This paper shows that the conventional Lagrangian modeling of flexible-link robots does not fully incorporate the bending mechanism of flexible links. The conventional link deflection model allows free link elongation in addition to link deflection; the link elongation increases as link deflection increases. The link elongation, however, causes certain degrees of modeling inaccuracy in association with the rotational motion of the links. Therefore, this paper proposes a new link deflection model, compatible with the bending mechanism of flexible links. Then a new nonlinear dynamic model is derived based on the new link deflection model, fixing the modeling inaccuracy of the conventional dynamic model.

1.
Cannon
,
R. H.
, and
Schmitz
,
E.
, Jr.
, 1984, “
Initial Experiments on the End-Point Control of a Flexible One-Link Robot
,”
Int. J. Robot. Res.
0278-3649,
3
, pp.
62
75
.
2.
Shung
,
I. Y.
, and
Vidyasagar
,
M.
, 1987, “
Control of a Flexible Robot Arm with Bounded Input: Optimum Step Response
,”
IEEE Int. Conf. Robotics Automation
, pp.
916
922
.
3.
Siciliano
,
B.
, and
Book
,
W.
, 1989, “
A Singular Perturbation Approach to Control of Light Weight Flexible Manipulators
,”
Int. J. Robot. Res.
0278-3649,
7
, pp.
79
90
.
4.
Magee
,
D.
, and
Book
,
W.
, 1993, “
Eliminating Multiple Modes of Vibration in a Flexible Manipulator
,”
Proc. IEEE Conf. Robotics Automation
, pp.
474
479
.
5.
Moallem
,
M.
,
Khorasoni
,
K.
, and
Patel
,
R.
, 1997, “
An Integral Manifold Approach for Tip-Position Tracking of Flexible Multi-link Manipulators
,”
IEEE Trans. Rob. Autom.
1042-296X,
13
, pp.
823
837
.
6.
Olfati-Saber
,
R.
, 2000, “
Trajectory Tracking for a Flexible One-Link Robot Using a Nonlinear Noncollocated Output
,”
Proceedings of the 39th IEEE Conf. on Decision and Control
, Sydney, Australia, pp.
4024
4029
.
7.
De Luca
,
A.
, and
Siciliano
,
B.
, 1989, “
Trajectory Control of a Non-Linear One-Link Flexible Arm
,”
Int. J. Control
0020-7179,
50
, pp.
1699
1715
.
8.
De Luca
,
A.
, and
Siciliano
,
B.
, 1991, “
Closed-Form Dynamic Model of Planar Multilink Lightweight Robots
,”
IEEE Trans. Syst. Man Cybern.
0018-9472,
21
, pp.
826
839
.
9.
Martins
,
J. M.
,
Mohamed
,
Z.
,
Tokhi
,
M. O.
, and
Sa da Costa
,
J.
, and
Botto
,
M. A.
, 2003, “
Approaches for Dynamic Modeling of Flexible Manipulator Systems
,”
IEE Proc.: Control Theory Appl.
1350-2379,
150
, pp.
401
411
.
10.
Meirovitch
,
L.
, 1986,
Elements of Vibration Analysis
,
2nd Ed.
,
McGraw-Hill
, New York.
11.
Crag
,
J.
, 1988,
Introduction to Robotics, Mechanics and Control
,
2nd Ed.
,
Addison-Wesley
, New York.
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