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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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