Stiffness Modeling of 3-PRS Mechanism

Authors: Xiaohui Han, Yuhan Wang, Jing Shi

Abstract:

This paper proposed a stiffness analysis method for a 3-PRS mechanism for welding thick aluminum plate using FSW technology. In the molding process, elastic deformation of lead-screws and links are taken into account. This method is based on the virtual work principle. Through a survey of the commonly used stiffness performance indices, the minimum and maximum eigenvalues of the stiffness matrix are used to evaluate the stiffness of the 3-PRS mechanism. Furthermore, A FEA model has been constructed to verify the method. Finally, we redefined the workspace using the stiffness analysis method.

Keywords: 3-PRS, parallel mechanism, stiffness analysis, workspace.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328394

References:

[1] J.-P. Merlet, Parallel Robots, Kluwer Academic Publishers, London,2000
[2] Huy-Hoang Pham, I-Ming Chen, Stiffness modeling of flexure parallel mechanism, Precision Engineering 29 (2005) 467-478.
[3] Clement Gosselin, Stiffness Mapping for Parallel Manipulators, IEEE Transactions On Robotics And Automation, Vol. 6, No.3, June 1990.
[4] Woo-Keun Yoon, Takashi Suehiro, Yuichi Tsumaki and Masaru Uchiyama, Stiffness Analysis and Design of a Compact Modified Delta Parallel Mechanism, Robotica (2004) volume 22, pp, 463-475.
[5] R. E. Stamper, L. W. Tsai and G. C. Walsh, "Optimization of a Three DOF Translational Platform for Well-Conditioned Workspace," Proc. of the 1997 IEEE Int. Conf. on Robotics and Automation (1997) pp. 3250-3255.
[6] L. Baron and J. Angeles, "The Direct Kinematics of Parallel Manipulators Under Joint-Sensor Redundancy," IEEE Transactions on Robotics and Automation 16(1), 12-19 (2000).
[7] M. J. Liu, C. X. Li and C. N. Li, Dynamics Analysis of the Gough-Stewart Platform Manipulator, IEEE Transactions on Robotics and Automation 16(1), 94-99 (2000).
[8] J. E. McInroy and J. C. Hamann, Design and Control of Flexure Jointed Hexapods, IEEE Transactions on Robotics and Automation 16(4), 372-381 (2000).
[9] X. J. Liu, J.Wang, F. Gao and L. P.Wang, "Mechanism design of a simplified 6-DOF 6-RUS parallel manipulator," Robotica 20(1), 81-91 (2002).
[10] Woronko A, Huang J, Altintas Y. Piezoelectric tool actuator for precision machining on conventional CNC turning centers. Prec Eng 2003;27:335-45.
[11] Zhang S, Fasse E. A finite-element-based method to determine the spatial stiffness properties of a notch hinge. ASME J Mech Des 2001;123:141-7.
[12] Xu G, Qu L. Some analytical problems of high performance flexure hinge and micro-motion stage design. In: Proceedings of IEEE International Conference on Industrial Technology. 1996.p. 771-5.
[13] Lobontiu N. Compliant mechanisms: design of flexure hinges. 2nd ed. CRC Press; 2003.
[14] Henein S, Bottinelli S, Clavel R. Parallel spring stages with flexures of micrometric cross-sections. In: Proceedings of the SPIE on Microrobotics and Micro-system Fabrication, vol. 3202. 2001. p. 209-20.
[15] Alici G, Shirinzadeh B. Kinematics and stiffness analyses of a flexure-jointed planar micromanipulation system for a decoupled compliant motion. In: Proceedings of IEEE International Conference on Intelligent Robots and Systems. 2003. p. 3282-7.
[16] T. Arai, Analysis and Synthesis of a Parallel Link Manipulator Based on Its Statics, J. Robotics Society of Japan 10(4), 526-533 (1992) (in Japanese).
[17] T. Oiwa and M. Hirano, Six Degree-of-Freedom Fine Motion Mechanism using Parallel Mechanism - Link Layout Design-, J. the Japan Society for Precision Engineering 65(10), 1425-1429 (1999) (in Japanese).
[18] C. Gosselin, Stiffness mapping for parallel manipulators, IEEE Trans. Robot. Automat. 6 (3) (1990) 377-382.
[19] N. Simaan, M. Shoham, Stiffness synthesis of a variable geometry six-degrees-of-freedom double planar parallel robot, Int. J. Robot. Res. 22 (9) (2003) 757-775.
[20] Yangmin Li, Qingsong Xu, Stiffness analysis for a 3-PUU parallel kinematic machine, Mechanism and machine Theory 43 (2008) 186-200.
[21] B.S. El-Khasawneh, P.M. Ferreira, Computation of stiffness and stiffness bounds for parallel link manipulators, Int. J. Mach. Tools Manuf. 39 (2) (1999) 321-342.