Lie algebra-based high-order constraint analysis of a novel multi-loop metamorphic mechanism derived from four-bar linkage for lower limb exoskeletons

Traditional lower limb exoskeletons are typically designed for fixed postures but struggle to adapt to dynamic, multi-scenario environments. This paper investigates a novel multi-loop metamorphic mechanism for lower limb exoskeletons, enabling smooth posture transitions among walking, sitting, kneeling, and intermediate states to meet variable support requirements. First, a topological structure connecting the lower limbs and support rods is established, and a four-bar linkage-based multi-loop metamorphic mechanism is proposed, achieving configuration changes via link overlap or axis collinearity. Next, first- and second-order kinematic equations are derived using Lie group and Lie algebra exponential products. Singular configurations and motion bifurcation are analyzed through the Jacobian matrix constructed with Lie bracket operations, leading to bifurcation conditions and corresponding motion branch diagrams. Finally, the proposed metamorphic mechanism is implemented in a lower limb exoskeleton, identifying five distinct motion branches, four corresponding to walking, sitting, kneeling, and transitional postures. Joint velocity constraints enable effective branch switching, resolving challenge of increased instantaneous degrees of freedom in singular configurations.