Dynamic Finite Element Analysis of the Position Control System of a Horizontal Flexible Robot Arm with Two Links : A Finite Element Formulation Method and Numerical Simulation in Applying Path Control Based on Trapezoidal Velocity Curve

Abstract

In this paper, first, a finite element formulation method for a horizontal flexible robot arm with two links is presented. In the analysis, the kinetic energy of the flexible arm is represented in brief compared with the previous method, and the matrix equation of motion in consideration of the nonlinear forces, such as the Coriolis force, is derived by the finite element method and the variational theorem. Then, the state equation of the mechatoronics system consisting of the flexible arm and the position control system is obtained. Second, the numerical simulations in the case of applying the path control based on the trapezoidal velocity curve are carried out by use of the Wilson-θ method, and the effects of the bending rigidity and the shape of the trapezoidal velocity curve on the dynamic characteristics of the mechatoronics system are demonstrated.