Vibration control and calculating inverse dynamics of the rigid-flexible two-link manipulator T-R




flexible manipulator, linearization, Floquet theory, vibration control, Taguchi method, inverse dynamics


The dynamics and control of flexible link manipulators (FLMs) are increasing in industrial robotics research. In which the problem of inverse dynamics of the flexible link manipulators is a problem that has been studied little and has no general solution. In this paper, an approximation method is presented to calculate the reverse dynamics of the serial manipulators with rigid-flexible links. The linearization of the motion equations for a rigid-flexible translation and rotation two-link manipulator (manipulator T-R) is addressed. The vibration control and calculating inverse dynamics of a periodic rigid-flexible two-link manipulator T-R are studied. The Taguchi method is used for the design of gain values of the controller PD for the manipulator. The results of numerical simulation show the efficiency and usefulness of the proposed approximation method.


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A. A. Shabana. Flexible multibody dynamics: Review of past and recent development. Multibody System Dynamics, 1, (2), (1997), pp. 189–222. DOI:

S. K. Dwivedy and P. Eberhard. Dynamic analysis of flexible manipulators, a literature review. Mechanism and Machine Theory, 41, (2006), pp. 749–777. DOI:

H. N. Rahimi and M. Nazemizadeh. Dynamic analysis and intelligent control techniques for flexible manipulators: a review. Advanced Robotics, 28, (2013), pp. 63–76. DOI:

K. Lochan, B. K. Roy, and B. Subudhi. A review on two-link flexible manipulators. Annual Reviews in Control, 42, (2016), pp. 346–367. DOI:

B. C. Chiou and M. Shahinpoor. Dynamic stability analysis of a two-link force-controlled flexible manipulator. Journal of Dynamic Systems, Measurement, and Control, 112, (1990), pp. 661–666. DOI:

A. S. Yigit. On the stability of PD control for a two-link rigid-flexible manipulator. Journal of Dynamic Systems, Measurement, and Control, 116, (1994), pp. 208–215. DOI:

N. Popplewell and D. Chang. Influence of an offset payload on a flexible manipulator. Journal of Sound and Vibration, 190, (1996), pp. 721–725. DOI:

S. Choura and A. S. Yigit. Control of a two-link rigid-flexible manipulator with a moving payload mass. Journal of Sound and Vibration, 243, (2001), pp. 883–897. DOI:

A. A. Ata, W. F. Fares, and M. Y. Saadeh. Dynamic analysis of a two-link flexible manipulator subject to different sets of conditions. Procedia Engineering, 41, (2012), pp. 1253–1260. DOI:

X. Yang, S. S. Ge, and W. He. Dynamic modelling and adaptive robust tracking control of a space robot with two-link flexible manipulators under unknown disturbances. International Journal of Control, 91, (2017), pp. 969–988. DOI:

P. Kumar and B. Pratiher. Modal characterization with nonlinear behaviors of a twolink flexible manipulator. Archive of Applied Mechanics, 89, (2019), pp. 1201–1220. DOI:

H. Asada, Z.-D. Ma, and H. Tokumaru. Inverse dynamics of flexible robot arms: modeling and computation for trajectory control. Journal of Dynamic Systems, Measurement, and Control, 112, (1990), pp. 177–185. DOI:

E. Bayo and H. Moulin. An efficient computation of the inverse dynamics of flexible manipulators in the time domain. In IEEE International Conference on Robotics and Automation, IEEE Computer Society, IEEE Computer Society, (1989), pp. 710–711.

E. Bayo, P. Papadopoulos, J. Stubbe, and M. A. Serna. Inverse dynamics and kinematics of multi-link elastic robots: an iterative frequency domain approach. The International Journal of Robotics Research, 8, (1989), pp. 49–62. DOI:

J. G. De Jalon and E. Bayo. Kinematic and dynamic simulation of multibody systems: the real-time challenge. Springer, Berlin, (1994).

J. K. Hale. Oscillations in nonlinear systems. McGraw-Hill, New York, (1963).

B. P. Demidovich. Lectures on the Mathematical Stability Theory. Nauka, Moscow, (1967). (in Rusian).

W. Schiehlen and P. Eberhard. Applied dynamics. Springer International Publishing Switzerland, (2014). DOI:

S. Briot and W. Khalil. Dynamics of parallel robot, from rigid bodies to flexible elements. Springer, Switzerland, (2015). DOI:

D. C. Dat, N. V. Khang, and N. T. V. Huong. Linearization of the motion equations of flexible robot manipulators. In Proceedings of the 2th National Conference on Dynamics and Control, Bach Khoa Publishing House, Hanoi, (2022).

N. V. Khang, N. P. Dien, and H. M. Cuong. Linearization and parametric vibration analysis of some applied problems in multibody systems. Multibody System Dynamics, 22, (2009), pp. 163–180. DOI:

N. V. Khang, N. S. Nam, and N. V. Quyen. Symbolic linearization and vibration analysis of constrained multibody systems. Archive of Applied Mechanics, 88, (2018), pp. 1369–1384. DOI:

N. V. Khang and N. P. Dien. Parametric vibration analysis of transmission mechanisms using numerical methods. Advances in Vibration Engineering and Structural Dynamics, Edited by FB Carbajal, Intech, Croatia, (2012), pp. 301–331.

G. Taguchi, S. Chowdhury, and Y. Wu. Taguchi’s quality engineering handbook. John Wiley & Sons, New Jersey, (2005). DOI:

R. A. Zambanini. The application of Taguchi’s method of parameter design to the design of mechanical systems. Master’s thesis, Lehigh University, (1992).

R. K. Roy. Design of experiments using the Taguchi approach. John Wiley and Sons, New York, (2001).

N. V. Khang, V. D. Phuc, N. T. V. Huong, and D. T. Duong. Optimal control of transverse vibration of Euler-Bernoulli beam with multiple dynamic vibration absorbers using Taguchi's method. Vietnam Journal of Mechanics, 40, (2018), pp. 265–283. DOI:

N. V. Khang, D. T. Duong, N. T. V. Huong, N. D. T. T. Dinh, and V. D. Phuc. Optimal control of vibration by multiple tuned liquid dampers using Taguchi method. Journal of Mechanical Science and Technology, 33, (2019), pp. 1563–1572. DOI:




How to Cite

Khang, N. V., & Dat, D. C. (2022). Vibration control and calculating inverse dynamics of the rigid-flexible two-link manipulator T-R. Vietnam Journal of Mechanics, 44(2), 169–189.



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