the final leg of the beam will be aligned correctly the use of the x y position sensor 24 and computer and rotator 26 to operate the beam derotator 30 requires an algorithm and software in an effort to improve and simplify the prior art device a study of the amount of rotation of the beam 12 from its desired orientation showed that the amount of rotation of the beam was directly related to the angle between the two articulated arms 20 and 22 and that the rotation between the arm 20 and the fixed arm 36 had no effect on the beam rotation it was also discovered that the angle between the two arms 20 and 22 is one half the angle between the rotated position of the beam and its desired orientation fig1 shows angle 34 a 34 between the two arms 20 and 22 and angle 2a a u00d7 2 between the beam vertical axis and the beam rotated axis in fig2 with this information the rotation problem was solved by this invention in the following manner fig3 illustrates a beam positioning system 10a constructed in accordance with this invention in this figure those elements having the same function as in fig1 are given the same reference number as in fig1 and those elements which have a similar function are given the same reference number as.