This investigation deals with singularity analysis of parallel manipulators and their instantaneous behavior while in or close to a singular configuration. The method presented utilizes line geometry tools and screw theory to describe a manipulator in a given position. Then, this description is used to obtain the closest linear complex, presented by its screw coordinates, to the set of governing lines of the manipulator. The linear complex axis and pitch provide additional information and a better physical understanding of the type of singularity and the motion the manipulator tends to perform in a singular point and in its neighborhood. Examples of Hunt’s, Fichter’s and 3-UPU singularities, along with a few selected examples taken from Merlet’s work [1], are presented and analyzed using this method.
Issue Section:
Technical Papers
1.
Merlet
, J. P.
, 1992
, “Singular Configurations of Parallel Manipulators and Grassmann Geometry
,” Int. J. Robot. Res.
, 8
(5
), pp. 45
–56
.2.
Hunt
, K. H.
, 1983
, “Structural Kinematics of In-Parallel-Actuated Robot Arms
,” ASME J. Mech. Des.
, 105
(4
), pp. 705
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.3.
St-Onge
, B. M.
, and Gosselin
, C. M.
, 2000
, “Singularity Analysis and Representation of the General Gaugh-Stewart Platform
,” Int. J. Robot. Res.
, 19
(3
), pp. 271
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.4.
Dasgupta
, B.
, and Mruthyunjaya
, T. S.
, 1998
, “Singularity-Free Path Planning for the Stewart Platform Manipulator
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, 33
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), pp. 711
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.5.
Gosselin
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7.
Ma
, O.
, and Angeles
, J.
, 1992
, “Architecture Singularities of Parallel Manipulators
,” Int. J. Robot. Res.
, 7
(1
), pp. 23
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.8.
Mohammadi Daniali
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, Zsombor-Murray
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, and Angeles
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, 1955
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,” J. Rob. Syst.
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), pp. 795
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.9.
Zlatanov
, D.
, Fenton
, R. G.
, and Benhabib
, B.
, 1995
, “A Unifying Framework for Classification and Interpretation of Mechanism Singularities
,” ASME J. Mech. Des.
, 117
, pp. 566
–572
.10.
Mayer St-Onge, B., and Gosselin, C. M., 1996, “Singularity Analysis and Representation of Spatial Six-Degree of Freedom Parallel Manipulator,” Advances in Robot Kinematics (ARK), J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publisher, pp. 389–398.
11.
Sefrioui
, J.
, and Gosselin
, C. M.
, 1995
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), pp. 533
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.12.
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.13.
Feng-Cheng
, Y.
, and Haug
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, 1994
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, 116
, pp. 111
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.14.
Funabashi, H., and Takeda, Y., 1995, “Determination of Singular Points and Their Vicinity in Parallel Manipulators Based on the Transmission Index,” Ninth World Congress on the Theory of Machines and Mechanisms, pp. 1977–1981.
15.
Karger, A., and Husty, M., 1996, “On Self-Motion of a Class of Parallel Manipulators,” Advances in Robot Kinematics, J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publisher, pp. 339–348.
16.
Karger, A., 1998, “Architecture Singular Parallel Manipulators,” Advanced in Robot Kinematics: Analysis and Control, J. Lenarcic and M. L. Husty, eds., Kluwer Academic Publisher, pp. 445–454.
17.
Merlet, J. P., 1989, “Parallel Manipulators Part 2: Theory, Singular Configurations and Grassmann Geometry,” Rapport de Recherche INRIA No 791, F’evrier.
18.
Merlet, J. P., 1992, “On the Infinitesimal Motion of a Parallel Manipulator in Singular Configurations,” IEEE Int. Conf. on Robotics and Automation, pp. 320–325, Nice, France.
19.
Fichter
, E. F.
, 1986
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,” Int. J. Robot. Res.
, 5
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), pp. 155
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Collins
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, and Long
, G. L.
, 1995
, “The Singularity Analysis of an In-Parallel Hand Controller for Force-Reflected Teleoperation
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.22.
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23.
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, M.
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26.
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29.
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30.
Tsai
, L.-W.
, and Joshi
, S.
, 2000
, “Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator
,” ASME J. Mech. Des.
, 122
(4
), pp. 439
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.31.
Tsai, L.-W., 1996, “Kinematics of a Three-DOF Platform With Three Extensible Limbs,” Advances in Robot Kinematics (ARK), J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publisher, pp. 401–410.
32.
Di Gregorio
, R.
, and Parenti-Castelli
, V.
, 2002
, “Mobility Analysis of the 3-UPU Parallel Mechanism Assembled in a Pure Translational Motion
,” ASME J. Mech. Des.
, 124
, pp. 259
–264
.33.
Tsai, L.-W., 1998, “The Jacobian Analysis of a Parallel Manipulator Using Reciprocal Screws,” Advances in Robot Kinematics (ARK): Analysis and Control, Lenarcic, J., and Husty, M. L., eds., Kluwer Academic Publishers, pp. 327–336.
34.
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, V.
, Di Gregorio
, R.
, and Bubani
, F.
, 2000
, “Workspace and Optimal Design of a Pure Translation Parallel Manipulator
,” Meccanica
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36.
Bonev, I., and Zlatanov, D., 2001, “The Mystery of the Singular SNU Translational Parallel Robot,” http://www.parallemic.org/Reviews/Review004.html.
37.
Zlatanov, D., Bonev, I., and Gosselin, C., 2001, “Constraint Singularities as Configuration Space Singularities,” http://www.parallemic.org/Reviews/Review008.html.
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