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On flexible link manipulators: modeling and analysis using the algebra of rotations

Published online by Cambridge University Press:  09 March 2009

F. Xi  and
R.G. Fenton
F. Xi
Affiliation:
Department of Mechanical Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario (Canada) M5S 1A4
R.G. Fenton
Affiliation:
Department of Mechanical Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario (Canada) M5S 1A4
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Summary

In this paper, a complete model of the elasto-kinematics is formulated in terms of a new kinematic notation, called the algebra of rotations. Based on this formulation, the elegant and concise expressions are derived for the displacement equation and especially the Jacobians governing the motion mapping between the manipulator tip and joint variables as well as link deflections. Introduction of the elasto-kinematics into the elasto-dynamics can directly take into consideration the nonlinear coupling between joint variables and link deflections, and thus improve the result of the elasto-dynamics.

Keywords

Flexible linkManipulatorsRotations algebraModeling.
Type
Article
Information
Robotica , Volume 12 , Issue 4 , July 1994 , pp. 371 - 382
Copyright
Copyright © Cambridge University Press 1994

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References

1.Sunada, W.H. and Dubowsky, S., “On the Dynamic Analysis and Behavior of Industrial Robotic Manipulators with Elastic Members” J. Mechanisms, Transmissions, and Automation in Design 105, 42–51 (03, 1983).Google Scholar
2.Book, W.J., “Recursive Lagranglian Dynamics of Flexible Manipulator Arms” Int. J. Robotics Research 3, No. 3, 87–101 (1984).CrossRefGoogle Scholar
3.Book, W.J., “Modeling, Design, and Control of Flexible Manipulator Arms: A Tutorial Review” Proceedings of the 29th IEEE Conference on Decision and Control (1990) pp. 500–506.CrossRefGoogle Scholar
4.Naganathan, G. and Soni, A.H., “Coupling Effects of Kinematics and Flexibility in Manipulators” Int. J. Robotics Research 6, No. 1, 75–85 (1987).CrossRefGoogle Scholar
5.Bayo, E., Papadopoulos, P., Stubbe, J. and Serna, M.A., “Inverse Dynamics and Kinematics of Multi-Link Elastic Robots: An Iterative Frequency Domain Approach” Int. J. Robotics Research 8, No. 6, 49–62 (1989).Google Scholar
6.Asada, H., Ma, Z.D. and Tokumaru, H., “Inverse Dynamics of Flexible Robot Arms: Modeling and Computation for Trajectory Control” J. Dynamic Systems, Measurement, and Control 112, 177–185 (06, 1990).CrossRefGoogle Scholar
7.Xi, F. and Fenton, R.G., “A Quasi-Static Motion Planner for Flexible Manipulators Using the Algebra of Rotations” Proceedings of the 1991 IEEE Int. Conference on Robotics and Automation 3 (1991) pp. 2363–2368.CrossRefGoogle Scholar
8.Fenton, R.G. and Xi, F., “Determinatin of the Robot Jacobían Using the Algebra of Rotations” Proceedings of the 1990 ASME Mechanism Conference, DE25 (1990) pp. 75–81.Google Scholar
9.Gebler, B., “Feed-forward Control Strategy for An Industrial Robot with Elastic Links and Joints” Proceedings of the 1987 IEEE Int. Conference on Robotics and Automation (1987) pp. 923–928.CrossRefGoogle Scholar
10.Pfeiffer, F. and Gebler, B., “A Multistage-Approach to the Dynamics and Control of Elastic Robots” Proceedings of the 1988 IEEE Int. Conference on Robotics and Automation (1988) pp. 2–8.Google Scholar
11.Jonker, B., “A Finite Element Dynamic Analysis of Flexible Manipulators” Int. J. Robotics Research 9, No. 4, 59–74 (1990).CrossRefGoogle Scholar
12.Xi, F. and Fenton, R.G., “A Sequential Integration Method for Inverse Dynamic Analysis of Flexible Link Manipulators” Proceedings of the 1993 Int. Conference on Robotics and Automation 3 (1993) pp. 743–748.CrossRefGoogle Scholar
13.Beggs, J.S., Advanced Mechanisms (Macmillan, New York, 1966).Google Scholar
14.Angeles, J., Rational Kinematics (springer Verlag, Berlin, 1989).Google Scholar
15.Chen, C.H., “Application of Algebra of Rotations in Robot Kinematics” Mechanism and Machine Theory 22, No. 1, 77–83 (1987).CrossRefGoogle Scholar
16.Paul, R.P., Robot Manipulators (MIT Press Cambridge, Mass., 1981).Google Scholar
17.Fenton, R.G. and Xi, F., “On the Efficiency of Computations for Robot Kinematics, Dynamics and Control Using the Algebra of Rotations” Proceedings of the 1993 IEEE int. Conference on Robotics and Automation 1 (1993) pp. 968–973.CrossRefGoogle Scholar
18.Hughes, P.C., “Dynamics of a Chain of Flexible Bodies”, J. of the Astronautical Science, XXVII, No. 4, 359–380 (1979).Google Scholar
19.Sicilliano, B. and Book, W.J., “A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators” Int. J. Robotics Research 7, No. 4, 79–90 (1988).Google Scholar
20.Derby, S., “Simulating Motion Elements of General Purpose Arms” Int. J. Robotics Research 2, No. 1, 3–12 (1983).Google Scholar