Dynamics of pendulum-based systems under human arm rotational movements

Understanding the dynamics of pendulum-based systems and their relation to human arm rotation movement can be useful in a variety of applications, such as designing prosthetics, wearable energy harvesting systems or analyzing sports movements. By understanding the dynamics of the human arm, engineers can design better systems and equipment that take into account the unique properties of human movement. For example, harvesting energy from human arm rotation movement is an exciting research area in the fields of biomechanics and energy harvesting. Human arm rotation movement can generate kinetic energy that can be converted into electrical energy using various technologies such as electromagnetic generators or piezoelectric transducers. One potential application of harvesting energy from human arm rotation movement is in wearable devices, such as fitness/health trackers or smartwatches. These devices require a relatively constant supply of energy to function, and harvesting energy from arm rotation movement could provide a sustainable energy source. There are several challenges in harvesting energy from human arm movement. One of the main challenges is the variability of the motion, which can affect the efficiency of the energy harvesting system. The frequency and amplitude of the arm rotation can vary depending on the activity being performed, and the energy harvesting system must be designed to accommodate this variability.

In new research published in peer-reviewed Journal Mechanical Systems and Signal Processing, Dr. Hesam Sharghi and Professor Onur Bilgen from the Mechanical and Aerospace Engineering Department at Rutgers University investigated the oscillatory and rotatory dynamical response of pendulum-based systems using the motion of the lower arm. Since linear systems are only effective when resonance frequency matches the source frequency, the authors used a non-linear system because such a system is much more effective when employed with human motion.

The authors used two different models for considering the rotation of lower arm: the pitching model and the rolling model. The first one represents the swing of the lower arm during walking and is used for in-plane excitation. The latter represents the twisting motion for a specific movement disorder, e.g., hand tremor.

The researchers used Lagrange formulation to derive the equations of motion around the stable equilibrium positions. To study the two models, non-dimensional forms of the governing equations were introduced which allowed the authors to interpret the dynamics of the system for  a wide range of parameters. In the formulation, all external non-conservative forces were neglected except viscosity. The final position vector was obtained by multiplying the position vector by the rotation matrix R_N for rotations around the X, Y, and Z axes. Rolling, pitching, and yawing angles were introduced as α(t), β(t) and ϒ(t), respectively in the rotation matrix. Also, kinetic energy and potential energy equations were formulated around stable equilibria. The final equation of motion was derived by substituting kinetic energy, potential energy, and Rayleigh dissipation function in the Lagrange formulation. The equations of motion showed that the length of the arm does not play any role whatsoever for the rolling model (i.e., out of plane excitation.)

For the purpose of experimental validation and system identification, a specific case of these models was developed in which the system parameters were determined by fitting frequency response functions to the experimental data. The experimental setup included a laser displacement sensor for measuring the base movement of servo driven moving platform, and a National Instruments data acquisition system to measure the output voltage from the pendulum-based system. The experiment was carried out using 100 cycles of base oscillation, and then a root mean square (RMS) of the last 25 cycles of the system output was considered as the steady-state response. The results showed numerous bifurcations such as symmetry breaking, limit point, and period doubling in the response.

The study explains how pendulum-based systems are complex non-linear systems, and they can be used to harvest energy from human motion. Dr. Sharghi and Professor Bilgen demonstrated that the rotary response has a greater angular velocity amplitude than the oscillatory response when the system showed a bi-stable response. Their model is expected to make significant progress in developing energy harvesting systems that can harvest energy from human arm movement. These systems have the potential to provide a sustainable and convenient energy source for wearable devices and other applications, and could play an important role in advancing the field of wearable technologies.