Position analysis in polynomial form of class-three Assur groups with two or three prismatic joints

This paper presents some new results on the position analysis in polynomial form of the class-three Assur group. The aim of this position analysis is to determine all possible configurations of the Assur group, for a given position of its external joints. Five new kinds of the class-three Assur group with two or three prismatic joints are investigated. The analysis leads to a non-linear system of equations. Using a successive elimination procedure, a final polynomial equation in one unknown is obtained. The real solutions of this polynomial equation correspond to assembly modes of the Assur group. Finally, five numerical applications of the proposed methods are presented.