This paper presents a synthesis method for the Stephenson III six-bar linkage that combines the direct solution of the synthesis equations with an optimization strategy to achieve increased performance for path generation. The path synthesis equations for a six-bar linkage can reach as many as 15 points on a curve; however, the degree of the polynomial system is 1046. In order to increase the number of accuracy points and decrease the complexity of the synthesis equations, a new formulation is used that combines 11 point synthesis with optimization techniques to obtain a six-bar linkage that minimizes the distance to 60 accuracy points. This homotopy directed optimization technique is demonstrated by obtaining a Stephenson III six-bar linkage that achieves a specified gait trajectory.

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