Position analysis in polynomial form of planar mechanisms with Assur groups of class 3 including revolute and prismatic joints

This paper presents the position analysis in analytical form of the Assur group of class 3 and order 3 with four links and six revolute/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. Four kinds of the Assur group of class 3, with one, two and three prismatic joints are investigated. The 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. Three numerical applications of the proposed methods are presented. Finally, a numerical application for position analysis of a planar mechanism with eight links including a triad with three external prismatic joints is also given.