Lateral and Torsional Vibration Analysis of Elastic Robot Manipulators With Prismatic Joint

Lateral and torsional vibrations of a robot manipulator with an elastic arm sliding in a prismatic joint are analyzed. The elastic arm is assumed as an Euler-Bernoulli beam. The mass of the end-effector is assumed as a point mass attached at the end of the elastic arm. The prismatic joint experiences 3-dimensional translational and rotational motion. The prismatic joint is assumed as rigid and frictionless. Rotational inertia of the beam is taken into consideration in obtaining the equations of motion. Elastic deformations are assumed as linear and small displacements. Axial vibrations are not considered but the effect of axial force is taken into account in the analysis. Elastic arm experiences both bending vibrations in two directions and torsional vibrations. The equations of motion are obtained by Lagrange’s equation of motion. Numerical solution of the equations of motion are obtained by Runge-Kutta method. A computer program is developed for implementation of the presented technique. Numerical simulations are presented in the form of graphics. Presented method is found to be versatile in dynamic analysis of elastic robot arms.