This paper presents a class of 6-DOF three-legged parallel robots that are practically free of parallel singularities. The robots of this class have legs with a characteristic passive pair of prismatic and spherical joints, the first being directly attached to the platform. First, the direct kinematics of this class is solved, showing that for a certain arrangement there exists only one assembly mode. Then, the robot singularities are derived, showing that they practically do not exist in this structure. The advantages of this class of robots are hence simple direct kinematics and no need of singularity calculations.
Issue Section:
Mechanisms and Robotics
1.
Chablat
, D.
, and Wenger
, P.
, 1998, “Working Modes and Aspects in Fully Parallel Manipulators
,” IEEE International Conference on Robotics and Automation
, pp. 1964
–1969
.2.
Gosselin
, C.
, and Angeles
, J.
, 1990, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Trans. Rob. Autom.
1042-296X, 6
(3
), pp. 281
–290
.3.
St-Onge
, B. M.
, and Gosselin
, C.
, 2000, “Singularity Analysis and Representation of the General Gough-Stewart Platform
,” Int. J. Robot. Res.
0278-3649, 19
(3
), pp. 271
–288
.4.
Hunt
, K. H.
, 1978, Kinematic Geometry of Mechanisms
, Oxford University Press
, New York
.5.
Kumar
, V.
, 1992, “Instantaneous Kinematics of Parallel-Chain Robotic Mechanisms
,” ASME J. Mech. Des.
1050-0472, 114
, pp. 349
–358
.6.
Merlet
, J. P.
, 1989, “Singular Configurations of Parallel Manipulators and Grassmann Geometry
,” Int. J. Robot. Res.
0278-3649, 8
(5
), pp. 45
–56
.7.
Notash
, L.
, 1998, “Uncertainty Configurations of Parallel Manipulators
,” Mech. Mach. Theory
0094-114X 33
(1∕2
), pp. 123
–138
.8.
Ebert-Uphoff
, I.
, Lee
, J.
, and Lipkin
, H.
, 2000, “Characteristic Tetrahedron on Wrench Singularities for Parallel Manipulators With Three Legs
,” Proceedings of a Symposium Commemorating the Legacy, Works and Life of Sir Robert Stawell Ball Upon the 100th Anniversary of a Treatise on the Theory of Screws
.9.
Kong
, X.
, and Gosselin
, C.
, 2001, “Uncertainty Singularity Analysis of Parallel Manipulators Based on the Instability Analysis of Structures
,” Int. J. Robot. Res.
0278-3649, 20
(11
), pp. 847
–856
.10.
Hunt
, K. H.
, Samuel
, A. E.
, and McAree
, P. R.
, 1991, “Special Configurations of Multi-Finger Multi-Freedom Grippers: A Kinematic Study
,” Int. J. Robot. Res.
0278-3649, 10
(2
), pp. 123
–134
.11.
Merlet
, J. P.
, 1998, “Determination of the Presence of Singularities in 6D Workspace of a Gough Parallel Manipulator
,” Advances in Robot Kinematics
, Springer
, New York
, pp. 39
–48
.12.
Hesselbach
, J.
, Bier
, C.
, Campos
, A.
, and Lowe
, H.
, 2005, “Direct Kinematic Singularity Detection of a Hexa Parallel Robot
,” Proceedings of the IEEE International Conference on Robotics and Automation
, Barcelona
, Spain
, pp. 3238
–3243
.13.
Bhattacharya
, S.
, Hatwal
, H.
, and Ghosh
, A.
, 1998, “Comparison of an Exact and an Approximate Method of Singularity Avoidance in Platform Type Parallel Manipulators
,” Mech. Mach. Theory
0094-114X, 33
(7
), pp. 965
–974
.14.
Dash
, A. K.
, Chen
, I.-M.
, Yeo
, S. H.
, and Yang
, G.
, 2003, “Singularity-Free Path Planning of Parallel Manipulators Using Clustering Algorithm and Line Geometry
,” IEEE International Conference on Robotics and Automation
, pp. 761
–766
.15.
