This paper studies underconstrained cable-driven parallel robots (CDPRs) with three cables. A major challenge in the study of these robots is the intrinsic coupling between kinematics and statics, which must be tackled simultaneously. Effective elimination procedures are presented which provide the complete solution sets of the inverse geometrico-static problems (IGPs) with assigned orientation or position. In the former case, the platform orientation is given, whereas the platform position and the cable lengths and tensions must be computed. In the latter case, the platform position is known, whereas the platform orientation and the cable lengths and tensions are to be calculated. The described problems are proven to admit at the most 1 and 24 real solutions, respectively.
Issue Section:
Research Papers
References
1.
Carricato
, M.
, and Merlet
, J.-P.
, 2010
, “Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots
,” Advances in Robot Kinematics: Motion in Man and Machine
, J.
Lenarčič
and M. M.
Stanišic`
, eds., Springer
, Dordrecht
, pp. 309
–319
.2.
Carricato
, M.
, and Merlet
, J.-P.
, 2013
, “Stability Analysis of Underconstrained Cable-Driven Parallel Robots
,” IEEE Trans. Rob.
, 29
(1
), pp. 288
–296
.10.1109/TRO.2012.22177953.
Merlet
, J.-P.
, 2013
, “Wire-Driven Parallel Robot: Open Issues
,” Romansy 19—Robot Design, Dynamics and Control
, V.
Padois
, P.
Bidaud
, and O.
Khatib
, eds., Springer
, Vienna
, pp. 3
–10
.4.
Albus
, J.
, Bostelman
, R.
, and Dagalakis
, N.
, 1993
, “The NIST Robocrane
,” J. Rob. Syst.
, 10
(5
), pp. 709
–724
.10.1002/rob.46201005095.
Kawamura
, S.
, Kino
, H.
, and Won
, C.
, 2000
, “High-Speed Manipulation by Using Parallel Wire-Driven Robots
,” Robotica
, 18
(1
), pp. 13
–21
.10.1017/S02635747990024776.
Tadokoro
, S.
, Murao
, Y.
, Hiller
, M.
, Murata
, R.
, Kohkawa
, H.
, and Matsushima
, T.
, 2002
, “A Motion Base With 6-DOF by Parallel Cable Drive Architecture
,” IEEE/ASME Trans. Mechatron.
, 7
(2
), pp. 115
–123
.10.1109/TMECH.2002.10112487.
Pusey
, J.
, Fattah
, A.
, Agrawal
, S.
, and Messina
, E.
, 2004
, “Design and Workspace Analysis of a 6-6 Cable-Suspended Parallel Robot
,” Mech. Mach. Theory
, 39
(7
), pp. 761
–778
.10.1016/j.mechmachtheory.2004.02.0108.
Hiller
, M.
, Fang
, S.
, Mielczarek
, S.
, Verhoeven
, R.
, and Franitza
, D.
, 2005
, “Design, Analysis and Realization of Tendon-Based Parallel Manipulators
,” Mech. Mach. Theory
, 40
(4
), pp. 429
–445
.10.1016/j.mechmachtheory.2004.08.0029.
Alikhani
, A.
, Behzadipour
, S.
, Vanini
, S. A. S.
, and Alasty
, A.
, 2009
, “Workspace Analysis of a Three DOF Cable-Driven Mechanism
,” ASME J. Mech. Rob.
, 1
(4
), 041005
.10.1115/1.320425510.
Rosati
, G.
, Zanotto
, D.
, and Agrawal
, S. K.
, 2011
, “On the Design of Adaptive Cable-Driven Systems
,” ASME J. Mech. Rob.
, 3
(2
), 021004
.10.1115/1.400358011.
Bosscher
, P.
, Riechel
, A. T.
, and Ebert-Uphoff
, I.
, 2006
, “Wrench-Feasible Workspace Generation for Cable-Driven Robots
,” IEEE Trans. Rob.
, 22
(5
), pp. 890
–902
.10.1109/TRO.2006.87896712.
Stump
, E.
, and Kumar
, V.
, 2006
, “Workspaces of Cable-Actuated Parallel Manipulators
,” ASME J. Mech. Des.
, 128
(1
), pp. 159
–167
.10.1115/1.212174113.
Ghasemi
, A.
, Eghtesad
, M.
, and Farid
, M.
, 2009
, “Workspace Analysis for Planar and Spatial Redundant Cable Robots
,” ASME J. Mech. Rob.
