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Causal inverse dynamics of a flexible hub-arm system through Liapunov's second method

Published online by Cambridge University Press:  09 March 2009

Atef Ata ,
Salwa Elkhoga ,
Mohamed Shalaby  and
Shihab Asfour
Atef Ata
Affiliation:
Department of Industrial Engineering University of Miami. Coral Gables. Fl. 33124 (USA).
Salwa Elkhoga
Affiliation:
Department of Engineering Mathematics. Faculty of Engineering, Alexandria University (Egypt).
Mohamed Shalaby
Affiliation:
Department of Engineering Mathematics. Faculty of Engineering, Alexandria University (Egypt).
Shihab Asfour
Affiliation:
Department of Industrial Engineering University of Miami. Coral Gables. Fl. 33124 (USA).
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Summary

The main objective of this work is to study the performance of a flexible single hub-arm system. The equations of motion are derived using the extended Hamilton principle. The Liapunov functional is used as a condition for the stability analysis. The Liapunov functional is considered as the sum of the internal energy of the flexible beam. The required drive torque was obtained directly through the solution of the inverse dynamic problem. Although the flexible link is nonminimum phase in nature, the use of Liapunov and the PD controller guarantee the causality for the stable case. The effects of tip mass as well as its inertia in the case of stable and asymptotic stable systems were investigated to ensure the validity of this procedure.

Keywords

Inverse dynamicsFlexible robotStabilityLiapunov.
Type
Article
Information
Robotica , Volume 14 , Issue 4 , July 1996 , pp. 381 - 389
Copyright
Copyright © Cambridge University Press 1996

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References

Song, J.O. and Haug, R.J.. “Dynamic Analysis of Planar Flexible Mechanisms” Comp. Meth. Appl. Mech. Engn. 24, 359–381 (1984).Google Scholar
Book, W.J.. “Recursive Lagrangian Dynamics of Flexible Manipulator Arms” Int. J. Robotic Research 3, 87–101 (1984).CrossRefGoogle Scholar
Sunada, H. and Dubowsky, S. “On the Dynamic Analysis and Behavior of Industrial Robotic Manipulator with Elastic Members” ASME Journal of Mechanisms Transmission and Automation in Design 105, 42–51 (1983).CrossRefGoogle Scholar
Naganathan, G. and Soni, A.H.. “Coupling Effects of Kinetmatics and Flexibility in Manipulators” Int. J. Robotics Research 6, 75–85 (1987).CrossRefGoogle Scholar
Simo, J.C. and Vu-Quoc, L.. “On the Dynamics of Flexible Beams Under Large Overall Motion, the Plan Case” ASME Paper No. 80-WA/AMP 41 (1986).Google Scholar
Cannon, R. and Schmitz, E. “Initial Experiment on End Point Motion of a Single Link Flexible Robot” Int. J. Robotics Research. 6, 62–75 (1984).Google Scholar
Bayo, E. “A Finite Element Approach to Control the End Point Motion of a Single Link Flexible Robot” Int. J. Robotics Systems 4, 63–75 (1987).Google Scholar
Bayo., E.Movaghar, R. and Medus, M. “Inverse Dynamics of a Single Link Flexible Robot Analytical and Experimental Results” J. Robotics and Automation 3, 150–157 (1988).Google Scholar
Bayo., E.Serene., M.Papadopoulos, P. and Stubbe, J. “Inverse Kinematics and Dynamics of Multi-Link Elastic Robots. An Iterative Frequency Domain Approach” Int. J. Robotics Research 8, 49–62 (1989).CrossRefGoogle Scholar
Fujii, P.Ohtsuka, T. and Udou, S. “Mission Function Control for a Slew Maneuver Experiment” J. Guidance, Dynamics, and Control 14, 986–992 (1991).CrossRefGoogle Scholar
Kown, D. and Book, W.J.. “An Inverse Dynamic Method Yielding Flexible Maniplator State Trajectory” Proceeding of the 1990 American Control Conference(1990) pp. 186–193.Google Scholar
Lam, E. “Modeling of the UNLV-ARO Light Weight Robot Using Lagrange';s Assumed Mode Method, Sympolic Manipulation and Numerical Simulation” M.S. Thesis (UNLV. 1991).Google Scholar
Meirovitch, L.. Analytical Methods in Vibration (Macmillan. New York. 1967).Google Scholar
Gorman, D.J., Free Vibration Analysis of Beams and Shafts (John Wiley & Sons. New York. 1975).Google Scholar
Claugh, W.R. and Penzien, J.Dynamics of Structures (McGraw Hill. New York. 1976).Google Scholar