A systematic approach is proposed to determine the tensionable workspace of multibody cable-driven mechanisms. The method is also capable of finding analytical descriptions for the boundaries of the tensionable regions for any number of redundant cables used. The presented approach builds upon the available methods for conventional (rigid body) cable-driven mechanisms, i.e., null space analysis and supporting/separating hyperplanes. It extends these methods to the case of a multibody driven by cables. For this purpose, the notion of generalized forces and Lagrange’s method is used to eliminate the constraint forces/moments from the equilibrium equations. This has resulted in a more compact equation form with fewer unknowns. The method is then applied to several one- and two-DOF mechanisms with various cable distributions. Analytical descriptions for the boundaries of their workspaces are found. These boundaries and the resulting regions are then used to improve the design for larger tensionable workspaces.

1.
Albus
,
J.
,
Bostelman
,
R.
, and
Dagalakis
,
N.
, 1993, “
The NIST ROBOCRANE
,”
J. Rob. Syst.
0741-2223,
10
(
5
), pp.
709
724
.
2.
Campbell
,
P. D.
,
Swaim
,
P. L.
, and
Thompson
,
C. J.
, 1995, “
Charlotte Robot Technology for Space and Terrestrial Applications
,” SAE Technical Series Paper No. 951520.
3.
Kawamura
,
S.
, and
Ito
,
K.
, 1993, “
A New Type of Master Robot for Teleoperation Using a Radial Wire Drive System
,”
Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems
, Yokohama, Japan, pp.
55
60
.
4.
Dekker
,
R.
,
Khajepour
,
A.
, and
Behzadipour
,
S.
, 2006, “
Design and Testing of an Ultra High-Speed Cable Robot
,”
Journal of Robotics and Automation
,
21
(
1
), pp.
25
34
.
5.
Rezazadeh
,
S.
, and
Behzadipour
,
S.
, 2007, “
Tensionability Conditions of a Multi-Body System Driven by Cables
,”
Proceedings of the ASME International Mechanical Engineering Congress and Exposition—IMECE
, Seattle, WA.
6.
Verhoeven
,
R.
, and
Hiller
,
M.
, 2000, “
Estimating the Controllable Workspace of Tendon-Based Stewart Platforms
,”
Proceedings of the Seventh International Symposium on Advances in Robot Kinematics—ARK
, Protoroz, Slovenia, pp.
277
284
.
7.
Alp
,
A. B.
, and
Agrawal
,
S. K.
, 2002, “
Cable-Suspended Robots: Design, Planning, and Control
,”
Proceedings of the IEEE Conference on Robotics and Automation
, Washington, DC.
8.
Pusey
,
J.
,
Fattah
,
A.
,
Agrawal
,
S.
,
Messina
,
E.
, and
Jacoff
,
A.
, 2003, “
Design and Workspace Analysis of a 6-6 Cable-Suspended Parallel Robot
,”
Proceedings of the IEEE International Conference on Intelligent Robots and Systems
, Las Vegas, NV.
9.
Bosscher
,
P.
,
Riechel
,
A. T.
, and
Ebert-Uphoff
,
I.
, 2006, “
Wrench-Feasible Workspace Generation for Cable-Driven Robots
,”
IEEE Transaction on Robotics
,
22
(
5
), pp.
890
902
.
10.
Barette
,
G.
, and
Gosselin
,
C. M.
, 2000, “
Kinematic Analysis and Design of Planar Parallel Mechanisms Actuated With Cables
,”
Proceedings of the DETC’00—ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Baltimore, MD.
11.
Gouttefarde
,
M.
, and
Gosselin
,
C. M.
, 2004, “
On the Properties and the Determination of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms
,”
Proceedings of the DETC’04—ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Salt Lake City, UT.
12.
Gouttefarde
,
M.
, and
Gosselin
,
C. M.
, 2006, “
Analysis of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms
,”
IEEE Transaction on Robotics
,
22
(
3
), pp.
434
445
.
13.
Williams
,
R. L.
, II
,
Albus
,
J. S.
, and
Bostelman
,
R. V.
, 2004, “
3D Cable-Based Cartesian Metrology System
,”
J. Rob. Syst.
0741-2223,
21
(
5
), pp.
237
257
.
14.
Pham
,
C. B.
,
Yeo
,
S. H.
,
Yang
,
G.
