This paper presents a classification of 3T1R parallel manipulators (PMs) based on the wrench graph. By using the theory of reciprocal screws, the properties of the three-dimensional projective space, the wrench graph, and the superbracket decomposition of Grassmann–Cayley algebra, six typical wrench graphs for 3T1R parallel manipulators are obtained along with their singularity conditions. Furthermore, this paper shows a way in which each of the obtained typical wrench graphs can be used in order to synthesize new 3T1R parallel manipulator architectures with known singularity conditions and with an understanding of their geometrical properties and assembly conditions.
Issue Section:
Research Papers
References
1.
Angeles
, J.
, Caro
, S.
, Khan
, W.
, and Morozov
, A.
, 2006
, “The Kinetostatic Design of an Innovative Schoenflies Motion Generator
,” Proc. Inst. Mech. Eng., Part C
, 220
(7
), pp. 935
–944
.2.
Pierrot
, F.
, Nabat
, V.
, Company
, O.
, and Poignet
, S. K. P.
, 2009
, “Optimal Design of a 4-DOF Parallel Manipulator: From Academia to Industry
,” IEEE Trans. Rob.
, 25
(2
), pp. 213
–224
.3.
Rat
, N.
, Neagoe
, M.
, and Gogu
, G.
, 2009
, “Theoretical and Experimental Research on the Dynamics of a 4 DOF Isoglide 4-T3R1 Parallel Robot
,” 10th IFToM International Symposium on Science of Mechanisms and Machines
, Brasov, Romania, Oct. 12–15, pp. 387
–396
.4.
Gogu
, G.
, 2010
, Structural Synthesis of Parallel Robots, Part 3: Topologies With Planar Motion of the Moving Platform
, Springer, Dordrecht
, The Netherlands
.5.
Kong
, X.
, and Gosselin
, C.
, 2010
, “Forward Displacement Analysis of a Quadratic 4-DOF 3T1R Parallel Manipulator
,” Meccanica
, 46
(1
), pp. 147
–154
.6.
Pierrot
, F.
, and Company
, O.
, 1999
, “H4: A New Family of 4-DOF Parallel Robots
,” IEEE/ASME
International Conference on Advanced Intelligent Mechatronics
, Atlanta, GA, Sept. 19–23, pp. 508
–513
.7.
Pierrot
, F.
, Marquet
, F.
, Company
, O.
, and Gil
, T.
, 2001
, “H4 Parallel Robot: Modeling, Design and Preliminary Experiments
,” IEEE
International Conference on Robotics and Automation
, Seoul, Korea, May 21–26, pp. 3256
–3261
.8.
Wu
, J.
, and Yin
, Z
, 2008
, “A Novel 4-DOF Parallel Manipulator H4
,” Parallel Manipulators, Towards New Applications
, H.
Wu
, ed., I-Tech Education and Publishing
, Vienna, Austria
, pp. 405
–448
.9.
Briot
, S.
, and Bonev
, I.
, 2009
, “Pantopteron: A New Fully Decoupled 3DOF Translational Parallel Robot for Pick-and-Place Applications
,” ASME J. Mech. Rob.
, 1
(2
), pp. 1
–9
.10.
Briot
, S.
, and Bonev
, I.
, 2010
, “Pantopteron-4: A New 3T1R Decoupled Parallel Manipulator for Pick-and-Place Applications
,” Mech. Mach. Theory
, 45
(5
), pp. 707
–721
.11.
Xie
, F.
, and Liu
, X.-J.
, 2015
, “Design and Development of a High-Speed and High-Rotation Robot With Four Identical Arms and a Single Platform
,” ASME J. Mech. Rob.
, 7
(4
), p. 041015
.12.
Wu
, G.
, Bai
, S.
, and Hjornet
, P.
, 2015
, “Multi-Objective Design Optimization of a Parallel Schönflies-Motion Robot
,” Advances in Reconfigurable Mechanisms and Robots II
(Mechanisms and Machine Science), Vol. 36
, Springer
, Cham, Switzerland
, pp. 657
–667
.13.
Carricato
, M.
, 2005
, “Fully Isotropic Four-Degrees-of-Freedom Parallel Mechanisms for Schoenflies Motion
,” Int. J. Rob. Res.
, 24
(5
), pp. 397
–414
.14.
Merlet
, J.-P.
, 1996
, “Redundant Parallel Manipulators
,” Lab. Rob. Autom.
, 8
(1
), pp. 17
–24
.15.
Wu
, J.
, Chen
, X.
