RIGID BODY POINTS APPROXIMATING COAXIAL CYLINDERS IN ALTERNATING SETS OF ITS POSITIONS

MACHINE SCIENCE

Abstract

The problem of determining special points of a moving body which in alternating sets of its given positions deviate least, in the least square sense, from coaxial circular cylinders is considered. The sought-for approximation is one which minimizes the sum of squared algebraic deviations of these points from the coaxial cylinders approximating their paths in each of the given sets of positions. The points of interest lie at the intersection of three 11th order surfaces determined from the stationary conditions of the least square objective function. The theory and methods developed in this paper can be readily applied to the synthesis of adjustable parallel robotic mechanisms of modular structure designed for the approximate generation of multiphase motions or multiple point-paths of the output link.