Dynamics and Control of a Four-Bar Mechanism with Relative Longitudinal Vibration of the Coupler Link
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Abstract
In the mechanisms and machines operating at high speeds, the elastic vibration of links is inevitable. In this paper the dynamic modeling and controller design for a flexible four-bar mechanism are studied. The fully coupled non-linear equations of motion are obtained by using the Lagrange's equations with multipliers for constrained multibody systems. The resulting differential-algebraic equations are solved using numerical methods. A simple PD controller is designed to reduce the influence of the elastic link on the desired motion.
Keywords
Dynamic analysis, control, Four-bar mechanism, Ritz-Galerkin method, Vibration
Article Details
References
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[2] Sung, C. K. and Chen, Y. C (1991) Vibration control of the elastodynamic response of high-speed flexible linkage mechanisms. ASME Journal of Vibration and Acoustics 113, 14-21.
[3] Beale, D. G. and Lee, S. W. (1995) The applicability of fuzzy control for flexible mechanisms. ASME Design Engineering Technical Conferences DE-Vol. 84-1, 203-209.
[4] Liao, W. H. Chou, J. H. and Horng, I. R (1997). Robust vibration control of flexible linkage mechanisms using piezoelectric films. Smart Materials and Structures 6, 457-463.
[5] Schwab, A. L. and Meijard, J. P. (1997) Small vibrations superim Posedon non-linear rigid body motion. Proceedings of the 1997 ASME Design Engineering Technical Conferences, Sacramento, CA.1-7.
[6] Yigit. A. Scott, R.A. and Ulsoy, A.G (1988), "Flexural motion of aradially rotating beam attached to a rigid body". Journal of Sound and Vibration 121, 201-210.
[7] Khang. N.V (2005), Engineering vibrations (in Vietnamese). Science and Technics Publishing House
[8] Khang. N.V (2017), Dynamic of multibody system (in Vietnamese, 2. Edition) Science and Technics Publishing House.
[9] Reddy, J.N (2002), Energy Principles and Variational Methods in Applied Mechanics, John Wiley and Son, ISBN: 978-0-471-17985-6.
[10] Bajodah, A. H. Hodges, D. H. and Chen, Y. H (2003) "New form of Kane's equations for constrained systems". Journal of Guidance, Control, and Dynamics 26:79-88.