Analytical-Form Position Analysis of the 7-Link Assur Kinematic Chain with Four Serially-Connected Ternary Links

Abstract

The paper addresses the position analysis of the 7-link Assur kinematic chain that features three binary links and four serially-connected ternary links. The analysis, aimed at finding all possible assembly configurations of the Assur kinematic chain, is carried out by first devising a set of three constraint equations in a corresponding number of unknowns. Then, by an original elimination procedure, two out of the three unknowns are simultaneously dropped out. As a result, a final algebraic equation of degree sixteen with only one unknown and free from extraneous roots is obtained. The sixteen solutions of this equation provide as many assembly configurations for the Assur kinematic chain in the complex field. Finally, a case study is reported.