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Three-dimensional flexural-joint stiffness analysis of flexible manipulator arms

Published online by Cambridge University Press:  09 March 2009

A. Meghdari  and
M. Shahinpoor
A. Meghdari
Affiliation:
Department of Mechanical Engineering, Robotics Research Laboratories, The University of New Mexico, Albuquerque, NM 87131 (USA)
M. Shahinpoor
Affiliation:
Department of Mechanical Engineering, Robotics Research Laboratories, The University of New Mexico, Albuquerque, NM 87131 (USA)
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Summary

This paper presents a complete derivation of the combined flexural-joint stiffness matrix and the elastic deformation field of flexible manipulator arms treated in a three-dimensional fashion. The stiffness properties are derived directly from the differential equations used in the engineering beam theory. The expressions developed here can readily be used in the modeling, control and design of light weight flexible robot manipulators. A two-link arm is used to formulate these expressions and the results can be generalized to n–link manipulators. The stiffness matrix for a robotic link element in 3-D is of the order of 12 X 12, and for an n–link robotic arm the total elemental and system stiffness matrices will be of the order of the (12n X 12n) and 6(n + 1) X 6(n + 1), respectively.

Keywords

ArmsRobotStiffnessJointsAnalysis
Type
Research Article
Information
Robotica , Volume 6 , Issue 3 , July 1988 , pp. 203 - 212
Copyright
Copyright © Cambridge University Press 1988

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References

1.Book, J.W., “Modeling, Design and Control of Flexible Manipulator Arms” Ph.D. Thesis (Department of Mechanical Engineering, MIT 1974).Google Scholar
2.Maizza-Meto, O., “Modal Analysis and Control of Flexible Manipulator Arms” Ph.D. Thesis (Department of Mechanical Engineering, MIT, 1974).Google Scholar
3.Book, W.J., Maizza-Neto, O. and Whitney, D.E., “Feedback Control of Two Beam, Two Joint Systems with Distributed Flexibility” Trans. ASME, J. Dyn. Syst. Measurement and Control 97, No. 4, 424–431 (1975).Google Scholar
4.Hughes, P.C., “Dynamics of a Flexible Arm for the Space Shuttle” 1977 AAS/A1AA Astrodynamics Conference,Jackson Lake Lodge, Wyoming (09, 1977).Google Scholar
5.Book, W.J., “Recursive Lagrangian Dynamics of Flexible Manipulator Arms” Int. J. Robotics Res. 3, No. 3, 186–201 (Fall 1984).CrossRefGoogle Scholar
6.Shahinpoor, M. and Meghdari, A., “Combined Flexural-Joint Stiffness Matrix and the Elastic Deformation of a Servo-Controlled Two-Link Robot Manipulator” Robotica 4, 237–242 (1986). Also presented at The Tenth U.S. National Congress of Applied Mechanics, June 16–20, 1986, Austin, Texas.CrossRefGoogle Scholar
7.Cannon, R.H. and Schmitz, E., “Initial Experiments on the End-Point Control of a Flexible One-Link Robot” Int. J. Robotics Res. 3, No. 3 (Fall, 1984).CrossRefGoogle Scholar
8.Sunada, W.H., “Dynamic Analysis of Flexible Spatial Mechanisms and Robotic Manipulators” Ph.D. Thesis (Department of Mechanical Engineering, UCLA, 1981).Google Scholar
9.Campbell, D., “An Iterative Algorithm for the Inverse Kinematics Solution of a General n–axis Robot Manipulator Using Powell's Optimization Technique” M.Sc. Thesis (Department of Mechanical Engineering, Clarkson University, 08 1984).Google Scholar
10.Meghdari, A. and Shahinpoor, M., “Elastic Deformation Characteristics of a Puma 560 Robot Manipulator,” Int. J. Robotics and Automation, 2, No. 1, 26–31 (1987).Google Scholar
11.Kanchi, M.B., Matrix Methods in Structural Analysis (Wiley Eastern Company, New York, 1981).Google Scholar
12.Timoshenko, S., Strength of Materials I & II (D. Van Nostrand Co., Inc., New York, 1956).Google Scholar
13.Pestel, E. and Leckie, A., Matrix Methods in Elastomechanics (McGraw-Hill Book Company, New York, 1963).Google Scholar
14.Gutkowski, R.M., Structures (Van Nostrand Reinhold Company, New York, 1981).Google Scholar
15.Turner, N.J., Clough, R., Martin, H.C., and Topp, L.J., “Stiffness and Deflection Analysis of Complex Structures” J. Aero. Sci. 23, 805–823 (1956).CrossRefGoogle Scholar
16.Przemieniecki, J.S., “Matrix Analysis of Aerospace Structures” Proc. 5th Intern. Symp. Space Techn. Sci., Tokyo, Japan 477–500 (09 2–7, 1963).Google Scholar