Mobility Identification of a Group of Single Degree-of-Freedom Eight-Bar Linkages

This paper presents the first complete and automated mobility identification method for a group of single-DOF planar eight-bar linkages and thus represents a breakthrough on the recognition and understanding of complex linkage mobility. The mobility identification in this paper refers to the configuration space, the range of motion, and configuration recognition. It is a troublesome problem encountered in any linkage analysis and synthesis. The problem becomes extremely confusing with complex multiloop linkages. The proposed approach is simple and straightforward. It recognizes that the loop equations are the mathematical fundamentals for the formation of branches, sub-branches, and other mobility issues of the entire linkage. The mobility information is then extracted through the discriminant method. The paper presents complete answers to all typical mobility issues, offers the mathematical insight as well as explanation on the effects of multiple loops via joint rotation space, and casts light for treating the mobility problems of other complex linkages. The merits of the discriminant method for mobility identification are clarified and examples are employed to showcase the proposed method. The computer-aided automated mobility analysis of eight-bar linkages is made possible for the first time.