Analytical model of one flexible link system with nonlinear kinematics

Abstract

The dynamical model of a flexible Euler–Bernoulli link system subject to high-speed motions is developed. Nonlinear kinematics are considered to take into account the foreshortening effect of the link. A continuous model with boundary conditions is derived using Hamilton's principle and spatially discretized dynamical equations are derived using Lagrange's equation based on the expression of the kinetic and potential energies of the flexible link system. The effect of the links foreshortening on the dynamical response is shown for a sinusoidal torque input at the links hub. The simulation results showed that for small torque amplitudes the difference between linear and nonlinear kinematics is small. However, for large amplitudes, this difference is prominent.