POSITION ANALYSIS IN POLYNOMIAL FORM OF ASSUR GROUPS OF CLASS 3 AND ORDER 3 WITH TWO AND THREE PRISMATIC JOINTS

摘要

This paper presents the position analysis in polynomial form of the Assur groups of class 3 and order 3 including two or three prismatic joints (triad). The aim of this position analysis is to determine all possible configurations of the Assur group, for a given position of its external joints, two kinds of the Assur group of class 3, with two and three prismatic joints are investigated. The position analysis leads to a nonlinear system of three equations with three unknown parameters. Using a successive elimination procedure, a final polynomial equation in one unknown is obtained. The real solutions of the polynomial equation correspond to assembly modes of the Assur group. The smaller upper-bound of the real solutions is established for the investigated triads. Two numerical applications of the proposed methods are presented.