The Synthesis of Planar Four-Bar Linkage for Mixed Motion and Function Generation

The synthesis of four-bar linkage has been extensively researched, but for a long time, the problem of motion generation, path generation, and function generation have been studied separately, and their integration has not drawn much attention. This paper presents a numerical synthesis procedure for four-bar linkage that combines motion generation and function generation. The procedure is divided into two categories which are named as dependent combination and independent combination. Five feasible cases for dependent combination and two feasible cases for independent combination are analyzed. For each of feasible combinations, fully constrained vector loop equations of four-bar linkage are formulated in a complex plane. We present numerical examples to illustrate the synthesis procedure and determine the defect-free four-bar linkages.

Discussion of Hwang and Chen's constraint equations to eliminate order, circuit and branch defects for the paper: Defect-free synthesis of Stephenson-III motion generators, published in Journal of Mechanical Engineering Science, 2008; 222: 2485–2494

Many studies to find solutions for the optimum synthesis problems of linkage mechanisms for path, motion or function generation have appeared in the literature. However, their main focus has been on the development of optimization algorithms or synthesis methods without the handling of the defect problems or only with consideration of the same assembly mode. Hwang and Chen's pioneering work proposed a defect-free optimum synthesis method with constraint equations to eliminate order, circuit and branch defects for Stephenson III six-bar motion generators. However, their proposed constraint equations for the three types of defects are incomplete or not clear enough. In this discussion, we not only examine these faults but also offer the correct and complete constraints to eliminate the three types of defects.