NDLI: Study of invariance properties in robotic systems: a Lagrangian formulation approach

Content Provider	IEEE Xplore Digital Library
Author	Lakhdari, Z. Makany, P. Rouff, M. Slamani, Y.
Copyright Year	2006
Description	Author affiliation: Lab. Univ. des Sci. Appliquees de Cherbourg, Ecole d'Ingenieurs de Cherbourg, Cherbourg-Octeville (Lakhdari, Z.; Makany, P.; Rouff, M.; Slamani, Y.)
Abstract	We present here some interesting properties of regularity regarding firstly the flexural deformation spectra and secondly the flexural and torsional spectra of mechanical loaded bodies which can be useful for the finite control of these systems. In these two cases, two main cases are studied: the non compliant and non dissipative case, and the compliant and non dissipative case. By studying flexural spectra of general deformable bodies versus the load, we found a noteworthy invariance property of the eigenfrequencies versus the system load. Roughly we found that under a preload condition the eigenfrequencies of deformation of the system are invariant versus loads, i.e. on a diagram eigenfrequencies versus loads, the curves are horizontal lines. As shown by our curves, these behaviors are not very distant from the asymptotic behaviors but occur for very small values of loads and frequencies, allowing the implementation of this property to real technological devices. For loaded flexural and torsional deformable bodies, we found that under a preload condition, each eigenfrequency is invariant versus the load $m_{N}.$ For the mode 7 and beyond, the preload conditions are less than $m_{N}=1,$ and the seven first modes (from 0 to 6) can be easily modelled by polynomial functions of mN in the neighborhood of useful $m_{N}$
Sponsorship	American Automatic Control Council IFAC
File Size	538502
File Format	PDF
ISBN	1424402093
e-ISBN	1424402107
DOI	10.1109/ACC.2006.1657325
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-06-14
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Robots Lagrangian functions Control systems Frequency Equations Mechanical factors Polynomials Helium Motion control Research and development
Content Type	Text
Resource Type	Article

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