Multi-Furcation Variations of Two Novel Double-Centered Mechanisms Based on Higher Order Kinematic Analyses and Singular Value Decomposition

This paper explores a class of extended double-centered linkages and presents two novel multi-bifurcated double-centered metamorphic and reconfigurable mechanisms. Higher order kinematic analyses and singular value decomposition are combined to demonstrate the characteristics of multi-furcation and to reveal motion branch transformation. These findings show that the presented double-centered linkages are able to evolve to distinct motion branches including two spherical 4R linkages, line-symmetric Bricard linkage or Bennett linkage. Furthermore, by exploring the local properties of singular configurations on geometric constraints and algebraic relationships, a systematic approach for the synthesis of the singular configurations can be designed to discover more novel multi-bifurcated metamorphic and reconfigurable mechanisms.