Comprehensive mathematicaI modelling of a transversely vibrating flexible link robot manipulator carrying a tip payload

• Autorzy: Loudini M. , Boukhetala D. , Tadjine M.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to describe the application of the Timoshenko beam theory (TBT) to the mathematical modelling of a planar one link flexible robot manipulator pinned at its actuated base and carrying a payload at its free end-point. The emphasis has been put on obtaining accurate and complete equations of motion that display the most relevant aspects of structural propenies inherent to the modelled lightweight flexible link. So, in addition to the classical effects of shearing and rotational inertia of the link cross-section, two imponant damping mechanisms: external viscous air damping and internal structural viscoelasticity effect (Kelvin-Voigt damping) have been included. Gravity, torsion, and longitudinal elongation have been neglected. Numerical simulations, performed to show the free vibrational behaviour of the modelled system, demonstrate the imponant effect of the carried payload on the amplitude and the frequency of vibrations.

Słowa kluczowe

EN

robot manipulator arm; flexible link; PDE model; Timoshenko beam theory; Lagrange; assumed modes method

PL

robotyka; manipulatory; teoria sprężystości

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2007
• Tom: Vol. 12, no 1
• Strony: 67--83
• Opis fizyczny: Bibliogr. 43 poz., tab., wykr.

Twórcy

autor

Loudini M.

autor

Boukhetala D.

autor

Tadjine M.

• Ecole Nationale Polytechnique, Laboratoire de Commande des Processus 10, avenue Hassan Badi, BP 182, 16200 El Harrach, AIgiers, ALGERIA,

