Nonlinear Dynamic Stability Analysis of a Human-Inspired Electromechanical Arm System Under Heavy External Loads

This study develops a nonlinear dynamic model of a human-inspired electromechanical arm system subjected to high loads. The proposed simplified representation preserves essential nonlinear dynamics using a reduced number of generalized coordinates. The model is represented by an electromechanical analog comprising a DC motor, a transmission system, and a multi-degree-of-freedom mechanical structure. The formulation is based on Lagrangian mechanics and accounts for inertia, damping, stiffness, and nonlinear kinematic coupling induced by joint misalignment. The numerical results were assessed using a consistency-based verification approach with several independent nonlinear analysis tools. The Lyapunov exponent was used in conjunction with bifurcation diagrams, Poincaré maps, and FFT spectra to identify the transition from stable operation to chaotic behavior as the external load increased. The results reveal a progressive transition from periodic motion to quasi-periodic oscillations and chaotic regimes, with fully developed chaotic behavior emerging for loads exceeding approximately 35 kg. Analysis of the Lyapunov exponent supports this interpretation, indicating stable, quasi-critical, or chaotic regimes depending on the sign of λ_max. The concordance among these independent indicators provides numerical verification of the observed stability transitions. The control gain significantly influences energy dissipation and system stability. The proposed model provides a reduced-order framework for studying nonlinear stability phenomena in human-inspired electromechanical systems. Potential applications involve rehabilitation devices and safety studies of human–robot interactions.