Dynamics of pendulum-based systems under human arm rotational movements

Abstract

Wearable devices have applications in health monitoring and patient assistance devices. Harvesting energy from human motion kinetic energy by the pendulum-based electromagnetic generator is a promising way of extending the battery life of these devices. In this paper, the oscillatory and rotary dynamical response of pendulum-based systems under an open-circuit condition is investigated for two different models considering the lower arm’s rotation. The arm pitching model (in-plane excitation) represents the swing of the lower arm during walking. The arm rolling rotation model (out-of-plane excitation) represents the twisting type of motion of the lower arm movement associated with a specific kind of disorder, for example, tremors experienced by Parkinson’s patients. The governing equations of motion around stable equilibria are derived using Lagrange formulation, and their nondimensional forms are introduced for the two models. A special case of these models is developed for experimental validation and system identification, where the system parameters are identified by fitting frequency response functions on the experimental data. The system’s nonlinear dynamical response shows various bifurcations, including limit point bifurcation (i.e., saddle-node bifurcation), pitchfork bifurcation, a cascade of period-doubling bifurcations under amplitude or frequency sweeps. When the system shows a bi-stable response, the rotary response usually has a higher angular velocity amplitude than the oscillatory response. Basins of attraction plots for different operating conditions are presented to show the effect of initial conditions on the system’s type of steady-state response: oscillatory or rotary.