This paper presents workspace analysis of planar and spatial cable robots having one or more redundant cables. The proposed approach, which is based on a variant of Bland’s pivot rule, provides all poses (positions/orientations) reachable by the cable robot platform with any number of cable redundancies. By virtue of this method, there is no need to use successive determinants to compute the workspace; this results in less computation time. Additionally, another algorithm, which takes advantage of reduced row-echelon form of the system matrix, is proposed for the case of cable robots with only one redundant cable and also to include upper limit for tensions in cables as an important factor in workspace analysis of the cable robots. Simulation results are provided to show the merits of the proposed methods to compute the available static workspace of the redundant cable robots.

1.
Bosscher
,
P.
,
Riechel
,
A. T.
, and
Ebert-Uphoff
,
I.
, 2006, “
Wrench-Feasible Workspace Generation for Cable-Driven Robots
,”
IEEE Trans. Rob.
1552-3098,
22
(
5
), pp.
890
902
.
2.
Riechel
,
A. T.
, and
Ebert-Uphoff
,
I.
, 2004, “
Force-Feasible Workspace Analysis for Underconstrained Point-Mass Cable Robots
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Los Angeles, CA, pp.
4956
4962
.
3.
Kawamura
,
S.
,
Choe
,
W.
,
Tanaka
,
S.
, and
Pandian
,
S. R.
, 2003, “
Development of an Ultrahigh Speed FALCON Using Wire Drive System
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, pp.
215
220
.
4.
Lafourcade
,
P.
,
Llibre
,
M.
, and
Reboulet
,
C.
, 2002, “
Design of a Parallel Wire-Driven Manipulator for Wind Tunnels
,”
Proceedings of the Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators
, Quebec, Canada, pp.
187
194
.
5.
Diao
,
X.
,
Ma
,
O.
, and
Paz
,
R.
, 2006, “
Study of 6-DOF Cable Robots for Potential Application of HIL Microgravity Contact-Dynamics Simulation
,”
Proceedings of the AIAA Modeling and Simulation Technologies Conference and Exhibit (M&ST 2006)
, Keystone, CO, pp.
1097
1110
.
6.
Gallina
,
P.
,
Rosati
,
G.
, and
Rossi
,
A.
, 2001, “
3-d.o.f. Wire Driven Planar Haptic Interface
,”
J. Intell. Robotic Syst.
0921-0296,
32
, pp.
23
36
.
7.
Albus
,
J.
,
Bostelman
,
R.
, and
Dagalakis
,
N.
, 1992, “
The NIST Robocrane
,”
J. Robot. Syst.
,
10
(
5
), pp.
709
724
. 0741-2223
8.
Diao
,
X.
, and
Ma
,
O.
, 2006, “
Workspace Analysis of a 6-DOF Cable Robot for Hardware-in-the-Loop Dynamic Simulation
,”
Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems
, China, pp.
4103
4108
.
9.
Verhoeven
,
R.
, and
Hiller
,
M.
, 2000, “
Estimating the Controllable Workspace of Tendon-Based Stewart Platform
,”
Proceedings of Seventh International Symposium on Advanced Robot Kinematics
, Slovenia, pp.
277
284
.
10.
Barrette
,
G.
, and
Gosselin
,
C. M.
, 2005, “
Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms
,”
ASME J. Mech. Des.
0161-8458,
127
(
2
), pp.
242
248
.
11.
Fattah
,
A.
, and
Agrawal
,
S. K.
, 2002, “
Design of Cable-Suspended Planar Parallel Robots for an Optimal Workspace
,”
Proceedings of the Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators
, Quebec, Canada, pp.
195
202
.
12.
Fattah
,
A.
, and
Agrawal
,
S. K.
, 2002, “
Workspace and Design Analysis of Cable-Suspended Planar Parallel Robots
,”
Proceedings of the ASME DETC
, Montreal, QC, Canada, pp.
1
9
.
13.
Alp
,
A. B.
, and
Agrawal
,
S. K.
, 2002, “
Cable Suspended Robots: Design, Planning and Control
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, pp.
4275
4280
.
14.
Ming
,
A.
, and
Higuchi
,
T.
, 1994, “
Study on Multiple Degree-of-Freedom Positioning Mechanism Using Wires (Part 2)—Development of a Planar Completely Restrained Positioning Mechanism
,”
Int. J. Jpn. Soc. Precis. Eng.
0916-782X,
28
(
3
), pp.
235
242
.
15.
Bosscher
,
P.
, and
Ebert-Uphoff
,
I.
, 2004, “
Wrench Based Analysis of Cable-Driven Robots
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, New Orleans, LA, pp.
4950
4955
.
16.
Gouttefarde
,
M.
, and
Gosselin
,
C. M.
, 2006, “
Analysis of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms
,”
IEEE Trans. Rob. Autom.
1042-296X,
22
(
3
), pp.
434
445
.
17.
Diao
,
X.
, and
Ma
,
O.
, 2007, “
A Method of Verifying Force-Closure Condition for General Cable Manipulators With Seven Cables
,”
Mech. Mach. Theory
0094-114X,
42
, pp.
1563
1576
.
18.
Diao
,
X.
, and
Ma
,
O.
, 2008, “
Workspace Determination of General 6-d.o.f. Cable Manipulators
,”
Adv. Rob.
0169-1864,
22
, pp.
261
278
.
19.
Diao
,
X.
, and
Ma
,
O.
, 2009, “
Force-Closure Analysis of 6-DOF Cable Manipulators With Seven or More Cables
,”
Robotica
0263-5747,
27
(
2
), pp.
209
215
.
20.
Gouttefarde
,
M.
,
Merlet
,
J. -P.
, and
Daney
,
D.
, 2006, “
Determination of the Wrench-Closure Workspace of 6-DOF Parallel Cable-Driven Mechanisms
,”
Tenth ARK International Symposium on Advances in Robot Kinematics
, pp.
315
322
.
21.
Gouttefarde
,
M.
,
Merlet
,
J. -P.
, and
Daney
,
D.
, 2006, “
Wrench-Feasible Workspace of Parallel Cable-Driven Mechanisms
,”
2007 IEEE International Conference on Robotics and Automation
, Italy, Apr., pp.
1492
1497
.
22.
Stump
,
E.
, and
Kumar
,
V.
, 2006, “
Workspace of Cable-Actuated Parallel Manipulators
,”
ASME J. Mech. Des.
0161-8458,
128
, pp.
159
167
.
23.
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
, pp.
53
69
.
24.
Rockafellar
,
R. T.
, 1970,
Convex Analysis
,
Princeton University Press
,
Princeton, NJ
.
25.
Avis
,
D.
, and
Kaluzny
,
B.
, 2004, “
Solving Inequalities and Proving Farkas’s Lemma Made Easy
,”
AMS Mathematical Monthly
,
111
, pp.
152
157
.
26.
Hoffman
,
K.
, and
Kunze
,
R.
, 1971,
Linear Algebra
,
Prentice-Hall
,
Englewood Cliffs, NJ
, Chap. 1.
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