Design and Dynamic Modeling of Planar Parallel Micro-Positioning Platform Mechanism with Flexible Links Based on Euler Bernoulli Beam Theory

Journal of Solid Mechanics

مقاله 6، دوره 5، شماره 2، شهریور 2013، صفحه 174-192   

نوع مقاله: Research Paper

نویسندگان

N.S Viliani^{* 1}؛ H Zohoor²؛ M.H Kargarnovin³

¹Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University

²Center of Excellence in Design, Robotics, and Automation, Sharif University of Technology; Fellow, The Academy of Sciences of Iran,

³School of Mechanical Engineering, Sharif University of Technology

چکیده

This paper presents the dynamic modeling and design of micro motion compliant parallel mechanism with flexible intermediate links and rigid moving platform. Modeling of mechanism is described with closed kinematic loops and the dynamic equations are derived using Lagrange multipliers and Kane’s methods. Euler-Bernoulli beam theory is considered for modeling the intermediate flexible link. Based on the Assumed Mode Method theory, the governing differential equations of motion are derived and solved using both Runge-Kutta-Fehlberg4, 5th and Perturbation methods. The mode shapes and natural frequencies are calculated under clamped-clamped boundary conditions. Comparing perturbation method with Runge-Kutta-Fehlberg4, 5th leads to same results. The mode frequency and the effects of geometry of flexure hinges on intermediate links vibration are investigated and the mode frequency, calculated using Fast Fourier Transform and the results are discussed.

کلیدواژه‌ها

Compliant mechanism؛ Flexible link؛ Kane’s method؛ Micro positioning؛ Lagrange multipliers

مراجع

[1] Lobontiu N., 2003, Compliant Mechanisms Design of Flexure Hinges, CRC Press, Florida.

[2] Yi B.J., Chung G.B., Na H.Y., Kim W.K., Suh I.H., 2003, Design and experiment of a 3-DOF parallel micromechanism utilizing flexure hinges, IEEE Transactions on Robotics and Automation 19: 604-612.

[3] Yong Y.K., Fu L.T., 2009, Kinetostatic modeling of a 3-RRR compliant micro-motion stages with flexure hinges, Mechanism and Machine Theory 44: 1156-1175.

[4] Yong Y.K., Fu L.T., 2008, The effect of the accuracies of flexure hinge equations on the output compliances of planar micro-motion stages, Mechanism and Machine Theory 43: 347-363.

[5] Yong Y.K., Fu L.T., 2009, Comparison of circular flexure hinge design equations and the derivation of empirical stiffness formulations, IEEE/ASME International Conference on Advanced Intelligent Mechatronics Suntec Convention and Exhibition Center, doi:10.1109/AIM.2009.5229961.

[6] Paros J.M., Weisbord L., 1965, How to design flexure hinges, Machine Design 37: 151-156.

[7] Anathasuresh G.K., Kota S., 1995, Designing compliant mechanisms, ASME Mechanical Engineering117: 93-96.

[8] Murphy M.D., Midha A., Howell L.L., 1996, The topological synthesis of compliant mechanisms, Mechanism and Machine Theory 31: 185-199.

[9] Tokin, 1996, Multilayer Piezoelectric Actuators, User’s Manual, Tokin Corporate Publisher.

[10] Saggere L., Kota S., 1997, Synthesis of distributed compliant mechanisms for adaptive structures application: an elasto-kinematic approach, Proceedings of the DETC 1997, ASME Design Engineering Technical Conferences, Sacramento, CA.

[11] Kota S., Joo J., Li Z., Rodgers S.M., Sniegowski J., 2001, Design of compliant mechanisms: applications to MEMS, Analog Integrated Circuits and Signal Processing-An international journal 29: 7-15.

[12] Rong Y.,Zhu Y., Luo Z., Xiangxi L., 1994, Design and analysis of flexure hinge mechanism used in micro-positioning stages, ASME proceeding of the 1994 international Mechanical Engineering Congress and Exposition 68: 979-985.

[13] Her I., Cheng J.C., 1994, A linear scheme for the displacement analysis of micro positioning stages with flexure hinges, ASME Journal of Mechanical Design 116: 770-776.

[14] Trindade M.A., Sampaio R., 2002, Dynamics of beams undergoing large rotations accounting for arbitrary axial deformation, AIAA journal of Guidance, Control and dynamics 25: 634-643.

[15] Yong Y.K., Lu T.F., Handley D.C., 2008, Review of circular flexure hinge design equations and derivation of empirical formulations, Precision Engineering 32: 63–70.

[16] Lobontiu N., Paine J.S.N., Garcia E., Goldfarb M., 2001, Corner-filleted flexure hinges, Transactions of the ASME, Journal of Mechanical Design 123: 346-352.

[17] Shim J., Song S.K., Kwon D.S., Cho H.S., 1997, Kinematic feature analysis of a 6-degree of freedom in-parallel manipulator for micro-positioning surgical, Proceedings of 1997 IEEE/RSJ International Conference on Intelligent Robots and Systems 3:1617-1623.

[18] Ryu J.W., Gweon D., Moon K.S., 1997, Optimal design of a flexure hinge based xyθ wafer stage, Precision Engineering 21: 18-28.

[19] Meirovitch L., 2001, Fundamentals of Vibrations, MC Grow Hill, New York.

[20] Yu H.Y., Bi S., Zong G., Zhao W., 2004, Kinematics feature analysis of a 3 DOF compliant mechanism for micro manipulation, Chinese Journal of Mechanical Engineering 17: 127-131.

[21] Choi K.B., Kim D.H., 2006, Monolithic parallel linear compliant mechanism for two axes ultraprecision linear motion, Review of Scientific Instruments 77(6): 065106.

[22] Tian Y., Shirinzadeh B., Zhang D., Zhong Y., 2010, Three flexure hinges for compliant mechanism designs based on dimensionless graph analysis, Precision Engineering 34: 92–100.

[23] Baruh H., 1999, Analytical Dynamics, McGraw-Hill.

[24] Dwivedy S.K., Wberhard P., 2006, Dynamic analysis of flexible manipulators, a literature review, Mechanism and Machine Theory 41: 749-777.

[25] Nayfeh A.H., 1981, Introduction to Perturbation Techniques, John Wiley & Sons, Inc.

[26] Benosman M., Vey G.L., 2004, Control of flexible manipulators: a survey, Robotica 22: 533-545.

[27] Lee J.D., Geng Z., 1993, Dynamic model of a flexible Stewart platform, Computers and Structures 48: 367-374.

[28] Zhou Z., Xi J., Mechefske C.K., 2006, Modeling of a fully flexible 3PRS manipulator for vibration analysis, Journal of Mechanical Design 128: 403-412.

[29] Piras G., Cleghorn W.L., Mills J.K., 2005, Dynamic finite-element analysis of planar high speed, high-precision parallel manipulator with flexible links, Mechanism and Machine Theory 40: 849-862.

[30] Wang X., Mills J.K., 2005, FEM dynamic model for active vibration control of flexible linkages and its application to a planar parallel manipulator, Journal of Applied Acoustics 66: 1151-1161.