On the dead-centre position analysis of Stephenson six-link linkages

Abstract

A new method for analysing the dead-centre positions of Stephenson type six-bar linkages is presented in this article. This method uses the input-output polynomial equation of the linkage and the corresponding Sturm functions to formulate the necessary condition of the dead-centre configurations as a polynomial equation in terms of the input parameter only. A simple analytical method for identifying the true dead-centre positions among the real solutions to the condition equation is also developed. The proposed method is conceptually straightforward and does not rely on any structure-related geometric conditions; therefore, it can be systematically applied to all types of Stephenson linkages and other multiple-loop, single degree-of-freedom linkages regardless of the selections of the input-output pair and the type of the joints.