On the dynamics of the flexible robot arm in a real deployment profile

Abstract

The dynamics of the flexible robot arm subjected to tip mass during an actual deployment is studied. The Euler-Bernoulli beam theory and the real deployment are considered in the simulation. A new real axial velocity profile is developed. This new suggested profile simulates the actual deployment such that the arm movement starts from immovability and after attaining the final required length comes back again to the static state. Using Lagrange's equation, the equations of motion of the system are derived to study the system dynamics in this suggested deployment profile. A series approximation is used to represent the lateral elastic displacements. Using variables separation and also some special shape functions satisfying the boundary conditions in the series, a system of ordinary differential equations governing the dynamics of the system is presented. Solving the ordinary differential equations, the response of the flexible robot arm during deployment is studied. The effects of deployment time and the payload mass which the arm carries, on the dynamic response of the system are investigated. The accuracy of the obtained response for the arm is dependent on the number of terms included in the considered series. The effects of the deployment time and payload mass on the “number of series terms” required to reach an acceptable solution convergence are investigated.