Bifurcation and configuration-space connectivity analysis of a multi-mode 6R linkage for reconfigurable mechanism design

Multi-mode kinematic linkages are important building blocks for reconfigurable mechanisms, but their configuration spaces often contain multiple motion branches connected through bifurcation configurations. This paper develops a configuration-space connectivity model for multi-mode linkages by partitioning the C-space into normal instantaneous mobility (NIM) manifolds and increased instantaneous mobility (IIM) configurations. Bipartite and reduced transition graphs are introduced to encode adjacency relations and feasible transitions among motion branches. The model is applied to a multi-mode 6R linkage with complex bifurcation behavior. Geometric and screw-theoretic analysis identifies four motion components, sixteen NIM manifolds, and eight IIM configurations. The resulting graph representation explicitly describes the global C-space connectivity and feasible transition paths without disassembly. Based on this model, a graph-guided design strategy is developed by selecting connected NIM manifolds as operating modes and their associated IIM configurations as transition configurations. Two representative reconfigurable mechanisms are constructed, and prototype experiments verify the predicted motion modes and transition configurations. The results show that the proposed approach provides a concise description of the global connectivity of multi-mode C-spaces and can support the design of reconfigurable mechanisms.