Abstract: The mobility problem is most fundamental and most difficult in the process of Stephenson six-bar chains analysis and synthesis. They are referred to the problems associated with the circuit defect, the existence of a crank, and the order of motion. A Stephenson six-bar chain is composed of a basis four-bar chain and a dyad, and its circuit properties are determined by the circuit properties of the basis four-bar chain and the configurations of dyad and the intersection between them. Based on the distance of two common joint between the basis four-bar and the dyad that a Stephenson six-bar chain contains, the theory and method to identify the circuits of Stephenson six-bar chain are presented. The procedures of identifying circuit defect are given, the conditions of crank existing of any type of Stephenson six-bar linkages are deduced, and the method of determining whether Stephenson six-bar linkages satisfy the order of motion is gained. The results resolve three of the most troublesome problems encountered in the precision point synthesis of Stephenson six-bar linkages. This research has significant value for linkages analysis and synthesis.

Key words: Circuit defect, Crank, Order of motion, Stephenson six-bar mechanism