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

Abstract

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.

Research of the manipulator dynamics installed on an elastic basis

“…and 0 2 = Q are generalized external forces in the form of driving moments; М 1 (α, t) -is the driving moment that creates the actuating mechanism of the manipulator for rotation of its arrow. A nonlinear differential equation of motion of the boom system is obtained as a result of the transformation of the system of equations (6). In work [9], the result of the transformation of the Lagrange equation and the obtaining of the dynamic equation of motion of such a boom-type manipulator.…”

“…Fluctuations cargo the cause errors in its position and reduce life of the machine. For eliminate fluctuation make use of the dampers and devices regulate speed of the working body of the manipulator [5,6].…”

Competition of fuzzy logic controllers applied on flexible manipulator

“…Thus, strong control actions are applied and, as a result, undesired controlled system features could appear if hidden vibrating modes are excited enough. Existing studies [1][2][3][4][5][6][7] on flexible robot manipulator can be divided into two groups: those on dynamic, and those on control.…”

Mathematical Modeling and Simulation of a Flexible Shaft-Flexible Link System With End Mass

“…The dynamics of flexible arm manipulators, especially flexible arm manipulators driven by flexible shaft, has attracted the attention of many investigators [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The methods used in solving such systems are mainly experimental methods, finite element method, modal analysis and approximate methods such as Galerkin's method and assumed modes method.…”