Dasgupta
, B.
, and Mruthyunjaya
, T. S.
, 1998, “Singularity-Free Path Planning for the Stewart Platform Manipulator
,” Mech. Mach. Theory
0094-114X, 33
(6
), pp. 711
–725
.16.
Sen
, S.
, Dasgupta
, B.
, and Mallik
, A. K.
, 2003, “Variational Approach for Singularity-Free Path-Planning of Parallel Manipulators
,” Mech. Mach. Theory
0094-114X, 38
, pp. 1165
–1183
.17.
Kim
, W. K.
, Lee
, J. H.
, Suh
, I. H.
, and Yi
, B. J.
, 2005, “Comparative Study and Experimental Verification of Singular-Free Algorithms for a 6 DOF Parallel Haptic Device
,” Mechatronics
0957-4158, 15
, pp. 403
–422
.18.
Ben-Horin
, R.
, 1997, “Criteria for Analysis of Parallel Robots
,” Ph.D. thesis, Technion-Israel Institute of Technology.19.
Kim
, J.
, Park
, F. C.
, Ryu
, S. J.
, Kim
, J.
, Hwang
, J. C.
, Park
, C.
, and Iurascu
, C. C.
, 2001, “Design and Analysis of a Redundantly Actuated Parallel Mechanism for Rapid Machining
,” IEEE Trans. Rob. Autom.
1042-296X, 17
(4
), pp. 423
–434
.20.
Notash
, L.
, and Podhorodeski
, R. P.
, 1994, “Uncertainty Configurations of Three-Branch Parallel Manipulators: Identification and Elimination
,” Robotics: Kinematics, Dynamics and Control
, 72
, pp. 459
–466
.21.
Chablat
, D.
, and Wenger
, P.
, 2003, “Architecture Optimization of a 3-DOF Translational Parallel Mechanism for Machining Applications: The Orthoglide
,” IEEE Trans. Rob. Autom.
1042-296X, 19
(3
), pp. 403
–410
.22.
Callegari
, M.
, and Tarantini
, M.
, 2003, “Kinematic Analysis of a Novel Translational Platform
,” ASME J. Mech. Des.
1050-0472, 125
, pp. 308
–315
.23.
Ottaviano
, E.
, and Ceccarelli
, M.
, 2002, “Optimum Design of Parallel Manipulators for Workspace and Singularity Performances
,” Proceedings of the Workshop on Fundamental Issues and future research directions for Parallel Mechanisms and Manipulators
, Quebec
, Canada
, pp. 98
–105
.24.
Gallant
, M.
, and Boudreau
, R.
, 2002, “The Synthesis of Planar Parallel Manipulators With Prismatic Joints for an Optimal, Singularity-Free Workspace
,” J. Rob. Syst.
0741-2223, 19
(1
), pp. 13
–24
.25.
Richard
, P. L.
, Gosselin
, C.
, and Kong
, X.
, 2007, “Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator
,” ASME J. Mech. Des.
1050-0472, 129
, pp. 611
–616
.26.
Ma
, O.
, and Angeles
, J.
, 1992, “Architecture Singularities of Parallel Manipulators
,” Int. J. Rob. Autom.
0826-8185, 7
(1
), pp. 23
–29
.27.
Kong
, X.
, and Gosselin
, C.
, 2001, “Generation of Architecturally Singular 6-SPS Parallel Manipulators With Linearly Related Planar Platforms
,” Proceedings of the Second Workshop on Computational Kinematics
, Seoul
, South Korea
.28.
Husty
, M.
, and Karger
, A.
, 2000, “Self-Motions of Griffis-Duffy Type Parallel Manipulators
,” IEEE International Conference on Robotics and Automation
, San Francisco, CA
, pp. 7
–12
.29.
Wohlhart
, K.
, 2003, “Mobile 6-SPS Parallel Manipulators
,” J. Rob. Syst.
