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Journal of Robotics
Volume 2011 (2011), Article ID 890258, 21 pages
Research Article

Vibration Analysis of Multilink Manipulators Based on Timoshenko Beam Theory

Dipartimento di Ingegneria dell'Innovazione, Università del Salento, 73100 Lecce, Italy

Received 11 October 2010; Revised 6 March 2011; Accepted 7 March 2011

Academic Editor: Danica Kragic

Copyright © 2011 Carmelo di Castri and Arcangelo Messina. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Timoshenko's theory is adopted in order to accurately describe the freely vibrating dynamics of a multilink flexible manipulator. It is herein presented an analytical modelling strategy that extends previous works through a more refined model which accounts for elastic complicating effects along with lumped inertial loads which are typically mounted on joints of manipulators; in this regard, more accurate results are provided. The eigenproblem is presented from an analytical point of view through a matrix formulation, thus providing an essentially closed formula. Apart from the limitations of the implementing calculator, the formulation can take into account an arbitrary number of links in an arbitrary settled configuration, thus allowing relevant analytical analysis and avoiding the need to recur to nonimmediate numerical schemes. Once the analytical model is introduced, solutions are compared to both those achieved by previous models and those obtained by a finite elements method.