Dynamic Modeling of Tow Flexible Link Manipulators

Authors: E. Abedi, A. Ahmadi Nadooshan, S. Salehi

Abstract:

Modeling and vibration of a flexible link manipulator with tow flexible links and rigid joints are investigated which can include an arbitrary number of flexible links. Hamilton principle and finite element approach is proposed to model the dynamics of flexible manipulators. The links are assumed to be deflection due to bending. The association between elastic displacements of links is investigated, took into account the coupling effects of elastic motion and rigid motion. Flexible links are treated as Euler-Bernoulli beams and the shear deformation is thus abandoned. The dynamic behavior due to flexibility of links is well demonstrated through numerical simulation. The rigid-body motion and elastic deformations are separated by linearizing the equations of motion around the rigid body reference path. Simulation results are shown on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics remarkably well. The proposed method can be used in both dynamic simulation and controller design.

Keywords: Flexible manipulator, flexible link, dynamicmodeling, end point.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071658

References:

[1] Yazdizadeh, A. & Khorasani, K. & Patel, R V. (2000). Identification of a two-link flexible manipulator using adaptive time delay neural networks: IEEE Trans. Syst., Man, Cybern. B, vol. 30, pp. 165-172.
[2] Su, Z. & Khorasani, K. (2001). A neural-network-based controller for a single-link flexible manipulator using the inverse dynamics approach: IEEE Trans. Ind. Electron., vol. 48, pp. 1074-1086, Apr.
[3] Martins, J M. & Mohamed, Z. & Tokhi, M O. & Costa, J. & Botto, M A. (2000). Approaches for dynamic modeling of flexible manipulator systems: Inst. Elec. Eng. Proc. Contr. Theory and Applications, vol. 150, no. 4, pp. 401-411.
[4] Yang, H. & Krishman, H. & Ang Jr, M H. (2000). Tip-trajectory tracking control of single-link flexible robots by output redefinition: Inst. Elec. Eng. Proc. Contr. Theory Applicat., vol. 147, no. 6, pp. 580-587.
[5] Du, Zhaocai. & Yu, Yueqing. (2008). Dynamic Modeling and Inverse Dynamic Analysis of Flexible Parallel Robots: International Journal of Advanced Robotic Systems, Vol. 5, no. 1, ISSN 1729-8806, pp. 115- 122.
[6] Ata, A. A. & Johar, H. (2004). Dynamic simulation of task constrained of a rigid-flexible manipulator: International Journal of Advanced Robotic Systems, Vol. 1, no. 2, ISSN 1729-8806, pp. 61 - 66.
[7] Tian, L. & Wang, J. & Mao, Z. (2004). Constrained Motion Control of Flexible Robot Manipulators Based on Recurrent Neural Networks: IEEE Transactions on systems, man, and cybernetics- part B: cybernetics, Vol. 34, no. 3.
[8] Book, W J. (1984). Recursive lagrangian dynamics of flexible manipulator arms: International Journal of Robotics Research, 3:87┬▒101.
[9] Erdman, A G. & Sandor, G N. & Oakberg, R G. (1972). A general method for Kineto-Elastodynamic analysis and synthesis of mechanisms: ASME Journal of Engineering for Industry, 94:1193┬▒205.
[10] Book, W J. (1990). Modeling, design, and control of flexible manipulator arms: A tutorial review, Proceedings of the 29th IEEE Conference on Decision and Control, IEEE Control Systems Society, pp.500-506, ISBN: 90CH2917-3.
[11] Santosha, K D. & Peter, E. (2006). Dynamic analysis of flexible manipulators, a literature review. Mechanism and Machine Theory, Vol.41, pp.749-777, ISSN: 0094-114X
[12] Kim, Hyoung-Kyu. Choi, Seung-Bok. & Thompson Brian S. (2000). Compliant control of two-link flexible manipulator featuring piezoelectric actuators: Mechanism and Machines Theory 36, 411-424.
[13] Ho, Cheol Shin. & Seung, Bok Choi. (2001). Position control of a two link flexible manipulator featuring piezoelectric actuators and sensors: Mechatronics 11, 707-729.
[14] Trigolo, Kuga, De Souza. (2003). Parameter Identification of a Rigid Flexible Satellite Using Kalman Filter: Proceedings, COBEM, November 10-14, Sao Paulo
[15] Turcic, D A. & Midha, A. (1984). Generalized equations of motion for the dynamic analysis of elastic mechanism systems: ASME Journal of Dynamic Systems, Measurements, and Control, 106:243┬▒8.