Nonlinear Biodynamic Models of the Hand-arm System and Parameters Identification using the Vibration Transmissibility or the Driving-point Mechanical Impedance

This study aims at deriving nonlinear expressions of the transmissibility and the driving-point mechanical impedance (DPMI) of two nonlinear biodynamic hand-arm models having active restoring and dissipative parameters. It aims also in computing explicitly the non-directly measurable stiffness and damping coefficients of the human hand-arm system (HAS). Multivariate Padé approximants are used to express the dependence of the HAS mechanical properties on various influencing factors. The harmonic balance method is used to derive analytical expressions of the transmissibility and the DPMI. Then, the models parameters are identified by minimizing constrained error functions between the theoretical DPMI or transmissibility and the measured data. The developed workflow is applied to three experimental data sets of Z-direction vibrations where the excitation frequency and/or the grip force are varied. Using the ISO-10068 (2012) limit DPMI values versus the excitation frequency, we derived upper and lower limits of the overall stiffness coefficient and damping ratio for the human HAS. Furthermore, the model reproduces with high accuracy experimental measurements of the transmissibility, the DPMI and the vibration power absorption.