The iterative calculation of the Cartesian geometry of general non-Cartesian structures

This paper describes an iterative scheme for the calculation of the Cartesi an coordinates of the nodes of any rigid structure from a knowledge of inte rnodal distances and angles. Since internodal distances can be determined a ccurately by laser interferometry, it is possible to derive coordinates to very high precision. The techniques constitute analytical vector and matrix methods which have been programmed in a general way to provide generic sof tware capable of finding iteratively the Cartesian geometry of complex stru ctures such as non-Cartesian machines. It has proved possible to include ce rtain constraints such that specified nodes should not move in certain Cart esian directions and specified connecting lines should remain horizontal or vertical, etc. The method requires an initial estimate of the Cartesian co ordinates of the nodes and then adjusts the coordinates until calculated in ternodal distances and angles are within tolerance. No reprogramming is nec essary to analyse a new structure. Full details of the mathematical derivat ions are included, as are details and results of the application of the met hod to the Stewart platform.