Evaluation of the Position Error of Four Non-Overconstrained Spherical Parallel Manipulators

Abstract:

The 3-RRR spherical parallel manipulator is known to be highly overconstrained, which causes several problems of mounting the mechanism, but has the advantage of having high rigidity thus a good precision. Several works in the literature proposed non-overconstrained versions of this mechanism. However, very few works dealt with the problem of the consequence of modifying an overconstrained mechanism into a non-overconstrained one, mainly from an accuracy point of view. In this work, we present an analysis of the accuracy of four different non-overconstrained SPMs, i.e., 3-RSR, 3-RCC, 3-RRS, and 3-RUU. These four SPM are then evaluated in translational and rotational accuracy due to manufacturing errors. The error on the position and orientation of the end-effector, due to manufacturing errors, are computed in 100 different configurations within their workspace. These SPMs are then compared among each other and we showed that the 3-RRS has the best compromise between the translational and rotational accuracy.

• Periodical: Applied Mechanics and Materials (Volume 162)
• Pages: 194-203
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.162.194
• Online since: March 2012
• Authors: A. Chaker, A. Mlika, M.A. Laribi, L. Romdhane, S. Zeghloul
• Keywords: Accuracy, Manufacturing Errors, Non-Overconstrained Mechanisms, Screw of Small Displacements, Spherical Parallel Manipulators

References

[1] C. Gosselin, E. Sl Pierre and M. Gagné, On the developpement of the Agile Eye, IEEE Robotics & Automation Magazine, pp.29-37, December (1996).

[2] S. Bai, Optimum design of spherical parallel manipulators, Mechanism and Machine Theory 45, pp.200-211, (2010).

DOI: 10.1016/j.mechmachtheory.2009.06.007

[3] R. D. Gregorio, The 3-RRS wrist : a new, simple and non-overconstrained spherical parallel manipulator, Journal of echanical Design, Transactions of the ASME, vol. 126, pp.850-855, September (2004).

DOI: 10.1115/1.1767819

[4] M. Karouia and J. M. Hervé, Enumération de mécanismes parallèles sphériques isostatiques, in 16ème Congrès de Mécanique, Nice-France, 1-5 September (2003).

[5] R. D. Gregorio, A new parallel wrist using only revolute pairs: the 3-RUU wrist, Robotica, vol. 19, pp.305-309, (2001).

DOI: 10.1017/s0263574700003192

[6] S. Bai, M. R. Hansen and J. Angeles, A robust forward-displacement analysis of spherical parallel robots, Mechanism and Machine Theory, vol. 44, pp.2204-2216, (2009).

DOI: 10.1016/j.mechmachtheory.2009.07.005

[7] K. Al-Widyan, Q. Ma X and J. Angeles, The robust design of parallel spherical robots, Mechnism and Machine Theory, vol. 46, pp.335-343, (2011).

DOI: 10.1016/j.mechmachtheory.2010.11.002

[8] AFNOR, Schémas Cinématiques, Norme Européenne, NF EN ISO 3952, (1995).

[9] R. D. Gregorio, Kinematics of a new spherical parallel manipulator with three equal legs: the 3-URC wrist, J. Rob. Syst. 18 (5) , p. p.213–219, (2001).

DOI: 10.1002/rob.1017

[10] E Cavallo, Michelini R C , A robotic equipment for the guidance of a vectored thrustor in, in 35th International Symposium on on Robotics (ISR 2004), Paris, (2004).

[11] M. Karouia and J. M. Hervé, Asymmetrical 3-dof spherical parallel mechanisms, European Journal of Mechanisms A/Solids, vol. 24, pp.47-57, (2005).

DOI: 10.1016/j.euromechsol.2004.10.001

[12] M. Fayet, Hyperstatisme au sens de la dynamique et au sens de la cinématique-dualité, Mechanism and Mchine Theory, vol. 30, pp.233-252, (1995).

DOI: 10.1016/0094-114x(94)00022-d

[13] M. Fayet, Distribution of wrench-twist duality in over-constrained mechanisms, Journal of Mechanical Design, vol. 125, pp.81-91, March (2003).

DOI: 10.1115/1.1541629

[14] J. Gallardo, R. Rodriguez, M. Caudillo and J. M. Rico, A family of spherical parallel manipulators with two legs, Mechanism and Machine Theory, vol. 43, pp.201-216, (2008).

DOI: 10.1016/j.mechmachtheory.2007.02.001

[15] J. M. Hervé and M. Karouia, A three-dof tripod for generating spherical rotation., In: J. Lenarcic and M.M. Stanisic, Editors, Advances in Robot Kinematics, p. p.395–402, (2000).

DOI: 10.1007/978-94-011-4120-8_41

[16] A. Chaker, M. A. Laribi, L. Romdhane and S. Zaghloul , Synthesis of Spherical Manipulator for Dexterous Medical Task, in 2nd IFToMM International Symposium on Robotics and Mechatronics, ISRM2011 November3-5, Shangai, China, (2011).

[17] X. Liu, Z. Jin and F. Gao, Optimum design of 3-DOF spherical parallel Manipulators with respect to the conditioning and stiffness indices, Mechanism and Machine Theory, vol. 35, pp. pp.1257-1267, (2000).

DOI: 10.1016/s0094-114x(99)00072-5