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Uncoupled actuation of overconstrained 3T-1R hybrid parallel manipulators

Published online by Cambridge University Press:  01 January 2009

Chung-Ching Lee  and
Jacques M. Hervé
Chung-Ching Lee*
Affiliation:
Department of Tool & Die-Making, National Kaohsiung University of Applied Sciences, 415 Chien Kung Road, Kaohsiung 80782, Taiwan R.O.C.
Jacques M. Hervé
Affiliation:
Ecole Centrale Paris, Grande Voie des Vignes, F-92295 Chatenay-Malabry, France
*
*Corresponding author. E-mail: cclee@cc.kuas.edu.tw
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Summary

Based on the Lie-group-algebraic properties of the displacement set and intrinsic coordinate-free geometry, several novel 4-dof overconstrained hybrid parallel manipulators (HPMs) with uncoupled actuation of three spatial translations and one rotation (3T-1R) are proposed. In these HPMs, three limbs are those of Cartesian translational parallel mechanisms (CTPMs) and the fourth limb includes an Oldham-type constant velocity shaft coupling (CVSC). The Lie subgroup of Schoenflies (X) displacements of the displacement Lie group and its mechanical generators with nine categories of their general architectures are recalled. A comprehensive enumeration of all possible Oldham-type CVSC limbs is derived from X-motion generators. Their constant velocity (CV) transmissions are verified by group-algebraic approach. Then, combining one CTPM and one CVSC, we synthesize a lot of uncoupled 3T-1R overconstrained HPMs, which are classified into nine distinct classes of general architectures. In addition, all possible architectures with at least one hinged parallelogram or with one cylindrical pair are disclosed too. At last, related non-overconstrained HPMs are attained by the addition of one idle pair in each limb of the previous HPMs.

Keywords

Lie groupUncoupled actuationOverconstrainedHybrid manipulatorOldham couplingConstant velocity shaft couplingSchoenflies motionSchönflies
Type
Article
Information
Robotica , Volume 27 , Issue 1 , January 2009 , pp. 103 - 117
Copyright
Copyright © Cambridge University Press 2008

