Tip Dynamic Response of Elastic Joint Manipulators Subjected to a Stochastic Base Excitation

An approach to study of the tip dynamic response (displacement and velocity) of elastic joint manipulators subjected to a vertical stochastic excitation of the base is presented. The crossing analysis of maximum displacement of the manipulator tip along a determined path is also investigated. The dynamic equations of motion of an n-link articulated elastic joint manipulator subjected to a vertical stochastic base excitation are derived by using the Euler-Lagrange equations and then extended by Taylor series expansion. The result dynamic equations are linearized with respect to links vibration. The power spectral density representation is used to compute the second moment matrix of angular displacement and velocity of the links and also to compute the second moment matrix of manipulator tip dynamic response. Then the crossing analysis and also the probability that any maximum peak displacement values of manipulator tip exceed from a determined level along a path are investigated. Finally, some of simulation results for a two-link planar robot manipulator subjected to a vertical stochastic excitation of the base are presented.