,
Kurbanhusen
,
M. S.
, and
Chen
,
I. -M.
, 2006, “
Force-Closure Workspace Analysis of Cable-Driven Parallel Mechanisms
,”
Mech. Mach. Theory
0094-114X,
41
(
1
), pp.
53
69
.
15.
Zhang
,
Ya.
,
Zhang
,
Yu.
,
Dai
,
X.
, and
Yang
,
Y.
, 2009, “
Workspace Analysis of a Novel 6-DoF Cable-Driven Parallel Robot
,”
Proceedings of the IEEE International Conference on Robotics and Biomimetics
, Guilin, China.
16.
Lim
,
W. B.
,
Yang
,
G.
,
Yeo
,
S. H.
,
Mustafa
,
S. K.
, and
Chen
,
I. -M.
, 2009, “
A Generic Tension-Closure Analysis Method for Fully-Constrained Cable-Driven Parallel Manipulators
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Kobe, Japan.
17.
Xu
,
L.
,
Cao
,
Y.
,
Chen
,
J.
, and
Jiang
,
S.
, 2010, “
Design and Workspace Optimization of a 6/6 Cable-Suspended Parallel Robot
,”
Proceedings of the International Conference on Computer Application and System Modeling (ICCASM)
, Taiyuan, China.
18.
Gouttefarde
,
M.
, 2008, “
Characterizations of Fully Constrained Poses of Parallel Cable-Driven Robots: A Review
,”
Proceedings of the IDETC/CIE—ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Brooklyn, NY.
19.
Diao
,
X.
, and
Ma
,
O.
, 2008, “
Workspace Determination of General 6-d.o.f. Cable Manipulators
,”
Adv. Robot.
,
22
(
2–3
), pp.
261
278
.
20.
Ghasemi
,
A.
,
Eghtesad
,
M.
, and
Farid
,
M.
, 2009, “
Workspace Analysis for Planar and Spatial Redundant Cable Robots
,”
ASME J. Mech. Rob.
1942-4302,
1
(
4
), p.
044502
.
21.
Bruckmann
,
T.
,
Mikelsons
,
L.
,
Hiller
,
M.
, and
Schramm
,
D.
, 2008, “
Continuous Workspace Analysis, Synthesis, and Optimization of Wire Robots
,”
Proceedings of the IDETC/CIE—ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Brooklyn, NY.
22.
Gouttefarde
,
M.
,
Merlet
,
J. -P.
, and
Daney
,
D.
, 2007, “
Wrench-Feasible Workspace of Parallel Cable-Driven Mechanisms
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Roma, Italy.
23.
Gouttefarde
,
M.
,
Daney
,
D.
, and
Merlet
,
J. -P.
, 2011, “
Interval-Analysis-Based Determination of the Wrench-Feasible Workspace of Parallel Cable-Driven Robots
,”
IEEE Transactions on Robotics
,
27
(
1
), pp.
1
13
.
24.
Stump
,
E.
, and
Kumar
,
V.
, 2006, “
Workspaces of Cable-Actuated Parallel Manipulators
,”
ASME J. Mech. Des.
0161-8458,
128
(
1
), pp.
159
167
.
25.
Behzadipour
,
S.
, and
Khajepour
,
A.
, 2005, “
A New Cable-Based Parallel Manipulator With Three Degrees of Freedom
,”
Multibody Syst. Dyn.
1384-5640,
13
(
4
), pp.
371
383
.
26.
Alikhani
,
A.
,
Behzadipour
,
S.
,
Sadough Vanini
,
S. A.
, and
Alasti
,
A.
, 2009, “
Workspace Analysis of a Three-DOF Cable-Driven Mechanism
,”
ASME J. Mech. Rob.
1942-4302,
1
(
4
), p.
041005
.
27.
Kino
,
H.
,
Yabe
,
S.
, and
Kawamura
,
S.
, 2005, “
A Force Display System Using Serial-Link Structure Driven by a Parallel-Wire Mechanism
,”
Adv. Rob.
0169-1864,
19
(
1
), pp.
21
37
.
28.
Rezazadeh
,
S.
, and
Behzadipour
,
S.
, “
Tensionability of Planar Two-Link and Three-Link Serial Multibodies Driven by Cables
,” to be published.
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