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.

1.
Shapiro
,
A.
, and
Rimon
,
E.
, 2004, “
On the Mechanics of Natural Compliance in Frictional Contacts and Its Effect on Grasp Stiffness and Stability
,”
IEEE Int. Conference on Robotics and Automation
, pp.
1264
1269
.
2.
Kliem
,
W. R.
, 1992, “
Symmetrizable Systems in Mechanics and Control Theory
,”
ASME J. Appl. Mech.
0021-8936,
59
, pp.
454
456
.
3.
Inman
,
D. J.
, 1989,
Vibration With Control Measurement and Stability
,
Prentice-Hall
, Englewood Cliffs, NJ.
4.
Inman
,
D. J.
, 1983, “
Dynamics of Asymmetric Nonconservative Systems
,”
ASME J. Appl. Mech.
0021-8936,
50
, pp.
199
203
.
5.
Ahmadian
,
M.
, and
Chou
,
S.-H.
, 1987, “
A New Method for Finding Symmetric Form of Asymmetric Finite-Dimensional Dynamic Systems
,”
ASME J. Appl. Mech.
0021-8936,
54
, pp.
700
705
.
6.
Caughey
,
T. K.
, and
Ma
,
F.
, 1993, “
Complex Modes and Solvability of Nonclassical Linear Systems
,”
ASME J. Appl. Mech.
0021-8936,
60
, pp.
26
28
.
7.
Ma
,
F.
, and
Caughey
,
T. K.
, 1995, “
Analysis of Linear Nonconservative Vibrations
,”
ASME J. Appl. Mech.
0021-8936,
62
, pp.
685
691
.
8.
Adhikari
,
S.
, 2000, “
On Symmetrizable Systems of Second Kind
,”
ASME J. Appl. Mech.
0021-8936,
67
, pp.
797
802
.
9.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University Press
, Cambridge, UK.
10.
Xydas
,
N.
, and
Kao
,
I.
, 1999, “
Modeling of Contact Mechanics and Friction-Limit-Surfaces for Soft Fingers in Robotics, With Experimental Results
,”
Int. J. Robot. Res.
0278-3649,
18
(
8
), pp.
941
950
.
You do not currently have access to this content.