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A Novel Approach for Obtaining Assembly Modes of a 3UPS-S Fully Spherical Parallel Manipulator

Published online by Cambridge University Press:  14 April 2016

J. Enferadi
J. Enferadi*
Affiliation:
Department of Mechanical EngineeringMashhad BranchIslamic Azad UniversityMashhad, Iran
*
*Corresponding author (enferadi5637@mshdiau.ac.ir)
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Abstract

The 3(UPS)-S fully spherical parallel manipulator is the most famous fully spherical parallel manipulator (FSPM). In this paper, we propose a novel approach to model the forward displacement analysis of the manipulator to obtain its assembly modes. Rodrigues’ formula is used as a mathematical tool to perform the proposed modeling. Utilizing geometry of the manipulator, two coupled trigonometric equations are obtained. Using Bezout's elimination method, the two coupled equations are transformed to one polynomial of degree eight. Finally, an example is given with eight real solutions. Therefore, the degree of the polynomial is minimal and the introduced modeling method is optimal. This is very important to control modelling and dynamics simulation. Also, the proposed method can be extended to the other FSPMs (e.g., 3(RPSP)-S, 3(RPSP)-S and 3(RSS)-S).

Keywords

Fully spherical parallel manipulator (FSPM)Rodrigues’ FormulaForward displacement problemBezout's elimination method
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 5 , October 2016 , pp. 555 - 563
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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References

