Computation of kinematic paths and bifurcation points for multi-degree-of-freedom mechanisms with singular value decomposition

Traditional methods often struggle with the intricate motion patterns and configurations arising from singularities and multi-degree-of-freedom (MDOF). This paper proposes a novel approach that combines Singular Value Decomposition (SVD) with higher-order kinematic analyses to overcome these challenges effectively. Our methodology systematically reveals local motion characteristics at singular configurations and accurately computes kinematic paths for various mechanism configurations. The proposed technique is applied to the equivalent mechanisms from magic cubes that show different shapes during motions. Through case studies, we demonstrate the effectiveness of our approach in exploring the bifurcation behavior of reconfigurable mechanisms, providing new insights into their design.