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Structural synthesis of maximally regular T3R2-type parallel robots via theory of linear transformations and evolutionary morphology

Published online by Cambridge University Press:  01 January 2009

G. Gogu
G. Gogu*
Affiliation:
Mechanical Engineering Research Group, French Institute of Advanced Mechanics and University Blaise Pascal Campus de Clermont-Ferrand-/-les Cezeaux, BP 265, 63175 Aubière, France E-mail: Grigore.Gogu@ifma.fr
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Summary

The paper presents structural synthesis of maximally regular T3R2-type parallel robotic manipulators (PMs) with five degrees of freedom. The moving platform has three independent translations (T3) and two rotations (R2). A method is proposed for structural synthesis of maximally regular T3R2-type PMs based on the theory of linear transformations and evolutionary morphology. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of maximally regular T3R2-type PMs presented in this paper is the 5×5 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. Kinematic analysis of maximally regular parallel robots is trivial and no computation is required for real-time control. This paper presents in a unified approach the structural synthesis of PMs with five degrees of freedom with decoupled and uncoupled motions, along with the maximally regular solutions.

Keywords

Parallel robotsFive-degree-of-freedomMaximally regularDecoupledUncoupledLinear transformationsEvolutionary morphology
Type
Article
Information
Robotica , Volume 27 , Issue 1 , January 2009 , pp. 79 - 101
Copyright
Copyright © Cambridge University Press 2008