, 1
(4
), 044502
.10.1115/1.321102614.
Bouchard
, S.
, Gosselin
, C.
, and Moore
, B.
, 2010
, “On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches
,” ASME J. Mech. Rob.
, 2
(1
), 011010
.10.1115/1.400055815.
Gouttefarde
, M.
, Daney
, D.
, and Merlet
, J.-P.
, 2011
, “Interval-Analysis-Based Determination of the Wrench-Feasible Workspace of Parallel Cable-Driven Robots
,” IEEE Trans. Rob.
, 27
(1
), pp. 1
–13
.10.1109/TRO.2010.209006416.
Lau
, D.
, Oetomo
, D.
, and Halgamuge
, S.
, 2011
, “Wrench-Closure Workspace Generation for Cable Driven Parallel Manipulators Using a Hybrid Analytical-Numerical Approach
,” ASME J. Mech. Des.
, 133
(7
), 071004
.10.1115/1.400422217.
Azizian
, K.
, and Cardou
, P.
, 2012
, “The Dimensional Synthesis of Planar Parallel Cable-Driven Mechanisms Through Convex Relaxations
,” ASME J. Mech. Rob.
, 4
(3
), 031011
.10.1115/1.400695218.
Behzadipour
, S.
, and Khajepour
, A.
, 2006
, “Stiffness of Cable-Based Parallel Manipulators With Application to Stability Analysis
,” ASME J. Mech. Des.
, 128
(1
), pp. 303
–310
.10.1115/1.211489019.
Behzadipour
, S.
, and Khajepour
, A.
, 2006
, “Erratum: Stiffness of Cable-Based Parallel Manipulators With Application to Stability Analysis
,” ASME J. Mech. Des.
, 128
(11
), pp. 1366
.10.1115/1.235443920.
Surdilovic
, D.
, Radojicic
, J.
, and Krüger
, J.
, 2013
, “Geometric Stiffness Analysis of Wire Robots: A Mechanical Approach
,” Cable-Driven Parallel Robots
, T.
Bruckmann
and A.
Pott
, eds., Springer-Verlag
, Berlin Heidelberg
, pp. 389
–404
.21.
Wischnitzer
, Y.
, Shvalb
, N.
, and Shoham
, M.
, 2008
, “Wire-Driven Parallel Robot: Permitting Collisions Between Wires
,” Int. J. Robot. Res.
, 27
(9
), pp. 1007
–1026
.10.1177/027836490809588422.
Perreault
, S.
, Cardou
, P.
, Gosselin
, C. M.
, and Otis
, M. J.-D.
, 2010
, “Geometric Determination of the Interference-Free Constant-Orientation Workspace of Parallel Cable-Driven Mechanisms
,” ASME J. Mech. Rob.
, 2
(3
), 031016
.10.1115/1.400178023.
Miermeister
, P.
, and Pott
, A.
, 2012
, “Auto Calibration Method for Cable-Driven Parallel Robots Using Force Sensors
,” Latest Advances in Robot Kinematics
, J.
Lenarčič
and M.
Husty
, eds., Springer
, Dordrecht
, pp. 269
–276
.24.
Alexandre dit Sandretto
, J.
, Daney
, D.
, and Gouttefarde
, M.
, 2013
, “Calibration of a Fully-Constrained Parallel Cable-Driven Robot
,” Romansy 19—Robot Design, Dynamics and Control
, V.
Padois
, P.
Bidaud
, and O.
Khatib
, eds., Springer
, Vienna
, pp. 77
–84
.25.
Notash
, L.
, 2012
, “Failure Recovery for Wrench Capability of Wire-Actuated Parallel Manipulators
,” Robotica
, 30
(6
), pp. 941
–950
.10.1017/S026357471100116026.
Yamamoto
, M.
, Yanai
, N.
, and Mohri
, A.
, 2004
, “Trajectory Control of Incompletely Restrained Parallel-Wire-Suspended Mechanism Based on Inverse Dynamics
,” IEEE Trans. Rob.
, 20
(5
), pp. 840
–850
.10.1109/TRO.2004.82950127.
Fattah
, A.
, and Agrawal
, S. K.
, 2006
, “On the Design of Cable-Suspended Planar Parallel Robots
,” ASME J. Mech. Des.
, 127
(5
), pp. 1021
–1028
.10.1115/1.190300128.
Heyden
, T.
, and Woernle
, C.