1. Merlet, J. P., Parallel Robots, 2nd Edition, Springer, Dordrecht (2006).Google Scholar
2. Dunlop, G. and Jones, T., “Position Analysis of a 3-DOF Parallel Manipulator,” Mechanism and Machine Theory, 32, pp. 903–920 (1997).CrossRefGoogle Scholar
3. Gherman, B., Pisla, D., Vaida, C. and Plitea, N., “Development of Inverse Dynamic Model for a SurGical Hybrid Parallel Robot with Equivalent Lumped Masses,” Robotics and Computer-Integrated Manufacturing, 28, pp. 402–415 (2012).CrossRefGoogle Scholar
4. Aman, M. N. S. B. S. and Basah, S. N. B., “Design and Kinematic Analysis of Parallel Robot for Ankle Rehabilitation,” Applied Mechanics and Materials, 446, pp. 1279–1284 (2014).Google Scholar
5. Fedewa, D., Mehrabi, M. G., Kota, S. and Gopalakrishnan, V., “Parallel Structures and Their Applications in Reconfigurable Machining Systems,” Journal of Manufacturing Science and Engineering, 124, pp. 483–485 (2002).Google Scholar
6. Bai, S., “Optimum Design of Spherical Parallel Manipulators for a Prescribed Workspace,” Mechanism and Machine Theory, 45, pp. 200–211 (2010).CrossRefGoogle Scholar
7. Di Gregorio, R., “A New Family of Spherical Parallel Manipulators,” Robotica, 20, pp. 353–358 (2002).CrossRefGoogle Scholar
8. Alici, G. and Shirinzadeh, B., “Topology Optimisation and Singularity Analysis of a 3-SPS Parallel Manipulator with a Passive Constraining Spherical Joint,” Mechanism and Machine Theory, 39, pp. 215–235 (2004).CrossRefGoogle Scholar
9. Innocenti, C. and Parenti-Castelli, V., “Echelon form Solution of Direct Kinematics for the General Fully-Parallel Spherical Wrist,” Mechanism and Machine Theory, 28, pp. 553–561 (1993).CrossRefGoogle Scholar
10. Wohlhart, K., “Displacement Analysis of the General Spherical Stewart Platform,” Mechanism and Machine Theory, 29, pp. 581–589 (1994).CrossRefGoogle Scholar
11. Vertechy, R. and Parenti-Castelli, V., “Real-Time Direct Position Analysis of Parallel Spherical Wrists by Using Extra Sensors,” Journal of Mechanical Design, 128, pp. 288–294 (2006).CrossRefGoogle Scholar
12. Bonev, I. A. and Gosselin, C. M., “Analytical Determination of the Workspace of Symmetrical Spherical Parallel Mechanisms,” IEEE Transactions on Robotics, 22, pp. 1011–1017 (2006).CrossRefGoogle Scholar
13. Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Springer, New York (2007).CrossRefGoogle Scholar
14. Borrás, J. and Di Gregorio, R., “Polynomial Solution to the Position Analysis of Two Assur Kinematic Chains with Four Loops and the Same Topology,” Journal of Mechanisms and Robotics, 1, pp. 021003-1-02103-11 (2009).CrossRefGoogle Scholar
15. Tsai, M. S., Shiau, T N., Tsai, Y. J. and Chang, T. H., “Direct Kinematic Analysis of a 3-PRS Parallel Mechanism,” Mechanism and Machine Theory, 38, pp. 71–83 (2003).CrossRefGoogle Scholar
16. Wu, X., Zhou, Z. D., Ai, Q. S. and Meng, W., “Forward Kinematics of Parallel Robot Based on Neuro-Fuzzy System,” Applied Mechanics and Materials, 470, pp. 636–643 (2014).CrossRefGoogle Scholar
17. Chebbi, A. H., Affi, Z. and Romdhane, L., “Modelling and Analysis of the 3-UPU Spherical Manipulator,” European Journal of Computational Mechanics/Revue Européenne De Mécanique Numérique, 22, pp. 157–169 (2013).Google Scholar
18. Boudreau, R. and Turkkan, N., “Solving the Forward Kinematics of Parallel Manipulators with a Genetic Algorithm,” Journal of Robotic Systems, 13, pp. 111–125 (1996).3.0.CO;2-W>CrossRefGoogle Scholar
19. Zheng, X., Bin, H. and Luo, Y., “Kinematic Analysis of a Hybrid Serial-Parallel Manipulator,” The International Journal of Advanced Manufacturing Technology, 23, pp. 925–930 (2004).CrossRefGoogle Scholar
20. Gosselin, C. M., Sefrioui, J. and Richard, M. J., “On the Direct Kinematics of General Spherical Three-Degree-of-Freedom Parallel Manipulators,” Proceedings of the 22nd ASME Mechanisms Conference, U.S.A. (1992).Google Scholar
21. Gosselin, C. and Gagné, M., “A Closed-Form Solution for the Direct Kinematics of a Special Class of Spherical Three-Degree-of-Freedom Parallel Manipulators,” Proceedings of the Second Workshop on Computational Kinematics, France (1995).Google Scholar
22. Gregorio, R. D., “Kinematics of the 3-UPU Wrist,” Mechanism and Machine Theory, 38, pp. 253–263 (2003).CrossRefGoogle Scholar
23. Husain, M. and Waldron, K. J., “Direct Position Kinematics of the 3-1-1-1 Stewart Platforms,” Journal of Mechanical Design, 116, pp. 1102–1107 (1994).CrossRefGoogle Scholar
24. Daniali, H. M., Zsombor-Murray, P. and Angeles, J., “The Kinematics of 3-DOF Planar and Spherical Double-Triangular Parallel Manipulators,” in Computational Kinematics, Academic Publishers, Dordrecht, pp. 153–164 (1993).CrossRefGoogle Scholar
25. Ma, L., Hao, K. and Ding, Y., “Forward Kinematics of Six-DOF Parallel Robot Based on Adaptive Differential Evolution,” Proceedings of International Conference, Sensors, Measurement and Intelligent Materials, China (2012).Google Scholar
26. Bai, S., Hansen, M. R. and Angeles, J., “A Robust Forward-Displacement Analysis of Spherical Parallel Robots,” Mechanism and Machine Theory, 44, pp. 2204–2216 (2009).CrossRefGoogle Scholar
27. Saafi, H., Laribi, M. A. and Zeghloul, S., “Improvement of the Direct Kinematic Model of a Haptic Device for Medical Application in Real Time Using an Extra Sensor,” Proceedings of International Conference on Intelligent Robots and Systems, U.S. (2014).Google Scholar
28. Ji, P. and Wu, H., “Algebraic Solution to Forward Kinematics of 3-DOF Spherical Parallel Manipulator,” Journal of Robotic Systems, 18, pp. 251–257 (2001).CrossRefGoogle Scholar
29. Kamali, K. and Tootoonchi, A. A., “A Novel Method for Direct Kinematics Solution of Fully Parallel Manipulators Using Basic Regions Theory,” Proceedings of the Institution of Mechanical Engineers - Part J, 225, pp. 701–683 (2011).Google Scholar
30. Tootoonchi, A. A. and Enferadi, J., “A Virtual Work Based Algorithm for Solving Direct Dynamics Problem of a 3-RRP Spherical Parallel Manipulator,” Journal of Intelligent and Robotic Systems, 63, pp. 25–49 (2011).Google Scholar