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Analysis of static equilibrium of a parallel manipulator

Published online by Cambridge University Press:  09 March 2009

Hyunsok Pang  and
Mohsen Shahinpoor
Hyunsok Pang
Affiliation:
Department of Mechanical EngineeringUniversity of New MexicoAlbuquerqueNew Mexico 87131 (USA)
Mohsen Shahinpoor
Affiliation:
Department of Mechanical EngineeringUniversity of New MexicoAlbuquerqueNew Mexico 87131 (USA)
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Summary

An analysis is presented in this paper for the equilibrium of a class of parallel manipulators resembling the Stewart platform in a general form. General coordinates and 4 x 4 homogeneous transformations are employed to arrive at exact expressions for the force distribution in all six legs given the general 6-dimensional wrench (generalized force) at the upper platform of a parallel manipulator. Numerical examples are carried out to examine the validity of the approach and the accuracy of the numerical technique employed.

Type
Research Article
Information
Robotica , Volume 11 , Issue 5 , September 1993 , pp. 433 - 443
Copyright
Copyright © Cambridge University Press 1993

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References

1.Shahinpoor, M., A Robot Engineering Textbook (Harper & Row Publishers, New York, London, 1987).Google Scholar
2.Fichter, E.F., “Kinematics of a Parallel-Connection Manipulator” ASME paper 84-DET-45, (1984), delivered at Design Engineering Tech. Conf. Cambridge, Massachusetts 1–8 (1984).Google Scholar
3.Fichter, E.F., “A Stewart Platform-Based Manipulator General Theory and Practical Construction” Int. J. Robotics. Res. 5, 2, 165–190 (1986).CrossRefGoogle Scholar
4.Stewart, D., “A Platform with Six Degrees of Freedom”, Proc. Inst. Mech. Eng., vol. 180, no. 1, pp. 371–386 (1965).CrossRefGoogle Scholar
5.Earl, C.F. and Rooney, J., “Some Kinematic Structures for Robot Manipulator Designs” Trans. ASME, J. Mechanism, Transmissions and Automation in Design 105, 15–22 (1983).CrossRefGoogle Scholar
6.Hunt, K.H., “Structural Kinematics of In-Parallel-Actuated Robot-Arms” Trans. ASME, J. Mechanisms, Transmissions and Automation in Designs 105, 705–712 (1983).Google Scholar
7.Yang, D.C.H. and Lee, T.W., “Feasibility Study of A Platform Type of Robotic Manipulator From A Kinematic Viewpoint” Trans. ASME, J. Mechanisms, Transmissions and Automation In Design, 106, 191–198 (1984).Google Scholar
8.Mohammed, M.G. and Duffy, J., “A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robotic Manipulator” ASME J. Mechanisms, Transmission, and Automation in Design 107, 226–229 (June 1985).CrossRefGoogle Scholar
9.Sugimoto, K., “Kinematics and Dynamics Analysis of Parallel Manipulators By Means of Motor Algebra” ASME J. Mechanisms, Transmissions and Automation in Design 109, 3–7 (1987).CrossRefGoogle Scholar
10.Sugimoto, K., “Computational Scheme for Dynamic Analysis of Parallel Manipulators” Trends and Developments in Mechanisms, Machines and Robotics- 1988, ASME Proceedings of the 20th Biennial Mechanisms Conf. 3, 59–64 (1988).Google Scholar
11.Merlet, J.P., “Contribution a la Formalisation de la Commanded par Retour d'Efforts Application a la Commande de Robots Paralleles Ph.D. Thesis (Paris VI University, June, 1986).Google Scholar
12.Merlet, J.P., “Singular Configurations of Parallel Manipulators and Grassman Geometry” Int. J. Robotic Research 8, 5, 45–56 (1989).CrossRefGoogle Scholar
13.Freeman, R.A. and Tesar, D., “Dynamic Modeling of Serial and Parallel Mechanisms Robotic Systems, Part IMethodology, Part-II-Applications” Trends and Developments in Mechanisms, Machines and Robotics–1988 ASME Proceedings of the 20th Biennial Mechanisms Conf. 3, 7–28 (1988).Google Scholar
14.Kerr, D.R., “Analysis, Properties, and Design of A Stewart Platform Transducer” Trends and Developments in Mechanisms, Machines, and Robotics-1988 ASME Proceedings of the 20th Biennial Mechanisms Conf. 3, 139–146 (1988).Google Scholar
15.Behi, F., “Kinematics Analysis for a Six-Degree of Freedom 3-PRPS Parallel Mechanism “IEEE J. Robotics and Automation” 4, 561–565 (1988).CrossRefGoogle Scholar
16.Griffis, M. and Duffy, J., “A Forward Displacement Analysis of A Class of Stewart Platforms” J. Robotic Systems 6, 6, 703–720 (1989).Google Scholar
17.Kang, H.J. and Freeman, R.A., An Interactive Software Package for the Dynamic Modeling and Simulation of Parallel Robotic Systems Including Redundancy”Proceedings of 1990 ASME International Computers in Engineering Conference (1990) vol. 1, pp. 117–123.Google Scholar
18.Shahinpoor, M., “A Novel Design for a Space Manipulator”Proc. Space Operations and Research Conference (SOAR 91) (1991) vol. 1, pp. 15–22.Google Scholar
19.Shahinpoor, M., “Kinematics of a Parallel-Serial (Hybrid) Robot Manipulator” J. Robotic Systems 9, No. 1, 32–44 (1992).Google Scholar
20.Shahinpoor, M. and Smith, B.L., “Depolyable Robotic Woven Wire Joints and Structures for Space Applications”Proc. Space Operations and Research Conference (SOAR (1991) vol. 1, pp. 159–166.Google Scholar
21.Shahinpoor, M. and Smith, B.L., “Robotic Applications” US Patent No. 5,114,300, (US Patent Office, May 19, 1992).Google Scholar
22.Do, W.Q.D. and Yang, D.C.H., “Inverse Dynamic Analysis and Simulation of a Platform Type of Robot Robotic Systems 5(3), 209–227 (1988).CrossRefGoogle Scholar
23.William, H.P., Brian, P.F., Saul, A.T. and William, T.V., Numerical Recipes in C (Cambridge University Press, New York, NY, 1988).Google Scholar
24.Noble, B. and Daniel, J.W., Applied Linear Algebra (3rd Edition) (Prentice Hall, Englewood Cliffs, NJ, 1988).Google Scholar
25.Zhang, C. and Song, S.M., “Forward Kinematics of a Class of Parallel (Stewart) Platforms with Closed-Form Solutions”Proceedings of IEEE International Conference on Robotics and Automation (1991) pp. 2676–2681.Google Scholar