A parallelogram-based 4 degrees-of-freedom parallel manipulator is presented in this paper. The manipulator can generate the so-called Schönflies motion that allows the end effector to translate in all directions and rotate around an axis parallel to a fixed direction. The theory of group of displacements is applied in the synthesis of this manipulator, which employs parallelograms in every limb. The planar parallelogram kinematic chain provides a high rotational capability and an improved stiffness to the manipulator. This paper shows the kinematic analysis of the manipulator, including the closed-form resolution of the forward and inverse position problems, the velocity, and the singularity analysis. Finally, a prototype of the manipulator, adding some considerations about its singularity-free design, and some technical applications in which the manipulator can be used are presented.
Issue Section:
Research Papers
Keywords:
manipulator kinematics
1.
Huang
, Z.
, and Li
, Q.
, 2002, “General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators
,” Int. J. Robot. Res.
0278-3649, 21
(2
), pp. 131
–145
.2.
Joshi
, S. A.
, and Tsai
, L. W.
, 2002, “Jacobian Analysis of Limited-dof Parallel Manipulators
,” ASME J. Mech. Des.
1050-0472, 124
, pp. 254
–258
.3.
Ball
, R. S.
, 1900, A Treatise on the Theory of Screws
, Cambridge University Press
, Cambridge
.4.
Kong
, X.
, and Gosselin
, C.
, 2004, “Type Synthesis of Three-Degree-of-Freedom Spherical Parallel Manipulators
,” Int. J. Robot. Res.
0278-3649, 23
(3
), pp. 237
–245
.5.
Kong
, X.
, and Gosselin
, C.
, 2004, “Type Synthesis of 3-dof Spherical Parallel Manipulators Based on Screw Theory
,” ASME J. Mech. Des.
1050-0472, 126
, pp. 101
–108
.6.
Fang
, Y.
, and Tsai
, L.-W.
, 2004, “Structure Synthesis of a Class of 3-dof Rotational Parallel Manipulators
,” IEEE Trans. Rob. Autom.
1042-296X, 20
(1
), pp. 117
–121
.7.
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
, C. M.
Gosselin
and I.
Ebert-Uphoff
, eds., pp. 25
–32
.8.
Carricato
, M.
, and Parenti-Castelli
, V.
, 2003, “Position Analysis of a New Family of 3-dof Translational Parallel Manipulators
,” ASME J. Mech. Des.
1050-0472, 125
, pp. 316
–322
.9.
Callegari
, M.
, and Tarantini
, M.
, 2003, “Kinematic Analysis of a Novel Translational Platform
,” ASME J. Mech. Des.
1050-0472, 125
, pp. 308
–315
.10.
Kong
, X.
, and Gosselin
, C.
, 2004, “Type Synthesis of 3-dof Translational Parallel Manipulators Based on Screw Theory
,” ASME J. Mech. Des.
1050-0472, 126
, pp. 83
–92
.11.
Kong
, X.
, and Gosselin
, C.
, 2005, “Type Synthesis of 4-dof sp-Equivalent Parallel Manipulators: A Virtual-Chain Approach
,” Proceedings of CK2005, International Workshop on Computational Kinematics
.12.
Kong
, X.
, and Gosselin
, C.
, 2004, “Type Synthesis of 3t1r 4-dof Parallel Manipulators Based on Screw Theory
,” IEEE Trans. Rob. Autom.
1042-296X, 20
(2
), pp. 181
–190
.13.
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
.14.
Hervé
, J. M.
, 1978, “Analyse Structurelle des Mécanismes par Groupe des Déplacements
,” Mech. Mach. Theory
0094-114X, 13
, pp. 437
–450
.15.
Hervé
, J. M.
, 1994, “The Mathematical Group Structure of the Set of Displacements
,” Mech. Mach. Theory
0094-114X, 29
(1
), pp. 73
–81
.16.
Hervé
, J. M.
, 1999, “The Lie Group of Rigid Body Displacements: A Fundamental Tool for Mechanism Design
,” Mech. Mach. Theory
0094-114X, 34
, pp. 719
–730
.17.
Angeles
, J.
, 2004, “The Qualitative Synthesis of Parallel Manipulators
,” ASME J. Mech. Des.
1050-0472, 126
, pp. 617
–624
.18.
Angeles
, J.
, 2005, “The Degree of Freedom of Parallel Robots: A Group-Theoretic Approach
,” Proceedings of the 2005 IEEE International Conference on Robotics and Automation
, pp. 1017
–1024
.19.
Gogu
, G.
, 2004, On Advances in Robot Kinematics
, Kluwer Academic
, Dordrecht
, pp. 265
–574
.20.
Liu
, X.-J.
, and Wang
, J.
, 2003, “Some New Parallel Mechanisms Containing the Planar Four-Bar Parallelogram
,” Int. J. Robot. Res.
0278-3649, 22
(9
), pp. 717
–732
.21.
Gao
, F.
, Li
, W.
, Zhao
, X.
, Jin
, Z.
, and Zhao
, H.
, 2002, “New Kinematic Structures for 2-, 3-, 4,- and 5-dof Parallel Manipulator Designs
,” Mech. Mach. Theory
0094-114X, 37
(11
), pp. 1395
–1411
.22.
Pierrot
, F.
, and Company
, O.
, 1999, “H4: A New Family of 4-dof Parallel Robots
,” Proceedings of the 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics
.23.
Company
, O.
, and Pierrot
, F.
, 1999, “A New 3t-1r Parallel Robot
,” Proceedings of the IEEE International Conference on Robotics and Automation
, pp. 557
–562
.24.
Rolland
, L. H.
, 1999, “The Manta and the Kanuk: Novel 4-dof Parallel Mechanisms for Industrial Handling
,” Proceedings of the ASME Dynamics, Systems and Control Division IMECE’99
.25.
Company
, O.
, Marquet
, F.
, and Pierrot
, F.
, 2003, “A New High-Speed 4-dof Parallel Robot Synthesis and Modelling Issues
,” IEEE Trans. Rob. Autom.
1042-296X, 19
(3
), pp. 411
–420
.26.
Barbeau
, E. J.
, 1989, Polynomials
, Springer-Verlag
, New York
.27.
Altuzarra
, O.
, Pinto
, C.
, Avilés
, R.
, and Hernández
, A.
, 2004, “A Practical Procedure to Analyse Singular Configurations in Closed Kinematic Chains
,” IEEE Trans. Rob. Autom.
1042-296X, 20
(6
), pp. 929
–940
.28.
Golub
, G. H.
, and Van Loan
, C. F.
, 1996, Matrix Computations
, 3rd ed., The Johns Hopkins University Press
, Baltimore
.29.
Gosselin
, C.
, and Angeles
, J.
, 1990, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Trans. Rob. Autom.
1042-296X, 6
(3
), pp. 281
–290
.30.
Zlatanov
, D.
, Fenton
, R. G.
, and Benhabib
, B.
, 1998, “Identification and Classification of the Singular Configurations of Mechanisms
,” Mech. Mach. Theory
0094-114X, 33
(6
), pp. 743
–760
.31.
Zlatanov
, D.
, Bonev
, I. A.
, and Gosselin
, C. M.
, 2002, “Constraint Singularities as c-Space Singularities
,” Eighth International Symposium on Advances in Robot Kinematics ARK 2002
.32.
Altuzarra
, O.
, Salgado
, O.
, Petuya
, V.
, and Hernández
, A.
, 2006, “Point-Based Jacobian Formulation for Computational Kinematics of Manipulators
,” Mech. Mach. Theory
0094-114X, 41
(12
), pp. 1407
–1423
.33.
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