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References

1.Carricato, M. and Parenti-Castelli, V., “Singularity-free fully isotropic translational parallel manipulators,” Int. J. Robot. Res. 21 (2), 161–174 (2002).CrossRefGoogle Scholar
2.Kim, H. S. and Tsaia, L. W., “Evaluation of a Cartesian Manipulator,” In: Advances in Robot Kinematic (Kluwer, Dordrecht, 2002) pp. 21–38.CrossRefGoogle Scholar
3.Kong, X. and Gosselin, C. M., “Type Synthesis of Linear Translational Parallel Manipulators,” In: Advances in Robot Kinematics (Kluwer, Dordrecht, 2002) pp. 453–462.CrossRefGoogle Scholar
4.Hervé, J. M., “Parallel Mechanisms With Pseudo-Planar Motion Generators”, In: Advances in Robot Kinematics (Kluwer, Dordrecht, 2004) pp. 431–440.CrossRefGoogle Scholar
5.Lee, C.-C. and Hervé, J. M., “Pseudo-Planar Motion Generators”, In: Advances in Robot Kinematics Mechanisms and Motion (Springer, Heidelberg, 2006) pp. 435–444.CrossRefGoogle Scholar
6.Lee, C.-C. and Hervé, J. M., “Cartesian parallel manipulators with pseudoplanar limbs,” ASME J. Mech. Design 129, 1256–1264 (2007).CrossRefGoogle Scholar
7.Hervé, J. M., “Analyse Structurelle des Mécanismes par Groupe des Déplacements,” Mech. Mach. Theory 13 (4), 437–450 (1978).CrossRefGoogle Scholar
8.Hervé, J. M., “Intrinsic formulation of problems of geometry and kinematics of mechanisms,” Mech. Mach. Theory 17 (3), 179–184 (1982).CrossRefGoogle Scholar
9.Hervé, J. M. and Sparacino, F., “Structural Synthesis of Parallel Robots Generating Spatial Translation,” Proceedings of 5th IEEE International Conference on Advanced Robotics (1991), Vol. 1, pp. 808–813.Google Scholar
10.Hervé, J. M., “The mathematical group structure of the set of displacements,” Mech. Mach. Theory 29 (1), 73–81 (1994).CrossRefGoogle Scholar
11.Hervé, J. M., “The Lie group of rigid body displacements: A fundamental tool for mechanism design,” Mech. Mach. Theory 34 (5), 719–730 (1999).CrossRefGoogle Scholar
12.Lee, C.-C. and Hervé, J. M., “On the Enumeration of Schoenflies Motion Generators,” Proceedings of the Ninth IFToMM International Symposium on Theory of Machines and Mechanisms (SYROM2005), Bucharest, Romania (Sep. 1–4, 2005) Vol. 3, pp. 673–678.Google Scholar
13.Schoenflies, A., Geometrie der Bewegung in synthetischer (Darstellung, Teubner, Leipzig, 1886).Google Scholar
14.Schoenflies, A., La géométrie du mouvement, Exposé synthétique (Gauthier-Villars, Paris, 1893).Google Scholar
15.Bottema, O. and Roth, B., Theoretical Kinematics (North-Holland, Amsterdam, 1979).Google Scholar
16.Gogu, G., “Structural synthesis of fully-isotropic parallel robots with Schönflies motions via theory of linear transformations and evolutionary morphology,” Eur. J. Mech.—A/Solids, 26 (2), 242–269 (2007).CrossRefGoogle Scholar
17.Kong, X.-W. and Gosselin, C. M., “Type synthesis of 3T1R 4-dof parallel manipulators based on screw theory,” IEEE Trans. Rob. Autom. 20 (2), 181–190 (2004).CrossRefGoogle Scholar
18.Angeles, J., “The qualitative synthesis of parallel manipulators,” ASME J. Mech. Design 126, 617–674 (2004).CrossRefGoogle Scholar
19.Hervé, J. M., “Design of Parallel Manipulators Via the Displacement Group,” Proceedings of the 9th World Congress on Mechanism and Machine Theory (1995) pp. 2079–2082.Google Scholar
20.Rolland, R., “The Manta and the Kanuk: Novel 4-DOF Parallel Mechanisms for Industrial Handling,” Proceedings of the ASME Dynamic Systems and Control Division, IMECE'99 Conference, Nashville, TN (1999) Vol. 67, pp. 831–844.Google Scholar
21.Pierrot, F. and Company, O., “H4: A New Family of 4-dof Parallel Robots,” Proceedings of IEEE/ASME International Conference on Advances Intelligent Mechatronics (1999) pp. 508–513.Google Scholar
22.Company, O. and Pierrot, F., “A New 3T-1R Parallel Robot,” Proceedings of IEEE International Conference on Robotics and Automation (1999) pp. 557–562.Google Scholar
23.Yang, T.-L., Jin, Q., Liu, A.-X., Yao, F. H. and Luo, Y., “Structural Synthesis of 4-DOF (3-Translation and 1-Rotation) Parallel Robot Mechanisms Based on the Units of Single-Open-Chain,” Proceedings of ASME Design Engineering Technical Conference and Computers and Information in Engineering Conference, Pittsburgh, PA (2001), DETC2001/DAC-21152.CrossRefGoogle Scholar
24.Huang, Z. and Li, Q. C., “General methodology for type synthesis of symmetrical lower-mobility parallel manipulators and several novel manipulators,” Int. J. Rob. Res. 21 (2), 131–145 (2002).CrossRefGoogle Scholar
25.Fang, Y. and Tsai, L.-W., “Structural synthesis of a class of 4-dof and 5-dof parallel manipulator with identical limb structures,” Int. J. Rob. Res. 21 (9), 799–810 (2002).CrossRefGoogle Scholar
26.Gao, F., Li, W., Ahao, X., Jin, Z. and Zhao, H., “New kinematic structures for 2-, 3-, 4-, and 5-DOF parallel manipulator designs,” Mech. Mach. Theory 37 (11), 1395–1411 (2002).CrossRefGoogle Scholar
27.Jin, Q. and Yang, T. L., “Structure Synthesis of Parallel Manipulators with Three-Dimensional Translation and One-Dimensional Rotation,” Proceedings of ASME Design Engineering Technical Conference, Montreal, Canada (2002), MECH-34307.Google Scholar
28.Li, Q. C. and Huang, Z., “Type Synthesis of 4-DOF Parallel Manipulators,” Proceedings of the IEEE International Conference on Robotics and Automation, Taipei (2003) pp. 181–190.Google Scholar
29.Liu, X.-J. and Wang, J., “Some new parallel mechanisms containing the planar four-bar parallelogram,” Int. J. Rob. Res. 22 (9), 717–732 (2003).CrossRefGoogle Scholar
30.Gogu, G., “Fully-isotropic T3R1-type Parallel Manipulators”, In: Advances in Robot Kinematics (Kluwer, Dordrecht, 2004) pp. 265–274.CrossRefGoogle Scholar
31.Carricato, M., “Fully isotropic four-degrees-of-freedom parallel mechanisms for Schoenflies motion,” Int. J. Rob. Res. 24 (5), 397–414 (2005).CrossRefGoogle Scholar
32.Company, O., Pierrot, F., Nabat, V. and Rodriguez, M., “Schoenflies Motion Generator: A New Non Redundant Parallel Manipulator with Unlimited Rotation Capability,” Proceedings of IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 3250–3255.Google Scholar
33.Gogu, G., “Singularity-free Fully-isotropic Parallel Manipulators With Schonflies Motions,” Proceedings of 12th International Conference on Advanced Robotics, Seattle, WA (2005) pp. 194–201.Google Scholar
34.Pierre-Luc, R., Gosselin, C. M. and Kong, X., “Kinematic Analysis and Prototyping of a Partially Decoupled 4-dof 3T1R Parallel Manipulator,” Proceedings of ASME IDETC/CIE International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Philadelphia, PA (September 10–13, 2006), DETC2006-99570.Google Scholar
35.Kong, X. and Gosselin, C. M., “Parallel Manipulators With Four Degrees of Freedom,” United States Patent No. 6997669 (2006).Google Scholar
36.Lee, C.-C. and Hervé, J. M., “Translational parallel manipulators with doubly planar limbs,” Mech. Mach. Theory 41 (4), 433–455 (2006).CrossRefGoogle Scholar
37.Selig, J. M., Geometrical Methods in Robotics (Springer-Verlag, New York, 1996).CrossRefGoogle Scholar
38.Selig, J. M., Geometrical Foundations of Robotics (World Scientific, Singapore, 2000).CrossRefGoogle Scholar
39.Lee, C.-C. and Hervé, J. M., “Discontinuously movable seven-link mechanisms via group-algebraic approach,” Proc. IMechE, Vol. 219, Part C, in J. Mech. Eng. Sci., 577–587 (2005).CrossRefGoogle Scholar