This paper develops analytical techniques to delineate the workspace boundaries for parallel mechanisms with cables. In such mechanisms, it is not only necessary to solve the closure equations but it is also essential to verify that equilibrium can be achieved with non-negative actuator (cable) forces. We use tools from convex analysis and linear algebra to derive closed-form expressions for the workspace boundaries and illustrate the applications using planar and spatial examples.
Issue Section:
Research Papers
1.
Cauchy
, A.
, 1813, “Deuxième Memoire sur les Polygones et les Polyhedres
,” J. Ec. Polytech. (Paris)
0368-2013, 9
, pp. 87
–98
.2.
Stewart
, D.
, 1965, “A Platform with 6 Degrees of Freedom
,” Proc. Inst. Mech. Eng.
0020-3483, 180
(Part 1, 15), pp. 371
–386
.3.
Merlet
, J.-P.
, 2000, Parallel Robots
, Kluwer
, Dordrecht.4.
Albus
, J.
, Bostelman
, R.
, and Dagalakis
, N.
, 1992. “The NIST SPIDER, a Robot Crane
,” J. Res. Natl. Inst. Stand. Technol.
1044-677X, 97
(3
), pp. 373
–385
.5.
Roberts
, R.
, Graham
, T.
, and Lippitt
, T.
, 1998. “On the Inverse Kinematics, Statics, and Fault Tolerance of Cable-Suspended Robots
,” J. Rob. Syst.
0741-2223, 15
(10
), pp. 581
–597
.6.
Verhoeven
, R.
, 2004, “Analysis of the workspace of tendon-based stewart platforms
,” Ph.D. thesis, University of Duisburg-Essen.7.
Verhoeven
, R.
, and Hiller
, M.
, 2000, “Estimating the Controllable Workspace of Tendon-Based Stewart Platforms
,” Advancements in Robot Kinematics, pp. 277
–284
.8.
Oh
, S.
, and Agrawal
, S.
, 2003. “Cable-Suspended Planar Parallel Robots with Redundant Cables: Controllers with Positive Cable Tensions
,” Proc. of IEEE International Conference on Robotics and Automation
, Taipei, Taiwan, September 14–19, pp. 3023
–3028
.9.
Takeda
, Y.
, and Funabashi
, H.
, 2000. “Kinematic Synthesis of Spatial In-Parallel Wire-Driven Mechanism with Six Degrees of Freedom with High Force Transmissibility
,” Proceedings of the ASME International Design Engineering Technical Conference
, Baltimore, MD, pp. 1
–9
.10.
Stump
, E.
, and Kumar
, V.
, 2004, “Workspace Delineation of Cable-Actuated Parallel Manipulators
,” Proceedings of the ASME International Design Engineering Technical Conference
, Salt Lake City, UT.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 ASME International Design Engineering Technical Conference
, Salt Lake City, UT.12.
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
.13.
Murray
, R.
, Li
, Z.
, and Sastry
, S.
, 1993, A Mathematical Introduction to Robotic Manipulation
, CRC Press
, Florida.14.
Mason
, M. T.
, and Salisbury
, J. K.
, 1985, Robot Hands and the Mechanics of Manipulation
. MIT Press
, Cambridge, Massachusetts.15.
Han
, L.
, Li
, Z.
, Trinkle
, J.
, Qin
, Z.
, and Jiang
, S.
, 2000. “The Planning and Control of Robot Dexterous Manipulation
,” Proceedings of the IEEE International Conference on Robotics and Automation
, San Francisco, CA, 1
, pp. 263
–269
.16.
Boyd
, S.
, and Vandenberghe
, L.
, 2004, Convex Optimization
. Cambridge University Press
, Cambridge, UK.17.
Mangasarian
, O.
, 1969, Nonlinear Programming
. McGraw-Hill
, New York.18.
Ohwovoriole
, M. S.
, and Roth
, B.
, 1981, “An Extension of Screw Theory
,” ASME J. Mech. Des.
0161-8458, 103
, pp. 725
–735
.19.
Cottle
, R.
, Pang
, J.-S.
, and Stone
, R.
, 1992, The Linear Complementarity Problem
, Academic Press
, Boston.20.
Merlet
, J.-P.
, 1989, “Singular Configurations of Parallel Manipulators and Grassmann Geometry
,” Geometry and Robotics
, J.-D.
Boissonnat
and J.-P.
Laumond
, eds., Vol. LNCS 391
. Springer-Verlag
, pp. 194
–212
.Copyright © 2006
by American Society of Mechanical Engineers
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