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.