Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-06T11:51:46.233Z Has data issue: false hasContentIssue false

Computer-aided-symbolic dynamic modeling for Stewart-platform manipulator

Published online by Cambridge University Press:  01 May 2009

J. Lin*
Affiliation:
Department of Mechanical Engineering, Ching Yun University, 229, Chien-Hsin Rd., Jung-Li City, Taiwan 320, R.O.C.
C.-W. Chen
Affiliation:
Department of Mechanical Engineering, Ching Yun University, 229, Chien-Hsin Rd., Jung-Li City, Taiwan 320, R.O.C.
*
*Corresponding author. E-mail: [email protected]

Summary

The Stewart platform manipulator is a fully kinematic linkage system that has major mechanical differences from typical serial link robots. It is a six-axis parallel robot manipulator with a high force-to-weight ratio and good positioning accuracy that exceeds that of a conventional serial link robot arm. This study examines the dynamic equations and control methodology for a Stewart platform. Because manual symbolic expansion of Stewart platform robot dynamic equations is tedious, time-consuming, and prone to errors, an automated derivation process is highly desired. The main goal of this work is to present an efficient procedure for computer generation of dynamic equations for a Stewart platform manipulator. As MATLAB has a powerful signal processing toolbox along with symbolic processing capabilities and is widely used as a common technical computing environment in many universities and research laboratories, the objective of this study was to develop a MATLAB-based approach for symbolic computation for a parallel linked robot. Additionally, a computed-torque control methodology is utilized for such a structure. Simulation results demonstrate the effectiveness of the proposed control methodology.

Type
Article
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Li, Q., “Experimental validation on the integrated design and control of a parallel robot,” Robotica 24 (2), 173181 (2006).CrossRefGoogle Scholar
2.Lebret, G., Liu, K. and Lewis, F. L., “Dynamic analysis and control of a Stewart platform manipulator,” J. Robot. Syst. 10 (5), 629655 (1993).CrossRefGoogle Scholar
3.Stewart, D., “A platform with six degrees of freedom,” Proc. Inst. Mech. Engr. (London) 180 (5), 371386 (1965).CrossRefGoogle Scholar
4.Lee, M. K. and Park, K. W., “Workspace and singularity analysis of a double parallel manipulator,” IEEE/ASME Trans. Mechatron. 5 (4), 367–275 (2000).Google Scholar
5.Donelan, P. S., “Singularity-theoretic methods in robot kinematics,” Robotica 25 (6), 641659 (2007).CrossRefGoogle Scholar
6.Kim, D. H., Kang, J.-Y. and Lee, K.-II, “Robust nonlinear observer for forward kinematics solution of a Stewart platform: An experimental verification,” Robotica 18 (6), 601610 (2000).CrossRefGoogle Scholar
7.Bandyopadhyay, S. and Ghosal, A., “Geometric characterization and parametric representation of the singularity manifold of a 6-6 Stewart platform manipulator,” Mech. Machine Theory 41, 13771400 (2006).CrossRefGoogle Scholar
8.Liu, K., Lewis, F. L., Lebret, G. and Taylor, D., “The singularities and dynamics of a Stewart platform manipulator,” J. Intell. Robot. Syst. 8, 287308 (1993).CrossRefGoogle Scholar
9.Harib, K. and Srinivasan, K., “Kinematic and dynamic analysis of Stewart platform-based machine tool structures,” Robotica 21 (5), 541554 (2003).CrossRefGoogle Scholar
10.Wang, Y., “A direct numerical solution to forward kinematics of general Stewart–Gough platforms,” Robotica 25 (1), 121128 (2007).CrossRefGoogle Scholar
11.Reboulet, C. and Berthomieu, T., “Dynamic models of a six degree of freedom parallel manipulators,” Proc. Conf. ICAR 91, Pise, Italy (1991) pp. 1153–1157.Google Scholar
12.Nguyen, C. C. and Pooran, F. J., “Dynamic analysis of a 6-DOF CKCM robot end-effector for dual-arm telerobot systems,” Robot. Autonom. Syst. 9 (4), 377394 (1989).CrossRefGoogle Scholar
13.Wu, J., Wang, J., Li, T., Wang, L. and Guan, L., “Dynamic dexterity of a planar 2-DOF parallel manipulator in a hybrid machine tool,” Robotica 26 (1), 9398 (2008).CrossRefGoogle Scholar
14.Lin, J. and Lewis, F. L., “A symbolic formulation of dynamic equations for a manipulator with rigid and flexible links,” Int. J. Robot. Res. 13 (5), 454466 (1994).CrossRefGoogle Scholar
15.Larcombe, P. J. and Brown, I. C., “Computer algebra: A brief overview and application to dynamic modeling,” Comput. Control Eng. J. 8 (2), 5357 (Apr. 1997).CrossRefGoogle Scholar
16.Munro, N., “Symbolic algebra tools for control teaching,” Comput. Control Eng. J. 8 (2), 5863 (Apr, 1997).CrossRefGoogle Scholar
17.Gawthrop, P. J. and Balance, D. J., “Symbolic algebra and physical-model-based control,” Comput. Control Eng. J. 8 (2), 7076 (Apr. 1997).CrossRefGoogle Scholar
18.Lutovac, M. D. and Tošié, D. V., “Symbolic analysis and design of control systems using Mathematica,” Int. J. Control 79 (11), 13681381 (2006).CrossRefGoogle Scholar
19.Tsai, L.-W., Robot Analysis—The Mechanics of Serial and Parallel Manipulators (John Wiley and Sons, Inc., New Jersey, 1999).Google Scholar
20.Chen, C.-W., Computed-Aided Symbolic Modeling for Stewart Platform, Master Thesis (Department of Mechanical Engineering, Ching Yun University, Taiwan, 2007).Google Scholar
21.Lewis, F. L., Abdallah, C. T. and Dawson, D. M., Control of Robot Manipulators (Macmillan, New York, 1993).Google Scholar