Equivalent Linkages and Dead Center Positions of Planar Single-Degree-of-Freedom Complex Linkages

Abstract

This paper proposes a simple and general approach for the identification of the dead center positions of single-degree-of-freedom (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 condition for the occurrence of a dead center position of a single-DOF planar linkage can be designated as when the three passive instantaneous joints of any equivalent four-bar linkage become collinear. By this way, the condition for the complex linkage at the dead center positions can be easily obtained. The proposed method is a general concept and can be systematically applied to analyze the dead center positions for more complex 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 verify the results. The proposed method extends the application of equivalent linkage and is presented for the first time. It paves a novel and straightforward way to analyze the dead center positions for single-DOF complex planar linkages. Examples of some complex planar linkages are employed to illustrate this method in this paper.