, Wang
, L.
, and Liu
, X.
, 2014
, “Dynamic Load-Carrying Capacity of a Novel Redundantly Actuated Parallel Conveyor
,” Nonlinear Dyn.
, 78
(1
), pp. 241
–250
.16.
Wu
, J.
, Chen
, X.
, and Wang
, L.
, 2016
, “Design and Dynamics of a Novel Solar Tracker With Parallel Mechanism
,” IEEE/ASME Trans. Mechatronics
, 21
(1
), pp. 88
–97
.17.
Huang
, Z.
, and Li
, Q.
, 2002
, “General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators
,” Int. J. Rob. Res.
, 21
(2
), pp. 131
–145
.18.
Huang
, Z.
, and Li
, Q.
, 2003
, “Type Synthesis of Symmetrical Lower-Mobility Parallel Mechanisms Using the Constraint–Synthesis Method
,” Int. J. Rob. Res.
, 22
(1
), pp. 59
–79
.19.
Kong
, X.
, and Gosselin
, C.
, 2007
, Type Synthesis of Parallel Mechanism
, Springer
, Heidelberg, Germany
.20.
Ling
, S.
, and Huang
, M. Z.
, 1995
, “Kinestatic Analysis of General Parallel Manipulators
,” ASME J. Mech. Des.
, 117
(4
), pp. 601
–606
.21.
Joshi
, S.
, and Tsai
, L.-W.
, 2002
, “Jacobian Analysis of Limited-DOF Parallel Manipulators
,” ASME J. Mech. Des.
, 124
(2
), pp. 254
–258
.22.
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.
, 22
(4
), pp. 577
–590
.23.
Ben-Horin
, P.
, and Shoham
, M.
, 2007
, “Singularity of Gough–Stewart Platforms With Collinear Joints
,” 12th IFToMM World Congress
, Besançon, France, June 17–20.24.
Kanaan
, D.
, Wenger
, P.
, Caro
, S.
, and Chablat
, D.
, 2009
, “Singularity Analysis of Lower-Mobility Parallel Manipulators Using Grassmann Cayley Algebra
,” IEEE Trans. Rob.
, 25
(5
), pp. 995
–1004
.25.
Amine
, S.
, Caro
, S.
, Wenger
, P.
, and Kanaan
, D.
, 2012
, “Singularity Analysis of the H4 Robot Using Grassmann–Cayley Algebra
,” Robotica
, 30
(7
), pp. 1109
–1118
.26.
Amine
, S.
, Tale Masouleh
, M.
, Caro
, S.
, Wenger
, P.
, and Gosselin
, C.
, 2012
, “Singularity Analysis of 3T2R Parallel Mechanisms Using Grassmann–Cayley Algebra and Grassmann Geometry
,” Mech. Mach. Theory
, 52
, pp. 326
–340
.27.
Amine
, S.
, Masouleh
, M. T.
, Caro
, S.
, Wenger
, P.
, and Gosselin
, C.
, 2012
, “Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures
,” ASME J. Mech. Rob.
, 4
(1
), pp. 1
–11
.28.
Amine
, S.
, 2011
, “Lower-Mobility Parallel Manipulators: Geometrical Analysis, Singularities and Conceptual Design
,” Ph.D. thesis, Ecole Centrale de Nantes, Nantes, France.29.
Kong
, X.
, Gosselin
, C.
, and Richard
, P.-L.
, 2007
, “Type Synthesis of Parallel Mechanisms With Multiple Operation Modes
,” ASME J. Mech. Des.
, 129
(6
), pp. 595
–601
.30.
Gan
, D.
, Dai
, J.
, and Liao
, Q.
, 2007
, “Mobility Change in Two Types of Metamorphic Parallel Mechanisms
,” ASME J. Mech. Rob.
, 1
(4
), p. 041007
.31.
Gan
, D.
, Dai
, J.
, Dias
, J.
, and Seneviratne
, L.
, 2013
, “Unified Kinematics and Singularity Analysis of a Metamorphic Parallel Mechanism With Bifurcated Motion
,” ASME J. Mech. Rob.
, 5
(3
), p. 031004
.32.
Zhao
, T. S.
, Dai
, J. S.
, and Huang
, Z.
, 2002
, “Geometric Analysis of Overconstrained Parallel Manipulators With Three and Four Degrees of Freedom
,” JSME Int. J. Ser. C
, 45
(3
), pp. 730
–740
.Copyright © 2017 by ASME
You do not currently have access to this content.
