Stability of Second-Order Asymmetric Linear Mechanical Systems With Application to Robot Grasping

[+] Author and Article Information
Amir Shapiro

Department of Mechanical Engineering, Ben Gurion University of the Negev, P. O. B. 653, Beer Sheva 84105, Israel

The matrix norm is defined as E=max{Eu} over all vectors u1.

J. Appl. Mech 72(6), 966-968 (Mar 03, 2005) (3 pages) doi:10.1115/1.2042484 History: Received July 18, 2004; Revised March 03, 2005

This technical correspondence presents a surprisingly simple analytical criterion for the stability of general second-order asymmetric linear systems. The criterion is based on the fact that if a symmetric system is stable, adding a small amount of asymmetry would not cause instability. We compute analytically an upper bound on the allowed asymmetry such that the overall linear system is stable. This stability criterion is then applied to robot grasping arrangements which, due to physical effects at the contacts, are asymmetric mechanical systems. We present an application of the stability criterion to a 2D grasp arrangement.

Copyright © 2005 by American Society of Mechanical Engineers
Topics: Stability , Robots , Grasping
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Grahic Jump Location
Figure 1

A two-finger grasp of a family of wedge-like objects



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