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Formulation of manipulator Jacobian using the velocity similarity principle

Published online by Cambridge University Press:  09 March 2009

K. C. Gupta  and
R. Ma
K. C. Gupta
Affiliation:
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, Illinois 60680 (USA)
R. Ma
Affiliation:
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, Illinois 60680 (USA)
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Summary

Velocity similarity principle V(θ., ṡ, ub, Qb) = DabV (θ., ṡ, ua, Qa)D ab–1 is presented and used to derive several useful forms of the Jacobian matrix for the manipulator from its basic kinematic equations in 4 X 4 matrix form. The zero reference position representation is used and, therefore, the base system is the only coordinate system utilized in the derivations. For manipulators with a spherical wrist, a modified form of the Jacobian is presented in which the Jacobian columns corresponding to the regional structure are completely decoupled from those corresponding to the wrist structure.

Keywords

Manipulator Jacobianvelocity similarityspherical wristkinematic equations
Type
Article
Information
Robotica , Volume 8 , Issue 1 , January 1990 , pp. 81 - 84
Copyright
Copyright © Cambridge University Press 1990

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References

1.Pieper, D.L., “The Kinematics of Manipulators under Computer Control Doctoral Dissertation. (Stanford University, Stanford, 1968).Google Scholar
2.Whitney, D. “The Mathematics of Coordinated Control of Prosthetic Arms and Manipulators” ASME J. Dynamic Systems, Measurement, and Control 303–309 (1972).CrossRefGoogle Scholar
3.Paul, R.P., Robot Manipulators (MIT Press, Cambridge, 1981).Google Scholar
4.Waldron, K.J., Wang, S.L. and Bolin, S.J., “A Study of the Jacobian Matrix of Serial Manipulators” ASME J. Mechanisms, Tr. Ant. Dgn. 107 230–237 (1985).Google Scholar
5.Gupta, K.C., “Discussion for “A Study of the Jacobian Matrix of Serial Manipulators” ASME J. Mechanisms, Tr. Aut. Dgn. 107 237–238 (1985).Google Scholar
6.Gupta, K.C. and Kazerounian, S.M.K., “Improved Numerical Solutions of Inverse Kinematics of Robots” Proc. IEEE Int. Conf. Robotics and Automation St. Louis, 743–748 (1985).Google Scholar
7.Litvin, F.L., Zhang, Y., Castelli, V.P. and Innocenti, C., “Singularities, Configurations and Displacement Functions for Manipulators” Int. J. Robotics Research 5(2), 66–74 (1986).CrossRefGoogle Scholar
8.Featherstone, R., “Position and Velocity Transformations between Robot End-Effector Coordinates and Joint Angles” Int. J. Robotics Research 2(2) 35–45 (1983).CrossRefGoogle Scholar
9.Wolovich, W.A., Robotics – Basic Analysis and Design (Holt, Rinehart and Winston, New York, 1987).Google Scholar
10.Pieper, D.L. and Roth, B., “The Kinematics of Manipulators under Computer Control” Proc. 2nd IFToMM Intl. Cong. Theory of Machines and Mechanisms Warsaw, 2 159–168 (1969).Google Scholar
11.Hunt, K.H., “Robot Kinematics – A Compact Analytic Inverse Solution for Velocities” ASME J. Mechanisms, Tr. Aut. Dgn. 109(1) 42–49 (1987); Also ASME Paper86-DET-127.Google Scholar
12.Gupta, K.C., “A Note on Position Analysis of Manipulators” Proc. 7th Applied Mechanisms Conf. Kansas City, 3.1–3.3 (1981); also Mechanism and Machine Theory, 195–8 (1984).Google Scholar
13.Gupta, K.C., “Kinematic Analysis of Manipulators Using the Zero Reference Position Description” Int. J. Robotics Research 5(2) 5–13 (1986).CrossRefGoogle Scholar
14.Ma, R. “Kinematics of Robots with Oblique Bevel – Geared Wrists” MS Thesis (University of Illinois at Chicago, Chicago, 1988).Google Scholar