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Relation between Euler–Bernoulli equation and contemporary knowledge in robotics

Published online by Cambridge University Press:  19 April 2011

Mirjana Filipovic
Mirjana Filipovic*
Affiliation:
Mihajlo Pupin Institute, University of Belgrade, Volgina 15, 11000 Belgrade, Serbia
*
*Corresponding author. Email: mirjana.filipovic@pupin.rs
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Summary

The motivation for this work is the state of modern structural mechanisms that are characterized by growing complexity and ever-increasing demands for rapid and accurate motion. These contradictory requirements are often achieved according to easier and easier structures characterized by flexibility segments. In most of cases, the elasticity of structures appears as an obstacle for a precise and rapid control of motion. The aim of this paper is to explore ways of implementation of structural properties of elasticity with the application of high fidelity models during synthesis and analysis of complex mechanisms. Precisely, the aim is to explore the possibility of using Euler–Bernoulli equation, if not in its original form, then to the same extent with the use of modern knowledge in robotics (based on the knowledge of classical mechanics), and to examine the affordability and confirmation of the method through simulation results for a typical robotic configuration.

Keywords

RobotModelingElastic deformationLinkCouplingDynamicsKinematicsTrajectory planning
Type
Articles
Information
Robotica , Volume 30 , Issue 1 , January 2012 , pp. 1 - 13
Copyright
Copyright © Cambridge University Press 2011

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References

1.Spong, M. W., “Modeling and control of elastic joint robots,” ASME J. Dyn. Syst. Meas. Control 109, 310–319 (1987).CrossRefGoogle Scholar
2.Filipovic, M. and Vukobratovic, M., “Modeling of Flexible Robotic Systems,” Proceedings of the International Conference on Computer as a Tool (EUROCON '05), Belgrade, Serbia and Montenegro 2 (Nov. 21–24, 2005) pp. 1196–1199.Google Scholar
3.Filipovic, M. and Vukobratovic, M., “Contribution to modeling of elastic robotic systems,” Eng. Autom. Probl. Int. J. 5 (1), 22–35 (Sep. 23, 2006).Google Scholar
4.Filipovic, M., Potkonjak, V. and Vukobratovic, M., “Humanoid robotic system with and without elasticity elements walking on an immobile/mobile platform,” J. Intell. Robot. Syst. Int. J. 48, 157–186 (2007).CrossRefGoogle Scholar
5.Filipovic, M. and Vukobratovic, M., “Complement of source equation of elastic line,” J. Intell. Robot. Syst. Int. J. 52 (2), 233–261 (Jun. 2008) (online Apr. 2008).CrossRefGoogle Scholar
6.Filipovic, M. and Vukobratovic, M., “Expansion of source equation of elastic line,” Robotica Int. J. 26 (6), 739–751 (Nov. 2008) (online Apr. 2008).CrossRefGoogle Scholar
7.Filipović, M., “New form of the Euler-Bernoulli rod equation applied to robotic systems” Theor. Appl. Mech., Society Mechanics, Belgrade 35 (4), 381–406 (2008).CrossRefGoogle Scholar
8.Moallem, M., Khorasani, K. and Patel, V. R., “Tip Position Tracking of Flexible Multi-Link Manipulators: An Integral Manifold Approach,” Proceedings of the International Conference on Robotics and Automation, Minneapolis, Minnesota (Apr. 22–28, 1996) pp. 2432–2436.CrossRefGoogle Scholar
9.Matsuno, F. and Kanzawa, T., “Robust Control of Coupled Bending and Torsional Vibrations and Contact Force of a Constrained Flexible Arm,” Proceedings of the International Conference on Robotics and Automation, Minneapolis, Minnesota (Apr. 22–28, 1996) pp. 2444–2449.CrossRefGoogle Scholar
10.Surdilovic, D. and Vukobratovic, M., “One method for efficient dynamic modeling of flexible manipulators,” Mech. Mach. Theory 31 (3), 297–315 (1996).CrossRefGoogle Scholar
11.Cheong, J., Chung, W. and Youm, Y., “Bandwidth Modulation of Rigid Subsystem for the Class of Flexible Robots,” Proceedings of the Conference on Robotics and Automation, San Francisco, CA, USA (Apr. 24–28, 2000) pp. 1478–1483.Google Scholar
12.Low, H. K., “A systematic formulation of dynamic equations for robot manipulators with elastic links,” J Robot. Syst. 4 (3), 435–456 (Jun. 1987).Google Scholar
13.Low, H. K. and Vidyasagar, M., “A lagrangian formulation of the dynamic model for flexible manipulator systems,” ASME J. Dyn. Syst. Meas. Control 110 (2), 175–181 (Jun. 1988).CrossRefGoogle Scholar
14.Low, H. K., “Solution schemes for the system equations of flexible robots,” J. Robot. Syst. 6 (4), 383–405 (Aug. 1989).CrossRefGoogle Scholar
15.De Luca, A. and Siciliano, B., “Closed-form dynamic model of planar multilink lightweight robots,” IEEE Trans. Syst. Man Cybern. 21, 826–839 (Jul./Aug. 1991).CrossRefGoogle Scholar
16.Khadem, S. E. and Pirmohammadi, A. A., “Analytical development of dynamic equations of motion for a three-dimensional flexible link manipulator with revolute and prismatic joints,” IEEE Trans. Syst. Man Cybern. B Cybern. 33 (2), 237–249 (April 2003).CrossRefGoogle ScholarPubMed
17.Meirovitch, L., Analytical Methods in Vibrations (Macmillan, New York, NY, USA, 1967).Google Scholar
18.Book, W. J., “Recursive lagrangian dynamics of flexible manipulator arms,” Int. J. Robot. Res. 3 (3), 87–101 (1984).CrossRefGoogle Scholar
19.Book, W. J., “Analysis of massless elastic chains with servo controlled joints,” Trans. ASME J. Dyn. Syst. Meas. Control 101, 187–192 (1979).CrossRefGoogle Scholar
20.Djuric, A. M., ElMaraghy, W. H. and ElBeheiry, E. M., “Unified Integrated Modelling of Robotic Systems,” Proceedings of the NRC International Workshop on Advanced Manufacturing, London, Canada (Jun. 1–2, 2004).Google Scholar
21.Despotovic, Z. and Stojiljkovic, Z., “Power converter control circuits for two-mass vibratory conveying system with electromagnetic drive: Simulations and experimental results,” IEEE Transl. Ind. Electron. 54 (1), 453–466 (Feb. 2007).CrossRefGoogle Scholar
22.Strutt, W. and Rayligh, Lord, Theory of Sound, 2nd ed. (Mc. Millan and Co., London and New York) 1894.Google Scholar
23.Potkonjak, V. and Vukobratovic, M., “Dynamics in contact tasks in robotics. Part I. general model of robot interacting with dynamic environment,” Mech. Mach. Theory 34 (6), 923–942 (1999).Google Scholar
24.Bayo, E., “A finite-element approach to control the end-point motion of a single-link flexible robot,” J. Robot. Syst. 4 (1)63–75 (1987).CrossRefGoogle Scholar