Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T04:56:43.440Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Fischer, U. and Stephan, W., Prinzipien und Methoden der Dynamik (VEB Verlag Leipzig, 1972) pp. 78–79.Google Scholar
2.Desoyer, K., Lugner, P. and Springer, H., “Dynamic Effects of Active Elements in Manipulators and their Influence upon the Controlling Drives”, IUTAM/IFToMM Symp. Dynamics of Multibody Systems, Udine 1985 (Eds. Bianchi, G. and Schiehlen, W.), (Springer Verlag Berlin Heidelberg, 1986) pp. 43–54.Google Scholar
3.Springer, H., Lugner, P. and Desoyer, K., “Equations of Motion for Manipulators Including Dynamic Effects of Active Elements” Proc. IFAC Symp. on Robot Control, Barcelona 11 1985, (Pergamon Press, Oxford), pp. 425–429.Google Scholar
4.Desoyer, K., Kopacek, P. and Troch, I., Industrieroboter und Handhabungsgeräte (R. Oldenbourg Verlag München Wien, 1985).Google Scholar
5.Tarn, T.J., A. K. Bejczy, Shuotiao, H. and Yun, X., “Inertia Parameters of PUMA 560 Robot Arm” Washington University, St. Louis, Robotics Laboratory Report SSM-RL-85–01 (1986).Google Scholar
6. Unimate PUMA Mark II Robot 500 Series Equipment Manual (08, 1985).Google Scholar