DYNAMIC MODELLING OF TWO LINK FLEXIBLE MANIPULATOR USING LAGRANGIAN ASSUMED MODES METHOD

Authors

  • Natraj Mishra, S.P. Singh, B.C. Nakra Assistant Professor, Mechanical Engineering, UPES, Dehradun, India Professor and N.T.P.C. Chair, Mechanical Engineering, IIT Delhi, New Delhi, India. INSA Senior Scientist, Mechanical Engineering, IIT Delhi, New Delhi, India.

Keywords:

Assumed Modes Method, Dynamic Modelling, Flexible Manipulator, Time-dependent Frequency

Abstract

In this paper, a mathematical model of two link flexible manipulator is presented. The model is prepared using Lagrangian-assumed modes method. The links are modelled as Euler-Bernoulli beams. A literature survey containing the work done by various authors in the area of flexible robotics is provided. A general expression for the frequency equation for the vibrating links is obtained which is found to be time-dependent. The effect of payload on the natural frequencies of the links is studied. Simulation results are obtained using both forward and inverse dynamics. The results thus obtained are compared with that found in the literature. 

References

Benosman and Vey, “Control of flexible manipulators: A survey”, Robotica, Vol. 22, Pp. 533-534, 2004.

Book et al, “Feedback control of two beam, two joint systems with distributed flexibility”, Journal of Dynamic Systems, Measurement and Control, 1975.

Luh et al, “Resolved-Acceleration Control of Mechanical Manipulators”, IEEE Transactions on Automatic Control, Vol. AC-25, No. 3, Pp. 468-474,1980.

Book and Majette, “Controller design for flexible, distributed parameter mechanical arms via combined state space and frequency domain techniques”, Journal of Dynamic Systems, Measurement and Control, Vol. 105, Pp. 245-254, 1983.

Judd and Falkenburg, “Dynamics of nonrigid articulated robot linkages”, IEEE Transactions on Automatic Control, Vol. 30, 1985.

Kanoh, et. al., “Modelling and Control of Flexible Robot Arms”, Proceedings IEEE Conference on Decision and Control, Athens, Greece, Pp. 1866- 1870, December 1986.

Bakr and Shabana, “Geometrically nonlinear analysis of multibody systems”, Computers & Structures, Vol. 23, Pp. 739-751, 1986.

Luca and Siciliano, “Closed-Form Dynamic Model of Planar Multilink Lightweight Robots”, IEEE Transactions on System, Man, and Cybernetics, Vol. 21, No. 4, Pp. 826-839, July/August 1991.

Li and Sankar, “Systematic methods for efficient modeling and dynamics computation of flexible robot manipulators”, IEEE Transactions on Systems, Man and Cybernetics, Vol. 23, Pp. 77-95, 1993.

DU, Lim and Liew, “A Non-Linear Finite Element Model for Dynamics of Flexible Manipulators”, Mech. Mach. Theory, Vol. 31, No. 8, Pp. 1109-1119, 1996.

Theodore and Ghosal, “Modeling of flexible-link manipulators with prismatic joints”, IEEE Transactions on Systems, Man and Cybernetics- Part B: Cybernetics, Vol. 27, Pp. 296-305, 1997.

Yuksel and Aksoy, “Flexural vibrations of a rotating beam subjected to different base excitations”, G.U. Journal of Science, Vol. 22, Pp. 33-40, 2009.

Atef A. Ata, Waleed F. Fares and Mohamed Y. Sa’adeh, “Dynamic analysis of a two-link flexible manipulator subject to different sets of conditions”, IRIS 2012, Procedia Engineering, Vol. 41, Pp. 1253- 1260, 2012.

Natraj Mishra, S.P. Singh, B.C. Nakra, “Dynamic analysis of a single link flexible manipulator using Lagrangian Assumed-modes approach”, IEEE Xplore, International Conference on Instrumentation and Control, College of Engineering Pune, 28-30 May 2015, Pp. 1144-1149.

Ghosal, Ashitava, “Robotics: Fundamental Concepts and Analysis”, Oxford University Press.

Mohan , Ashish, “Dynamic Analysis of Flexible Multibody Robotic Systems”, Ph.D Thesis, IIT Delhi, Pp. 153-189, 2006.

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Published

2015-11-30

Issue

Vol. 4 No. 12 (2015): NOVEMBER 2015

Section

Articles

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