Title: Comprehensive mathematical modelling of a lightweight flexible link robot manipulator

Authors: Malik Loudini, Djamel Boukhetala, Mohamed Tadjine

Addresses: Institut National d'Informatique, Oued Smar, El Harrach 16309, Algiers, Algeria. ' Laboratoire de Commande des Processus, Ecole Nationale Polytechnique, El Harrach 16200, Algiers, Algeria. ' Laboratoire de Commande des Processus, Ecole Nationale Polytechnique, El Harrach 16200, Algiers, Algeria

Abstract: This paper deals with a comprehensive study of the application of the Timoshenko Beam Theory (TBT) concepts to the mathematical modelling of a planar lightweight single link flexible robot manipulator arm pinned at its actuated base and carrying a payload at its free end-point. The emphasis being essentially set on obtaining accurate and complete equations of the transversely vibrating motion that display the most relevant aspects of structural properties inherent to the modelled lightweight flexible link, two important damping mechanisms, internal structural viscoelasticity (Kelvin-Voigt damping) and external viscous air damping, have been included in addition to the TBT classical effects of cross section shear deformation and rotational inertia. Torsional, gravitational and longitudinal elongation effects have been neglected. Digital simulations are performed to show the free vibrational behaviour of the modelled robotic system.

Keywords: robot manipulators; flexible links; PDE model; damping; Timoshenko beam theory; TBT; Lagrange; assumed modes method; robot design; flexible robots; mathematical modelling; lightweight manipulators; shear deformation; rotational inertia; robot vibration.

DOI: 10.1504/IJMIC.2007.016414

International Journal of Modelling, Identification and Control, 2007 Vol.2 No.4, pp.313 - 321

Published online: 28 Dec 2007 *

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