A cable-driven parallel manipulator is an economic way to achieve manipulation over large workspace. However, unavoidable vibration in long cables can dramatically degenerate the positioning performance of manipulators. In this paper, dynamic models of large cable-driven parallel manipulators (CDPMs) are addressed where each cable is considered with distributed mass and can change in length during operation. The dynamic equation of a cable deployed or retrieved is derived using Hamilton's principle. The dynamic model of the system is characterized by partial differential equations with algebraic constraints. By properly selecting the independent unknowns, we solve the model using assumed-mode method.

References

References
1.
Khosravi
,
M. A.
, and
Taghirad
,
H. D.
,
2011
, “
Dynamic Analysis and Control of Cable Driven Robots With Elastic Cables
,”
Trans. Can. Soc. Mech. Eng.
,
35
(
4
), pp.
543
557
.
2.
Bostelman
,
R.
,
Shackleford
,
W.
,
Proctor
,
F.
,
Albus
,
J.
, and
Lytle
,
A.
,
2002
, “
The Flying Carpet: A Tool to Improve Ship Repair Efficiency
,”
American Society of Naval Engineers Symposium
, Manufacturing Technology Ship Construction Repair, Bremerton, WA, Sept. 10–12, pp.
1
9
.
3.
Bosscher
,
P.
,
Williams
,
R. L.
, II
,
Bryson
,
L. S.
, and
Castro-Lacouture
,
D.
,
2007
, “
Cable-Suspended Robotic Contour Crafting System
,”
Autom. Constr.
,
17
(
1
), pp.
45
55
.10.1016/j.autcon.2007.02.011
4.
Du
,
J. L.
,
Bao
,
H.
,
Cui
,
C. Z.
, and
Yang
,
D. W.
,
2012
, “
Dynamic Analysis ofCable-Driven Parallel Manipulators With Time-Varying Cable Lengths
,”
Finite Elem. Anal. Des.
,
48
(
1
), pp.
1392
1399
.10.1016/j.finel.2011.08.012
5.
Meunier
,
G.
,
Boulet
,
B.
, and
Nahon
,
M.
,
2009
, “
Control of an Overactuated Cable-Driven Parallel Mechanism for a Radio Telescope Application
,”
IEEE Trans. Control Syst. Technol.
,
17
(
5
), pp.
1043
1054
.10.1109/TCST.2008.2004812
6.
Oh
,
S. R.
, and
Agrawal
,
S. K.
,
2005
, “
A Reference Governor-Based Controller for a Cable Robot Under Input Constraints
,”
IEEE Trans. Control Syst. Technol.
,
13
(
4
), pp.
639
645
.10.1109/TCST.2004.841668
7.
Borgstrom
,
P. H.
,
Borgstrom
,
N. P.
,
Stealey
,
M. J.
,
Jordan
,
B.
,
Sukhatme
,
G. S.
,
Batalin
,
M. A.
, and
Kaiser
,
W. J.
,
2009
, “
Design and Implementation of NIMS3D, a 3-D Cabled Robot for Actuated Sensing Applications
,”
IEEE Trans. Rob.
,
25
(
2
), pp.
325
339
.10.1109/TRO.2009.2012339
8.
Zhang
,
Y.
,
Agrawal
,
S. K.
, and
Piovoso
,
M. J.
,
2006
, “
Coupled Dynamics of Flexible Cables and Rigid End-Effector for a Cable Suspended Robot
,”
American Control Conference
(
ACC
),
Minneapolis
, MN, June 14–16, pp.
3880
3885
.10.1109/ACC.2006.1657324
9.
Diao
,
X.
, and
Ma
,
O.
,
2009
, “
Vibration Analysis of Cable-Driven Parallel Manipulators
,”
Multibody Syst. Dyn.
,
21
(
4
), pp.
347
360
.10.1007/s11044-008-9144-0
10.
Bedoustani
,
Y. B.
,
Bigras
,
P.
,
Taghirad
,
H. D.
, and
Bonev
,
I. A.
,
2011
, “
Lagrangian Dynamics of Cable-Driven Parallel Manipulators: A Variable Mass Formulation
,”
Trans. Can. Soc. Mech. Eng.
,
35
(
4
), pp.
529
542
.
11.
Bedoustani
,
Y. B.
,
Taghirad
,
H. D.
, and
Aref
,
M. M.
,
2008
, “
Dynamics Analysis of a Redundant Parallel Manipulator Driven by Elastic Cables
,”
10th International Conference on Control, Automation, Robotics and Vision
(
ICARCV 2008
),
Hanoi, Vietnam
, Dec. 17–20, pp.
536
542
.10.1109/ICARCV.2008.4795575
12.
Collard
,
J. F.
,
Lamaury
,
J.
, and
Gouttefarde
,
M.
,
2011
, “
Dynamics Modelling of Large Suspended Parallel Cable-Driven Robots
,”
ECCOMAS Thematic Conference on Multibody Dynamics
,
Brussels, Belgium
, July 4–7.
13.
Amati
,
N.
,
Tonoli
,
A.
, and
Zenerino
,
E.
,
2014
, “
Modeling the Flexural Dynamic Behavior of Axially Moving Continua by Using the Finite Element Method
,”
ASME J. Vib. Acoust.
,
136
(
1
), p.
011012
.10.1115/1.4025551
14.
Zhu
,
W. D.
, and
Ren
,
H.
,
2013
, “
An Accurate Spatial Discretization and Substructure Method With Application to Moving Elevator Cable-Car Systems—Part I: Methodology
,”
ASME J. Vib. Acoust.
,
135
(
5
), p.
051036
.10.1115/1.4024557
15.
Du
,
J. L.
,
Cui
,
C. Z.
,
Bao
,
H.
, and
Qiu
,
Y. Y.
,
2015
, “
Dynamic Analysis of Cable-Driven Parallel Manipulators Using a Variable Length Finite Element
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
1
), p.
011013
.10.1115/1.4026570
16.
Zi
,
B.
,
Duan
,
B. Y.
,
Du
,
J. L.
, and
Bao
,
H.
,
2008
, “
Dynamic Modeling and Active Control of a Cable-Suspended Parallel Robot
,”
Mechatronics
,
18
(
2
), pp.
1
12
.10.1016/j.mechatronics.2007.09.004
17.
Mankala
,
K. K.
, and
Agrawal
,
S. K.
,
2008
, “
Dynamic Modeling of a Satellite Tethered System Using Newton's Laws and Variational Principles
,”
ASME J. Vib. Acoust.
,
130
(
1
), p.
014501
.10.1115/1.2776342
18.
Mankala
,
K. K.
, and
Agrawal
,
S. K.
,
2005
, “
Dynamic Modeling and Simulation of Satellite Tethered Systems
,”
ASME J. Vib. Acoust.
,
127
(
2
), pp.
144
156
.10.1115/1.1891811
19.
Lee
,
T.
,
Leok
,
M.
, and
McClamroch
,
N. H.
,
2011
, “
Computational Dynamics of a 3D Elastic String Pendulum Attached to a Rigid Body and an Inertially Fixed Reel Mechanism
,”
Nonlinear Dyn.
,
64
(
1–2
), pp.
97
115
.10.1007/s11071-010-9849-5
20.
Baumgarte
,
J.
,
1972
, “
Stabilization of Constraints and Integrals of Motion in Dynamical Systems
,”
Comput. Methods Appl. Mech. Eng.
,
1
(
1
), pp.
1
16
.10.1016/0045-7825(72)90018-7
You do not currently have access to this content.