Equivalent Linkages and Dead Center Positions of Planar Single-DOF Complex Linkages

This paper proposes a simple and general approach for the identification of the dead center positions of single-DOF complex planar linkages. This approach is implemented through the first order equivalent four-bar linkages. The first order kinematic properties of a complex planar linkage can be represented by their instant centers. The basic idea behind this method is obvious and straightforward. The condition for the occurrence of a dead center position can be designed as when the three passive joints of the equivalent four-bar linkage become collinear. The proposed method is a general concept in the sense that it can be systematically applied to analyze the dead center positions for any type of single-DOF planar linkages regardless of the number of kinematic loops or the type of the kinematic pairs involved. The velocity method for the dead center analysis is also used to compare the results. The proposed method paves a novel and easy way to analyze the dead center positions for complex planar linkages. This concept is presented for the first time for the dead center analysis of planar complex linkages. Examples of complex linkages are employed to illustrate this concept in this paper.