Abstract：Flexure-based mechanisms are widely used in industry as highly precise micro-motion mechanisms. This paper presents a compliance calculation method for planar flexure-based mechanisms. The compliance of flexure hinges is used to relate the deformations to the loads on flexure member with the end-effector motion obtained using the virtual work principle. Then, a matrix method is used to derive concise compliance equations for serial and parallel flexure mechanisms. The compliance and the relationship between the compliance terms and variable geometric parameters are analyzed for three typical flexure-based mechanisms. The model results compare well with finite element method (FEM) predictions with a maximum difference of 7% and an average difference of 3%. This method provides theoretical and technical support for the design and optimization of flexure-based mechanisms.
 Lobontiu N. Compliant Mechanisms: Design of Flexure Hinges [M]. Boca Raton, FL: CRC Press, 2010.
 Yao Q, Dong J, Ferreira P M. Design, analysis, fabrication and testing of a parallel-kinematic micropositioning XY stage [J]. International Journal of Machine Tools and Manufacture, 2007, 47(6): 946-961.
 Zubir M N M, Shirinzadeh B, Tian Y. Development of a novel flexure-based microgripper for high precision micro-object manipulation [J]. Sensors and Actuators A: Physical, 2009, 150(2): 257-266.
 贠远, 徐青松, 李杨民. 并联微操作机器人技术及应用进展 [J]. 机械工程学报, 2009, 44(12): 12-23.YUN Yuan, XU Qingsong, LI Yangmin, et al. Survey on parallel manipulators with micro/nano manipulation technology and applications [J]. Journal of Mechanical Engineering, 2009, 44(12): 12-23. (in Chinese)
 于靖军, 裴旭, 毕树生, 等. 柔性铰链机构设计方法的研究进展 [J]. 机械工程学报, 2010, 46(13): 2-13.YU Jingjun, PEI Xu, BI Shusheng, et al. State-of-arts of design method for flexure mechanisms [J]. Journal of Mechanical Engineering, 2010, 46(13): 2-13. (in Chinese)
 Li Y, Xu Q. A novel piezoactuated XY stage with parallel, decoupled, and stacked flexure structure for micro-/ nanopositioning [J]. IEEE Transactions on Industrial Electronics, 2011, 58(8): 3601-3615.
 Xiao S, Li Y. Development of a large working range flexure-based 3-DOF micro-parallel manipulator driven by electromagnetic actuators [J]. International Journal of Precision Engineering and Manufacturing, 2014, 15(4): 735-744.
 Pei X, Yu J, Zong G, et al. An effective pseudo-rigid-body method for beam-based compliant mechanisms [J]. Precision Engineering, 2010, 34(3): 634-639.
 Li Y, Xu Q. Design and analysis of a totally decoupled flexure-based XY parallel micromanipulator [J]. IEEE Transactions on Robotics, 2009, 25(3): 645-657.
 Lobontiu N, Paine J S N, Garcia E, et al. Design of symmetric conic-section flexure hinges based on closed-form compliance equations [J]. Mechanism and Machine Theory, 2002, 37(5): 477-498.
 Lobontiu N, Paine J S N, Garcia E, et al. Corner-filleted flexure hinges [J]. Journal of Mechanical Design, 2001, 123(3): 346-352.
 Pham H H, Chen I M. Stiffness modeling of flexure parallel mechanism [J]. Precision Engineering, 2005, 29(4): 467-478.
 Qin Y, Tian Y, Zhang D. Design and dynamic modeling of a 2-DOF decoupled flexure-based mechanism [J]. Chinese Journal of Mechanical Engineering, 2012, 25(4): 688-696.
 Lobontiu N. Compliance-based matrix method for modeling the quasi-static response of planar serial flexure-hinge mechanisms [J]. Precision Engineering, 2014, 38(3): 639-650.
 Qin Y, Shirinzadeh B, Zhang D, et al. Compliance modeling and analysis of statically indeterminate symmetric flexure structures [J]. Precision Engineering, 2013, 37(2): 415-424.
 Jia X, Liu J, Tian Y, et al. Stiffness analysis of a compliant precision positioning stage [J]. Robotica, 2012, 30(6): 925-939.