Hostname: page-component-84b7d79bbc-g7rbq Total loading time: 0 Render date: 2024-07-26T02:22:14.975Z Has data issue: false hasContentIssue false
  • English
  • Français

A closed-form solution for the position analysis of a novel fully spherical parallel manipulator

Published online by Cambridge University Press:  17 September 2015

Javad Enferadi  and
Amir Shahi
Javad Enferadi*
Affiliation:
Department of mechanical engineering, Mashad Branch, Islamic Azad University, Mashad, Iran
Amir Shahi*
Affiliation:
Department of mechanical engineering, Mashad Branch, Islamic Azad University, Mashad, Iran
*
*Corresponding authors. E-mail: Enferadi5637@mshdiau.ac.ir, e.a.shahi@gmail.com
*Corresponding authors. E-mail: Enferadi5637@mshdiau.ac.ir, e.a.shahi@gmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, a novel 3(RPSP)-S fully spherical parallel manipulator (SPM) is introduced. Also, an innovative method based on the geometry of the manipulator is presented for solving the forward position problem of the manipulator. The presented method provides a framework for the future research to solve the forward position problem of the other fully spherical PMs (for examples 3(UPS)-S and 3(RSS)-S). In the proposed method, two coupled trigonometric equations are obtained by utilizing the geometry of the manipulator and Rodrigues' rotation formula. Using Bezout's elimination technique, the two coupled equations lead to a polynomial of degree eight. We show that the polynomial is minimal and optimal. Furthermore, the other method is proposed for selecting an admissible solution of the forward position problem. This algorithm is required to control modeling and dynamic simulations.

Keywords

Spherical parallel manipulatorPosition analysisBezout's elimination techniqueAdmissible solution
Type
Articles
Information
Robotica , Volume 33 , Issue 10 , December 2015 , pp. 2114 - 2136
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Enferadi, J. and Tootoonchi, A. A., “Inverse dynamics analysis of a general spherical star-triangle parallel manipulator using principle of virtual work,” Nonlinear Dyn. 61 (3), 419–434 (2010).Google Scholar
2. Dunlop, G. and Jones, T., “Position analysis of a 3-DOF parallel manipulator,” Mech. Mach. Theory 32 (8), 903–920 (1997).Google 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,” Robot. Comput.-Integr. Manuf. 28 (3), 402–415 (2012).Google Scholar
4. Aman, M. N. S. B. S. and Basah, S.N.B., “Design and kinematic analysis of parallel robot for ankle rehabilitation,” Appl. Mech. Mater. 446, 1279–1284 (2014).Google Scholar
5. Koren, Y., Heisel, U., Jovane, F., Moriwoki, T., Pritschow, G., Ulosy, A. G. and Brussel, H., “Parallel structures and their applications in reconfigurable machining systems,” J. Manuf. Sci. Eng. 124 (2), 483–485 (2002).Google Scholar
6. Gosselin, C. and Angeles, J., “The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator,” ASME 111 (2), 202–207 (1989).Google Scholar
7. Di Gregorio, R., “A new family of spherical parallel manipulators,” Robotica 20 (04), 353–358 (2002).Google Scholar
8. Alici, G. and Shirinzadeh, B., “Topology optimisation and singularity analysis of a 3-SPS parallel manipulator with a passive constraining spherical joint,” Mech. Mach. Theory 39 (2), 215–235 (2004).Google Scholar
9. Innocenti, C. M. and Parenti-Castelli, V., “Echelon form solution of direct kinematics for the general fully-parallel spherical wrist,” Mech. Mach. Theory 28 (4), 553–561 (1993).Google Scholar
10. Wohlhart, K., “Displacement analysis of the general spherical Stewart platform,” Mech. Mach. Theory 29 (4), 581–589 (1994).Google Scholar
11. Vertechy, R. and Parenti-Castelli, V., “Real-time direct position analysis of parallel spherical wrists by using extra sensors,” J. Mech. Des. 128 (1), 288–294 (2006).Google Scholar
12. Bonev, I. A. and Gosselin, C. M., “Analytical determination of the workspace of symmetrical spherical parallel mechanisms,” IEEE Trans. Robot. 22 (5), 1011–1017 (2006).Google Scholar
13. Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, (Springer, New York, 2007).Google Scholar
14. Enferadi, J. and Tootoonchi, A. A., “A novel approach for forward position analysis of a double-triangle spherical parallel manipulator,” Eur. J. Mechanics-A/Solids 29 (3), 348–355 (2010).Google Scholar
15. Tsai, M. S., Shiau, T. N., Tsai, Y. J. and Chang, T. H., “Direct kinematic analysis of a 3-PRS parallel mechanism,” Mech. Mach. Theory 38 (1), 71–83 (2003).Google Scholar
16. Wu, X., Zhou, Z., Ai, Q. and Meng, W., “Forward kinematics of parallel robot based on neuro-fuzzy system,” Appl. Mech. Mater. 470, 636–643 (2014).Google Scholar
17. Chebbi, A. H., Affi, Z. and Romdhane, L., “Modelling and analysis of the 3-UPU spherical manipulator,” Eur. J. Comput. Mech. Rev. Européenne de Mécanique Numérique 22 (2–4), 157–169 (2013).Google Scholar
18. Boudreau, R. and Turkkan, N., “Solving the forward kinematics of parallel manipulators with a genetic algorithm,” J. Robot. Syst. 13 (2), 111–125 (1996).Google Scholar
19. Zheng, X., Bin, H. and Luo, Y., “Kinematic analysis of a hybrid serial-parallel manipulator,” Int. J. Adv. Manuf. Technol. 23 (11–12), 925–930 (2004).Google 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 ASME Mechanisms Conference, Phoenix (1992) pp. 7–12.Google Scholar
21. Gosselin, C. and Gagne, M., “A Closed-form Solution for the Direct Kinematics of a Special Class of Spherical Three-degree-of-freedom Parallel Manipulators,” In: Computational Kinematics (Merlet, J. P. and Ravani, B., eds.) (Kluwer Academic Publishers, Dordrecht, Netherlands, 1995) pp. 231–240.Google Scholar
22. Gregorio, R. D., “Kinematics of the 3-UPU wrist.” Mech. Mach. Theory 38 (3), 253–263 (2003).Google Scholar
23. Husain, M. and Waldron, K. J., “Direct position kinematics of the 3-1-1-1 Stewart platforms,” J. Mech. Des. 116 (4), 1102–1107 (1994).Google Scholar
24. Mohammadi Daniali, H. R., Zsombor-Murray, P. J. and Angeles, J., “The kinematics of 3-dof planar and spherical double-triangular parallel manipulators,” In: Computational Kinematics (Angeles, J., Hommel, G. and Kovacs, P., eds.) (Kluwer Academic Publishers, Dordrecht, Netherlands, 1993) pp. 153–164.Google Scholar
25. Enferadi, J. and Tootoonchi, A. A., “Accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator,” Robotica 29 (2), 193–209.Google Scholar
26. Bai, S., Hansen, M. R., Angeles, J., “A robust forward-displacement analysis of spherical parallel robots,” Mech. and Mach. Theory 44 (12), 2204–2216 (2009).Google 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,” International Conference on Intelligent Robots and Systems, Chicago (2014) pp. 1697–1702.Google Scholar