, 2006
, “Dynamics and Flatness-Based Control of a Kinematically Undetermined Cable Suspension Manipulator
,” Multibody Syst. Dyn.
, 16
(2
), pp. 155
–177
.10.1007/s11044-006-9023-529.
Michael
, N.
, Kim
, S.
, Fink
, J.
, and Kumar
, V.
, 2009
, “Kinematics and Statics of Cooperative Multi-Robot Aerial Manipulation With Cables
,” ASME 2009 International Design Engineering Technical Conferences
, Vol. 7
, pp. 83
–91
, Paper No. DETC2009–87677.
30.
Jiang
, Q.
, and Kumar
, V.
, 2010
, “The Inverse Kinematics of 3-D Towing
,” Advances in Robot Kinematics: Motion in Man and Machine
, J.
Lenarčič
and M. M.
Stanišic`
, eds., Springer
, Dordrecht
, pp. 321
–328
.31.
Jiang
, Q.
, and Kumar
, V.
, 2013
, “The Direct Kinematics of Objects Suspended From Cables,” ASME 2010 International Design Engineering Technical Conferences
, Vol. 2
, pp. 193
–202
, Paper No. DETC2010–28036.32.
Collard
, J.-F.
, and Cardou
, P.
, 2013
, “Computing the Lowest Equilibrium Pose of a Cable-Suspended Rigid Body
,” Optim. Eng.
, pp. 1–20.10.1007/s11081-012-9191-533.
Merlet
, J.-P.
, 2006
, Parallel Robots
, Springer
, Dordrecht
.34.
McCarthy
, J. M.
, 2011
, “21st Century Kinematics: Synthesis, Compliance, and Tensegrity
,” ASME J. Mech. Rob.
, 3
(2
), 020201
.10.1115/1.400318135.
Abbasnejad
, G.
, and Carricato
, M.
, 2012
, “Real Solutions of the Direct Geometrico-Static Problem of Under-Constrained Cable-Driven Parallel Robots With 3 Cables: A Numerical Investigation
,” Meccanica
, 47
(7
), pp. 1761
–1773
.10.1007/s11012-012-9552-336.
Berti
, A.
, Merlet
, J.-P.
, and Carricato
, M.
, 2013
, “Solving the Direct Geometrico-Static Problem of 3-3 Cable-Driven Parallel Robots by Interval Analysis: Preliminary Results
,” Cable-Driven Parallel Robots
, T.
Bruckmann
and A.
Pott
, eds., Springer-Verlag
, Berlin, Heidelberg
, pp. 251
–268
.37.
Carricato
, M.
, 2013
, “Direct Geometrico-Static Problem of Under-Constrained Cable-Driven Parallel Robots With Three Cables
,” ASME J. Mech. Rob.
(accepted).10.1115/1.402429338.
Carricato
, M.
, Abbasnejad
, G.
, and Walter
, D.
, 2012
, “Inverse Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots With Four Cables
,” Latest Advances in Robot Kinematics
, J.
Lenarčič
and M.
Husty
, eds., Springer
, Dordrecht
, pp. 365
–372
.39.
Carricato
, M.
, and Abbasnejad
, G.
, 2013
, “Direct Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots With 4 Cables
,” Cable-Driven Parallel Robots
, T.
Bruckmann
and A.
Pott
, eds., Springer-Verlag
, Berlin, Heidelberg
, pp. 269
–285
.40.
Hunt
, K. H.
, 1978
, Kinematic Geometry of Mechanisms
, Clarendon Press
, Oxford
.41.
Bottema
, O.
, and Roth
, B.
, 1990
, Theoretical Kinematics
, Dover Publications
, New York
.42.
Salmon
, G.
, 1964
, Lessons Introductory to the Modern Higher Algebra
, Chelsea Publishing Company
, New York
.43.
Raghavan
, M.
, and Roth
, B.
, 1995
, “Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators
,” ASME J. Mech. Des.
, 117
(2B
), pp. 71
–79
.10.1115/1.283647344.
Manocha
, D.
, and Krishnan
, S.
, 1996
, “Solving Algebraic Systems Using Matrix Computations
,” ACM SIGSAM Bull.
, 30
(4
), pp. 4
–21
.10.1145/242961.24296545.
Cox
, D.
, Little
, J.
, and O'Shea
, D.
, 2007
, Ideals, Varieties, and Algorithms
, Springer
, New York
.Copyright © 2013 by ASME
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