A new nonlinear finite element model for the dynamic modeling of flexible link manipulators undergoing large deflections

The main objective of the present paper is to develop the geometrically nonlinear formulation of very flexible link manipulators undergoing large deflection. A new nonlinear finite element model for the dynamic analysis is employed to describe nonlinear modeling for three-dimensional flexible link manipulators, in which both the geometric elastic nonlinearity and the foreshortening effects are considered. In comparison to other large deformation formulations, the motion equations contain constant stiffness matrix because the terms arising from geometric elastic nonlinearity are moved from elastic forces to inertial, reactive and external forces, which are originally nonlinear. This makes the formulation particularly efficient in computational terms and numerically more stable than alternative geometrically nonlinear formulations based on lower-order terms. In this investigation, Finite Element Method (FEM), which is able to consider the full nonlinear dynamic of flexible manipulator, is applied to derive the kinematic and dynamic equations. The proposed approach has been implemented and tested on a single-link very flexible arm. The results illustrate the power and efficiency of the method to overcome the high nonlinearity nature of the problem.