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Recursive formulation for the analytical or numerical application of the Gibbs-Appell method to the dynamics of robots*

Published online by Cambridge University Press:  09 March 2009

K. Desoyer  and
P. Lugner
K. Desoyer
Affiliation:
University of Technology, Wiedner Hauptstraß 8–10, A-1040 Wien (Austria)
P. Lugner
Affiliation:
University of Technology, Wiedner Hauptstraß 8–10, A-1040 Wien (Austria)
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Summary

To derive the equations of motion for a multibody system using the Gibbs-Appell calculus – the partial derivatives of the Gibbs function G = 1/2 ∫ a2 dm with respect to the generalized accelerations equal the generalized forces-shows special advantages. Describing the kinematics with Jacobi matrices and local terms, these equations can be written in such a way that the partial derivations need not be performed explicitly. Kinetic effects of fast rotating driving devices attached to the moving links can be included in a similar way. Though an analytical formulation of the equations of motion is especially desirable with respect to its application for industrial robots, such a formulation becomes too extended and susceptible to errors for systems with more than 3 or 4 bodies. Therefore an approach is developed for tree structured robots with rotational or translational joints for calculating the Jacobi matrices and the local terms without employing any differentiation process. So it is possible to use the Gibbs-Appell method numerically in a recursive way e.g. for calculating the torques of the actuators of a robot with 6 or more degrees of freedom for a given motion.

Keywords

Robot dynamicsGibbs-Appell methodRecursive formulationMultibody systemIndustrial robot
Type
Research Article
Information
Robotica , Volume 7 , Issue 4 , October 1989 , pp. 343 - 347
Copyright
Copyright © Cambridge University Press 1989

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References

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