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References

1.Merlet, J. P., Parallel Robots (2nd ed., Springer, Dordrecht, 2006).Google Scholar
2.Salisbury, J. K. and Craig, J. J., “Articulated hands: Force and kinematic issues,” Int. J. Robot. Res. 1, 1–17 (1982).CrossRefGoogle Scholar
3.Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms (Springer, New York, 1997).CrossRefGoogle Scholar
4.Fattah, A. and Ghasemi, A. M. Hasan, “Isotropic design of spatial parallel manipulators,” Int. J. Robot. Res. 21, 811–824 (2002).CrossRefGoogle Scholar
5.Hay, A. M. and Snyman, J. A., “Design of Parallel Manipulators for Optimal Conditioning throughout a Prescribed Workspace,” Proceedings of the Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Quebec, Canada (2002) pp. 267–271.Google Scholar
6.Tsai, K. Y. and Huang, K. D., “The design of isotropic 6-DOF parallel manipulators using isotropy generators,” Mech. Mach. Theory 38, 1199–1214 (2003).CrossRefGoogle Scholar
7.Hay, A. M. and Snyman, J. A., “Methodologies for the optimal design of parallel manipulators,” Int. J. Numer. Methods Eng. 59, 131–152 (2003).CrossRefGoogle Scholar
8.Tsai, K. Y. and Zhou, S. R., “The optimum design of 6-DOF isotropic parallel manipulators,” J. Robot. Systems 22, 333–340 (2005).CrossRefGoogle Scholar
9.Fassi, I., Legnani, G. and Tosi, D., “Geometrical conditions for the design of partial or full isotropic hexapods,” J. Robot. Syst. 22, 507–518 (2005).CrossRefGoogle Scholar
10.Gogu, G., “Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations,” Eur. J. Mech.– A/Solids 23, 1021–1039 (2004).CrossRefGoogle Scholar
11.Zamanov, V. B. and Sotirov, Z. M., “Parallel Manipulators in Robotics,” Proceedings of IMACS/SICE International Symposium on Robotics, Mechatronics and Manufacturing Systems, Kobe, Japan (1992) pp. 409–418.Google Scholar
12.Fang, Y. and Tsai, L.-W., “Structural synthesis of a class of 4-dof and 5-dof parallel manipulators with identical limb structures,” Int. J. Robot. Res. 21, 799–810 (2002).CrossRefGoogle Scholar
13.Gao, F., Li, W., Zhao, X., Jin, Z. and Zhao, H., “New kinematic structures for 2-, 3-, 4-, and 5-DOF parallel manipulator designs,” Mech. Mach. Theory 37, 1395–1411 (2002).CrossRefGoogle Scholar
14.Huang, Z. and Li, Q. C., “General methodology for type synthesis of symmetrical lower-mobility parallel manipulators and several novel manipulators,” Int. J. Robot. Res. 21, 131–145 (2002).CrossRefGoogle Scholar
15.Huang, Z. and Li, Q. C., “Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method,” Int. J. Robot. Res. 22, 59–79 (2003).Google Scholar
16.Gao, F., Peng, B., Li, W. and Zhao, H., “Design of a novel 5-DOF parallel kinematic machine tool based on workspace,” Robotica 23, 35–43 (2005).CrossRefGoogle Scholar
17.Gogu, G., “Fully-Isotropic Redundantly-Actuated Parallel Manipulators with Five Degrees of Freedom,” Proceedings of EuCoMeS, the first European Conference on Mechanism Science, Obergurgl, Austria (2006).Google Scholar
18.Gogu, G., “Fully-Isotropic Parallel Manipulators with Five Degrees of Freedom,” Proceedings of 2006 IEEE International Conference on Robotics and Automation, Orlando, USA (2006) pp. 1141–1146.Google Scholar
19.Gogu, G., “Fully-Isotropic T3R2-Type Parallel Manipulators,” Proceedings of IEEE 2006 International Conference on Robotics, Automation and Mecatronics, Bangkok, Thailand (2006) pp. 248–256.Google Scholar
20.Gogu, G., “Fully-Isotropic T3R1-Type Parallel Manipulators,” In: On Advances in Robot Kinematics (Lenarčič, J. and Galletti, C., Eds.) (Kluwer Academic Publishers, Dordrecht, The Netherlands, 2004) pp. 265–274.CrossRefGoogle Scholar
21.Gogu, G., “Fully-Isotropic Over-Constrained Planar Parallel Manipulators,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan (2004) pp. 3519–3520.Google Scholar
22.Gogu, G., “Fully-Isotropic Over-Constrained Parallel Wrists with Two Degrees of Freedom,” Proceedings of IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 4025–4030.Google Scholar
23.Gogu, G., “Mobility Criterion and Overconstraints of Parallel Manipulators,” Proceedings of International Workshop on Computational Kinematics, Cassino, Italy (2005), Paper 22-CK2005.Google Scholar
24.Gogu, G., “Singularity-Free Fully-Isotropic Parallel Manipulators with Schönflies Motions,” Proceedings of 12th International Conference on Advanced Robotics, Seattle, USA (2005) pp. 194–201.Google Scholar
25.Caricato, M., “Fully-isotropic four degrees-of-freedom parallel mechanisms for Schoenflies motion,” Int. J. Robot. Res. 24, 397–414 (2005).CrossRefGoogle Scholar
26.Gogu, G., “Fully-Isotropic Parallel Robots with Four Degrees of Freedom T2R2-Type,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Edmonton, Canada (2005) pp. 1190–1195.Google Scholar
27.Gogu, G., “Fully-Isotropic T1R2-Type Parallel Manipulators with Three Degrees of Freedom,” Proceedings of International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Long Beach, USA (2005), Paper DETC2005-84313.CrossRefGoogle Scholar
28.Liu, X.-J. and Wang, J., “Some new parallel mechanisms containing the planar four-bar parallelogram,” Int. J. Robot. Res. 22, 717–732 (2003).CrossRefGoogle Scholar
29.Hervé, J. M., “New Translational Parallel Manipulators with Extensible Parallelogram,” Proceedings of the 11th World Congress in Mechanism and Machine Science, vol. 4, China Machine Press, Tianjin, China (2004) pp. 1599–1603.Google Scholar
30.Angeles, J., “The qualitative synthesis of parallel manipulators,” J. Mech. Des. 126, 617–624 (2004).CrossRefGoogle Scholar
31.Hervé, J. M. and Sparacino, F., “Structural Synthesis of Parallel Robots Generating Spatial Translation,” Proceeding 5th IEEE International Conference on Advanced Robotics, Pise, Italy (1991) pp. 808–813.Google Scholar
32.Hervé, J. M., “Design of Parallel Manipulators via the Displacement Group,” Proceedings of the 9th World Congress on the Theory of Machines and Mechanisms, Milan, Italy (1995) pp. 2079–2082.Google Scholar
33.Li, Q., Huang, Z. and Hervé, J. M., “Type synthesis of 3R2T 5-DOF parallel mechanisms using the Lie group of displacements,” IEEE Trans. Robot. Autom. 20, 173–180 (2004).CrossRefGoogle Scholar
34.Frisoli, A., Checcacci, D., Salsedo, F. and Bergamasco, M., “Synthesis by Screw Algebra of Translating In-Parallel Actuated Mechanisms,” In: Advances in Robot Kinematics (Lenarčič, J. and Stanišić, C. M., Eds.) (Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000) pp. 433–440.CrossRefGoogle Scholar
35.Kong, X. and Gosselin, C. M., “Generation of Parallel Manipulators with Three Translational Degrees of Freedom Based on Screw Theory,” Proceedings of CCToMM Symposium on Mechanisms, Machines and Mechatronics, Saint-Hubert, Canada (2001).Google Scholar
36.Kong, X. and Gosselin, C. M., “Type Synthesis of Analytic Translational Parallel Manipulators,” Proceeding 11th World Congress in Mechanism and Machine Science vol. 4, China Machine Press, Tianjin, China (2004) pp. 1642–1646.Google Scholar
37.Kong, X. and Gosselin, C. M., “Type synthesis of 3-dof translational parallel manipulators based on screw theory,” J. Mech. Des. 126, 83–92 (2004).CrossRefGoogle Scholar
38.Kong, X. and Gosselin, C. M., “Type synthesis of 3T1R parallel manipulators based on screw theory,” IEEE Trans. Robot. Autom. 20, 181–190 (2004).CrossRefGoogle Scholar
39.Gogu, G., “Mobility and spatiality of parallel robots revisited via theory of linear transformations,” Eur. J. Mech. / A –Solids 24, 690–711 (2005).CrossRefGoogle Scholar
40.Gogu, G., “Chebychev-Grubler-Kutzbach's criterion for mobility calculation of multi-loop mechanisms revisited via theory of linear transformations,” Eur. J. Mech. / A –Solids 24, 427–441 (2005).CrossRefGoogle Scholar
41.Gogu, G., “Evolutionary Morphology: A Structured Approach to Inventive Engineering Design,” In: Advances in Integrated Design and Manufacturing in Mechanical Engineering (Bramley, A., Brissaud, D., Coutellier, D. and McMahon, C., Eds.) (Springer, Dordrecht, The Netherlands, 2005) pp. 389–402.Google Scholar
42.Zwicky, F., Discovery, -Invention, -Research (Macmillan, New York, 1969).Google Scholar
43.Bäck, T., Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms (Oxford University Press, New York, 1996).CrossRefGoogle Scholar
44.Gogu, G., Coiffet, P. and Barraco, A., Mathématiques pour la robotique: Représentation des déplacements des robots (HERMES, Paris, 1997).Google Scholar
45.Chablat, D. and Wenger, P., “Architecture optimization of a 3-DOF translational parallel mechanism for machining applications, the Orthoglide,” IEEE Trans. Robot. Autom. 19, 403–410 (2003).CrossRefGoogle Scholar
46.Greenberg, M. D., Advanced Engineering Mathematics (Prentice Hall, Englewood Cliffs, NJ, 1998).Google Scholar