0741-2223, 20
(8
), pp. 509
–516
.30.
Carricato
, M.
, and Parenti-Castelli
, V.
, 2002, “Singularity-Free Fully-Isotropic Translational Parallel Mechanisms
,” Int. J. Robot. Res.
0278-3649, 21
(2
), pp. 161
–174
.31.
Kong
, X.
, and Gosselin
, C.
, 2002, “Kinematics and Singularity Analysis of a Novel Type of 3-CRR 3-DOF Translational Parallel Manipulator
,” Int. J. Robot. Res.
0278-3649, 21
(9
), pp. 791
–798
.32.
Kong
, X.
, and Gosselin
, C.
, 2002, “A Class of 3-DOF Translational Parallel Manipulators With Linear Input-Output Equations
,” Proceedings of the Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators
, Quebec
, Canada
, pp. 25
–32
.33.
Kim
, H. S.
, and Tsai
, L. W.
, 2002, “Evaluation of a Cartesian Parallel Manipulator
,” Advances in Robot Kinematics
, pp. 21
–28
.34.
Carricato
, M.
, 2005, “Fully Isotropic Four-Degrees-of-Freedom Parallel Mechanisms for Schoenflies Motion
,” Int. J. Robot. Res.
0278-3649, 24
(5
), pp. 397
–414
.35.
Gogu
, G.
, 2005, “Singularity-Free Fully-Isotropic Parallel Manipulators With Schonflies Motions
,” IEEE International Conference on Advanced Robotics
, pp. 194
–201
.36.
Byun
, Y. K.
, and Cho
, H. S.
, 1997, “Analysis of a Novel 6-DOF,3-PPSP Parallel Manipulator
,” Int. J. Robot. Res.
0278-3649, 16
(6
), pp. 859
–872
.37.
Ben-Horin
, P.
, and Shoham
, M.
, 2006, “A Class of 6-DOF Parallel Robots Free of Parallel Singularities
,” Proceedings of the EuCoMes: The First European Conference on Mechanism Science
, Obergurgl
, Austria
, M.
Husty
, and H.-P.
Schrocker
, eds.38.
Ben-Horin
, P.
, and Shoham
, M.
, 2006, “Singularity Condition of Six Degree-of-Freedom Three-Legged Parallel Robots Based on Grassmann-Cayley Algebra
,” IEEE Trans. Rob. Autom.
1042-296X, 22
(4
), pp. 577
–590
.39.
Byun
, Y. K.
, Cho
, H. S.
, Kim
, W. K.
, Baek
, S. E.
, Chang
, H. S.
, and Ro
, K. C.
, 1998, “Kinematic∕Dynamic Analysis of a 6-DOF Parallel Manipulator With 3-PPSP Serial Subchains and Its Implementation
,” IEEE∕RSJ International Workshop on Intelligent Robots and Systems
, pp. 1981
–1986
.40.
Kim
, W. K.
, Byun
, Y. K.
, and Cho
, H. S.
, 2001, “Closed-Form Forward Position Solution for a 6-DOF 3-PPSP Parallel Mechanism and Its Implementation
,” Int. J. Robot. Res.
0278-3649, 20
(1
), pp. 85
–99
.41.
Roth
, B.
, 1993, “Computations in Kinematics
,” Computational Kinematics
, Kluwer Academic
, Dordrecht
, pp. 3
–14
.42.
Simaan
, N.
, and Shoham
, M.
, 2001, “Singularity Analysis of a Class of Composite Serial In-Parallel Robots
,” IEEE Trans. Rob. Autom.
1042-296X, 17
(3
), pp. 301
–311
.43.
Tsai
, L. W.
, 1998, “The Jacobian Analysis of a Parallel Manipulator Using Reciprocal Screws
,” Advances in Robot Kinematics
, pp. 327
–336
.44.
Dandurand
, A.
, 1984, “The Rigidity of Compound Spatial Grids
,” Structural Topology
, 10
, pp. 41
–56
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