Bibliografia

• Anderson R.A. (1953): Flexural vibrations in uniform beams according to the Timoshenko theory. - Journal of Applied Mechanics, vol.75, pp.504-510.
• Baker W.E., Woolam W.E. and Young D. (1967): Air and internal damping of thin cantilever beams. - International Journal of Mechanical Sciences, vol.9, pp.743-766.
• Banks H.T. and Inman D.J. (1991): On damping mechanisms in beams. - Journal of Applied Mechanics, vol.58, pp.716-723.
• Banks H.T., Wang Y. and Inman D.J. (1994): Bending and shear damping in beams: frequency domain techniques. - Journal of Applied Mechanics, vol.116, pp.188-198.
• Banks H.T., Smith R.C. and Wang Y. (1996): Smart Material Structures: Modeling, Estimation and Control. - New York: Wiley-Masson.
• Baruh H. and Taikonda S.S.K. (1989): Issues in the dynamics and control of flexible robot manipulators. - AIAA Journal of Guidance, Control and Dynamics, vol.12, No.5, pp.659-671.
• Bellezza F., Lanari L. and Ulivi G. (1990): Exact modeling of the slewing flexible link. - Proceedings of the IEEE International Conference on Robotics and Automation, pp.734-739.
• Boley B.A. and Chao C.C. (1955): Some solutions of the Timoshenko beam equations. - Journal of Applied Mechanics, vol.75, pp.579-586.
• Book W.J. (1993): Controlled motion in an elastic world. - Journal of Dynamic Systems, Measurement and Control, vol.115, pp.252-261.
• Cannon R.H. Jr and Schmitz E. (1984): Initial experiments on the end-point control of a flexible one-link robot. - International Journal of Robotics Research, vol.3, No.3, pp.62-75.
• Canudas de Wit C., Siciliano B. and Bastin G. (1996): Theory of Robot Control. - London: Springer-Verlag.
• Cetinkunt S. and Yu W.L. (1991): Closed loop behaviour of a feedback controlled flexible arm: a comparative study. - International Journal of Robotics Research, vol.10, No.3, pp.263-275.
• Davis J.H. and Hirschorn R.M. (1988): Tracking control of a flexible robot link. - IEEE Transactions on Automatic Control, vol.33, No.3, pp.238-248.
• Dolph C. (1954): On the Timoshenko theory of transverse beam vibrations. - Quarterly of Applied Mathematics, vol.12, pp.175-187.
• Dwivedy S.K. and Eberhard P. (2006): Dynamic analysis of flexible manipulators, a literature review. - Mechanism and Machine Theory, vol.41, No.7, pp.749-777.
• Ekwaro-Osire S., Maithripala D.H.S. and Berg J.M. (2001): A series expansion approach to interpreting the spectra of the Timoshenko beam. - Journal of Sound and Vibration, vol.240, pp.667-678.
• Geist B. and McLaughlin J.R. (2001): Asymptotic formulas for the eigenvalues of the Timoshenko beam. - Journal of Mathematical Analysis and Applications, vol.253, pp.341-380.
• Han S.M., Benaroya H., and Wei T. (1999): Dynamics of transversely vibrating beams using four engineering theories. - Journal of Sound and Vibration, vol.225, No.5, pp.935-988.
• Hastings G.G. and Book W.J. (1987): A linear dynamic model for flexible robotic manipulators. - IEEE Control Systems Magazine, vol.7, No.1, pp.61-64.
• Huang T.C. (1961): The effect of rotary inertia and of shear deformation on the frequency and normal mode equations of uniform beams withs simple end conditions. - Journal of Applied Mechanics, vol.28, pp.579-584.
• Junkins J.L. and Kim Y. (1993): Introduction to Dynamics and Control of Flexible Structures, In Education Series (J.S. Przemieniecki, Editor-in-Chief). - Washington DC: AIAA.
• Kanoh H. and Lee H.G. (1985): Vibration control of a one-link flexible arm. - Proceedings of the 24th Conference on Decision and Control, pp.1172-1177.
• Krishnan H. and Vidyasagar M. (1988): Control of a single-link flexible beam using a Hankel-norm-based reduced order model. - Proceedings of the IEEE Conference on Robotics and Automation, vol.1, pp.9-14.
• Lin Y.-J. and Lee T.-S. (1992): Comprehensive modeling for simultaneous position and force control of deformable manipulators. - Proceedings of the 31st Conference on Decision and Control, pp.1887-1892.
• Macchelli A. and Melchiorri C. (2004): Modeling and control of the Timoshenko beam. The distributed port hamiltonian approach. - SIAM J. Control Optim., vol.43, No.2, pp.743-767.
• Meirovitch L. (1997): Principles and Techniques of Vibrations. - Upper Saddle River, NJ, USA: Prentice-Hall.
• Ortner N. and Wagner P. (1996): Solution of the initial-boundary value problem for the simply supported semi-finite Timoshenko beam. - Journal of Elasticity, vol.42, pp.217-241.
• Piedboeuf J.-C., Farooq M., Bayoumi M.M., Labinaz G. and Argoun M.B. (1993): Modelling and control of flexible manipulators - Revisited. - Proceedings of the 36th Midwest Symposium on Circuits and Systems, pp.1480-1483.
• Qi X. and Chen G. (1992): Mathematical modeling of kinematics and dynamics of certain single flexible-link robot arms. - Proceedings of the IEEE Conference on Control Applications, vol.1, pp.288-293.
• Lord Rayleigh (1945): Theory of Sound. - New York: Dover Publications.
• Robinett R.D., Dohrmann C., Eisler G.R., Feddema J., Parker G.G., Wilson D.G. and Stokes D. (2002): Flexible Robot Dynamics and Controls. - International Federation for Systems Research International Series on Systems Science and Engineering, vol.19, Dordrecht: Kluwer.
• Sooraksa P. and Chen G. (1998): Mathematical modeling and fuzzy control of a flexible-link robot arm. - Mathematical and Computer Modelling, vol.27, No.6, pp.73-93.
• Stephen N.G. (1982): The second frequency spectrum of Timoshenko beams. - Journal of Sound and Vibration, vol.80, pp.578-582.
• Stephen N.G. (2006): The second spectrum of Timoshenko beam theory. - Journal of Sound and Vibration, vol.292, pp.372-389.
• Timoshenko S.P. (1921): On the correction for shear of the differential equation for transverse vibrations of prismatic bars. - Philosophical Magazine, vol.6, No.41, pp.744-746.
• Timoshenko S.P. (1922): On the transverse vibrations of bars of uniform cross section. - Philosophical Magazine, vol.6, No.43, pp.125-131.
• Timoshenko S., Young D.H. and Weaver W. Jr. (1974): Vibration Problems in Engineering. - New York: Wiley.
• Trail-Nash P.W. and Collar A.R. (1953): The effects of shear flexibility and rotary inertia on the bending vibrations of beams. - Quarterly Journal of Mechanics and Applied Mathematics, vol.6, pp.186-222.
• Wang F.-Y. and Guan G. (1994): Influences of rotary inertia, shear and loading on vibrations of flexible manipulators. - Journal of Sound and Vibration, vol.171, No.4, pp.433-452.
• Wang F.-Y., Zhou P. and Lever P. (1996): Dynamic effects of rotary inertia and shear deformation on flexible manipulators. - Proceedings of the IEEE Int. Conf. on Systems, Man and Cybernetics, vol.3, pp.2315-2320.
• White M.W.D. and Heppler G.R. (1995): Timoshenko model of a flexible slewing link. - Proceedings of the American Control Conference, vol.4, pp.2815-2819.
• Yurkovich Y. (1992): Flexibility effects on performance and control. - Robot Control, vol.8, pp.321-323.
• Zener C. (1948): Elasticity and inelasticity of metals. - Chicago: University of Chicago Press.