With the Timoshenko beam theory and the Finite Element Method, the dynamic equation of planar cooperative manipulators with link flexibility is proposed in absolute coordinates. Taking the actual position of the mass center of the cooperated object as the boundary condition, the inverse dynamic equation is developed with the load distribution method. With the solution of the inverse dynamic equations, the cooperated object can track a given trajectory accurately and the errors between the actual internal forces and the specified internal forces on the cooperated manipulators converge to zero. A new method is also developed for the optimum load distribution and load capacity of cooperative manipulator system. A numerical simulation of two planar flexible robot arms manipulating a rigid load is presented.

Issue Section:
Technical Papers
Keywords:
flexible manipulators, cooperative systems, manipulator dynamics, optimisation, finite element analysis
Topics:
Dynamics (Mechanics), Equations of motion, Manipulators, Robots, Stress, Trajectories (Physics), Flexible manipulators, Structural mechanics
1.
Walker
,
I. D.
,
Freeman
,
R. A.
, and
Marcus
,
S. I.
,
1991
, “
Analysis of Motion and Internal Loading of Objects Grasped by Multiple Cooperating Manipulators
,”
Int. J. Robot. Res.
,
10
(
4
), pp.
369
–
409
.
2.
Liu
,
Y. H.
, and
Arimoto
,
S.
,
1998
, “
Decentralized Adaptive and Nonadaptive Position/Force Controllers for Redundant Manipulators in Cooperation
,”
Int. J. Robot. Res.
,
17
(
3
), pp.
232
–
247
.
3.
Wang
,
L. T.
, and
Luo
,
M. J.
,
1994
, “
Dynamic Load-carrying Capacity and Inverse Dynamics of Multiple Cooperating Robotic Manipulators
,”
IEEE Trans. Rob. Autom.
,
10
(
1
), pp.
71
–
77
.
4.
Jankowski
,
K.
, et al.,
1993
, “
Dynamic Coordination of Multiple Robot Arms with Flexible Joints
,”
Int. J. Robot. Res.
,
12
(
6
), pp.
505
–
528
.
5.
Sun
,
Q.
,
Sharf
,
I.
, and
Nahon
,
M.
,
1999
, “
Stability Analysis of the Force Distribution Algorithm for Flexible-Link Cooperating Manipulators
,”
Mech. Mach. Theory
,
34
, pp.
753
–
763
.
6.
Matsuno
,
F.
, and
Hatayama
,
M.
,
1999
, “
Robust Cooperative Control of Two Two-Link Flexible Manipulators on the Basis of Quasi-Static Equations
,”
Int. J. Robot. Res.
,
18
(
4
), pp.
414
–
428
.
7.
Dou
,
J. W.
, and
Yu
,
Y. Q.
,
2000
, “
On the Dynamic Modeling of Two Flexible Manipulator Cooperation and Its Inverse Dynamic Analysis
,”
Robot
,
22
(
1
), pp.
9
–
47
(in Chinese).
8.
Damaren
,
C. J.
,
2000
, “
On the Dynamics and Control of Flexible Multi-Body Systems with Closed Loops
,”
Int. J. Robot. Res.
,
19
(
3
), pp.
238
–
253
.
9.
Yang
,
Z.
, and
Sadler
,
J. P.
,
1999
, “
A One-pass Approach to Dynamics of High-speed Machinery Through Three-node Lagrangian Beam Elements
,”
Mech. Mach. Theory
,
34
, pp.
995
–
1007
.
10.
Yang
,
Z.
, and
Sadler
,
J. P.
,
1990
, “
Large-displacement Finite Element Analysis of Flexible Linkages
,”
ASME J. Mech. Des.
,
112
, pp.
175
–
182
.
11.
Simo
,
J. C.
, and
Vu-Quoc
,
L.
,
1986
, “
On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part 1
,”
ASME J. Appl. Mech.
,
53
, pp.
849
–
854
.
12.
Simo
,
J. C.
, and
Vu-Quoc
,
L.
,
1986
, “
On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part 2
,”
ASME J. Appl. Mech.
,
53
, pp.
855
–
863
.
13.
Bathe, K. J., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
Copyright © 2004
 by ASME
You do not currently have access to this content.