Classification and branch identification of Stephenson six-bar chains

Abstract

A Stephenson six-bar chain contains a four-bar loop and a five-bar loop, and its branch condition may be affected by the rotatability of both loops and the interaction between them. It may have up to six branches and its branch condition is far more complicated than that of a four-bar chain. In this article, the method to identify the effects of both loops on the rotatability of any Stephenson six-bar linkage and the algorithms to identify its branch condition are presented. The results resolve one of the most complicated and troublesome problems encountered in the finite position synthesis of Stephenson linkages. The proposed method is based on the rotatability of the common joints between the two loops and no coupler curve is used. The method is directly applicable to any type of Stephenson linkages regardless of whichever link is used as the input or fixed link. It is also valid for linkages containing prism joints. The algorithms are equally effective for path, motion, and function generation and also for any number of precision positions. Once the branch problem is resolved, other mobility problems, such as the full rotation, dead center positions, and the motion order, can be identified easily as in planar four-bar linkages.