Abstract
In the mechanisms and machines operating at high speeds, the elastic vibration of links is inevitable. The present paper deals with the problem of modelling and model-based controller design for a flexible four-bar mechanism. The fully coupled non-linear equations of motion are derived using the Lagrange’s equations with multipliers for constrained multibody systems. The resulting differential-algebraic equations are solved using numerical methods. Based on the obtained modelling results, a simple PD controller is designed to minimize the influence of elastic link on the desired motion.
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References
Bremer, H.: Elastic Multibody Dynamics—A Direct Ritz Approach. Springer, Berlin (2008)
Geradin, M., Cardona, A.: Flexible Multibody Dynamics—A Finite Element Approach. Wiley, Chichester (2001)
De Jalon, J.G., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems. Springer, New York (1994)
Khang, N.V.: Dynamics of Multibody Systems, 2nd edn in Vietnamese. Science and Technics Publishing House, Hanoi (2017)
Sung, C.K., Chen, Y.C.: Vibration control of the elastodynamic response of high-speed flexible linkage mechanisms. ASME J. Vib. Acoust. 113, 14–21 (1991)
Beale, D.G., Lee, S.W.: The applicability of fuzzy control for flexible mechanisms. ASME Des. Eng. Tech. Conf. 84(1), 203–209 (1995)
Liao, W.H., Chou, J.H., Horng, I.R.: Robust vibration control of flexible linkage mechanisms using piezoelectric films. Smart Mater. Struct. 6, 457–463 (1997)
Karkoub, M., Yigit, A.S.: Vibration control of a four-bar mechanism with a flexible coupler. J. Sound Vib. 222(2), 171–189 (1999)
Xianmin, Z., Changjian, S., Erdman, A.G.: Active vibration controller design and comparison study of flexible linkage mechanism systems. Mech. Mach. Theory 37, 985–997 (2002)
Wang, X., Mills, J.K.: A FEM model for active vibration control of flexible linkages. In: Proceedings of the IEEE International Conference on Robotics and Automation, New Orleans (2004)
Zhang, X., Mills, J.K., Cleghorn, W.L.: Coupling characteristics of rigid body motion and elastic deformation of a 3-PRR parallel manipulator with flexible links. Multibody Syst. Dyn. 21, 167–192 (2009)
Hill, D.: Dynamics and control of a rigid and flexible four bar coupler. J. Vib. Control. 20(1), 131–145 (2012)
Zhang, Q., Mills, J.K., Cleghorn, W.L., Jin, J., Zhao, Ch.: Trajectory tracking and vibration suppression of a 3-PRR parallel manipulator with flexible links. Multibody Syst. Dyn. 33, 27–60 (2015)
Liang, D., Song, Y., Sun, T., Jin, X.: Rigid-flexible coupling dynamic modeling and investigation of a redundantly actuated parallel manipulator with multiple actuation modes. J. Sound Vib. 403, 129–151 (2017)
Inman, D.J.: Engineering Vibrations, 2 edn. Prentice Hall, Upper Saddle River, NJ (2001)
Reddy, J.N.: Energy Principles and Variational Methods in Applied Mechanics, 2nd edn. Wiley, Upper Saddle River, NJ (2002)
Acknowledgements
This paper was completed with the financial support of the Vietnam National Foundation for Science and Technology Development (NAFOSTED).
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Van Khang, N., Nam, N.S., Dien, N.P. (2019). Modelling and Model-Based Control of a Four-Bar Mechanism with a Flexible Coupler Link. In: (Chunhui) Yang, R., Takeda, Y., Zhang, C., Fang, G. (eds) Robotics and Mechatronics. ISRM 2017. Mechanisms and Machine Science, vol 72. Springer, Cham. https://doi.org/10.1007/978-3-030-17677-8_6
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DOI: https://doi.org/10.1007/978-3-030-17677-8_6
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