工程科学学报，第38卷，第7期：986992,2016年7月 Chinese Journal of Engineering,Vol.38,No.7:986-992,July 2016 DOI:10.13374/j.issn2095-9389.2016.07.014:http://journals.ustb.edu.cn 基于等效耦合刚度的平面折展滑块机构分析 印思琪，邱丽芳四，陈家兴，阳建宏 北京科技大学机械工程学院，北京100083 ☒通信作者，Email:qlf@usth.cedu.cn 摘要柔性较链是实现平面折展柔顺机构运动的关键部分.如何设计得到柔度好、精度高的柔性铰链一直是柔顺机构研 究的关键问题.综合考虑影响平面折展机构铰链刚度和精度特性的等效弯扭及拉压刚度，以LET铰链为例，分析在不同载荷 下各个参数对弯扭与拉压等效耦合刚度的影响趋势，从而提出弯扭与拉压等效耦合刚度的概念.通过大量的实例计算和分 析，推导出LET较链弯扭与拉压等效耦合刚度的经验公式.基于等效耦合刚度经验公式，对平面折展柔顺滑块机构进行分 析.应用等效耦合刚度公式与不应用等效耦合刚度公式两种情况的分析结果和有限元仿真结果表明，应用等效耦合刚度经 验公式的滑块位移计算精度得到很大的提高，验证了等效耦合刚度经验公式的适用性 关键词平面折展机构：铰链：刚度：柔顺机构：理论计算：有限元法 分类号TH122 Analysis of LEMs slider mechanisms based on equivalent coupling stiffness YIN Si-qi,QIU Li-fang,CHEN Jia-xing,YANG Jian-hong School of Mechanical Engineering,University of Science and Technology Beijing.Beijing 100083,China Corresponding author,E-mail:qlf@ustb.edu.cn ABSTRACT The flexure hinge is the key part to implement the movement of lamina emergent mechanisms (LEMs).Designing a flexure hinge with good flexibility and high accuracy is always the key problem to research compliant mechanisms.Considering the ben- ding and tension equivalent stiffness comprehensively which influence the stiffness and accuracy characteristics of LEMs hinges and taking the LET hinge as an example,the effects of different parameters on bending and tension equivalent coupling stiffness are ana- lyzed under different loads and the concept of bending torsion and tension compression coupling is introduced.Through the calculations and analyses of a large number of examples,an empirical formula of bending torsion and tension compression equivalent coupling stiff- ness is derived for the LET flexure hinge.The LEMs slider mechanism is studied based on equivalent coupling stiffness.By the com- parison of theoretical calculation and simulation results,the calculating accuracy of the slider's displacement is proved to be improved by the application of the equivalent coupling stiffness formula,and thus the applicability of the equivalent coupling stiffness formula is verified. KEY WORDS lamina emergent mechanisms:hinges:stiffness:compliant mechanisms;theoretical calculations:finite element method 以尽可能少的构件实现复杂的动作，以尽可能小新型柔顺机构习.体积小、制造简单、成本低、运输方 的占用空间完成精密的运动过程是现代机构学中重要 便等优点O使得LEMs机构存在广阔的发展空间.文 的创新思想m.平面折展机构(lamina emergent mecha- 献5]基于刚体替代综合法回设计了一个以高平行度 nisms,LEMs)是由二维平面加工而成实现三维运动的 的双四边形机构为提升平台的LEMs机构，文献]设 收稿日期：201505-28 基金项目：国家自然科学基金资助项目(51475037)工程科学学报，第 38 卷，第 7 期: 986--992，2016 年 7 月 Chinese Journal of Engineering，Vol． 38，No． 7: 986--992，July 2016 DOI: 10． 13374 /j． issn2095--9389． 2016． 07． 014; http: / /journals． ustb． edu． cn 基于等效耦合刚度的平面折展滑块机构分析 印思琪，邱丽芳，陈家兴，阳建宏 北京科技大学机械工程学院，北京 100083  通信作者，E-mail: qlf@ ustb． edu． cn 摘 要 柔性铰链是实现平面折展柔顺机构运动的关键部分． 如何设计得到柔度好、精度高的柔性铰链一直是柔顺机构研 究的关键问题． 综合考虑影响平面折展机构铰链刚度和精度特性的等效弯扭及拉压刚度，以 LET 铰链为例，分析在不同载荷 下各个参数对弯扭与拉压等效耦合刚度的影响趋势，从而提出弯扭与拉压等效耦合刚度的概念． 通过大量的实例计算和分 析，推导出 LET 铰链弯扭与拉压等效耦合刚度的经验公式． 基于等效耦合刚度经验公式，对平面折展柔顺滑块机构进行分 析． 应用等效耦合刚度公式与不应用等效耦合刚度公式两种情况的分析结果和有限元仿真结果表明，应用等效耦合刚度经 验公式的滑块位移计算精度得到很大的提高，验证了等效耦合刚度经验公式的适用性． 关键词 平面折展机构; 铰链; 刚度; 柔顺机构; 理论计算; 有限元法 分类号 TH122 Analysis of LEMs slider mechanisms based on equivalent coupling stiffness YIN Si-qi，QIU Li-fang ，CHEN Jia-xing，YANG Jian-hong School of Mechanical Engineering，University of Science and Technology Beijing，Beijing 100083，China  Corresponding author，E-mail: qlf@ ustb． edu． cn ABSTＲACT The flexure hinge is the key part to implement the movement of lamina emergent mechanisms ( LEMs) ． Designing a flexure hinge with good flexibility and high accuracy is always the key problem to research compliant mechanisms． Considering the ben￾ding and tension equivalent stiffness comprehensively which influence the stiffness and accuracy characteristics of LEMs hinges and taking the LET hinge as an example，the effects of different parameters on bending and tension equivalent coupling stiffness are ana￾lyzed under different loads and the concept of bending torsion and tension compression coupling is introduced． Through the calculations and analyses of a large number of examples，an empirical formula of bending torsion and tension compression equivalent coupling stiff￾ness is derived for the LET flexure hinge． The LEMs slider mechanism is studied based on equivalent coupling stiffness． By the com￾parison of theoretical calculation and simulation results，the calculating accuracy of the slider’s displacement is proved to be improved by the application of the equivalent coupling stiffness formula，and thus the applicability of the equivalent coupling stiffness formula is verified． KEY WOＲDS lamina emergent mechanisms; hinges; stiffness; compliant mechanisms; theoretical calculations; finite element method 收稿日期: 2015--05--28 基金项目: 国家自然科学基金资助项目( 51475037) 以尽可能少的构件实现复杂的动作，以尽可能小 的占用空间完成精密的运动过程是现代机构学中重要 的创新思想［1］． 平面折展机构( lamina emergent mecha￾nisms，LEMs) 是由二维平面加工而成实现三维运动的 新型柔顺机构［2--3］． 体积小、制造简单、成本低、运输方 便等优点［4］使得 LEMs 机构存在广阔的发展空间． 文 献［5］基于刚体替代综合法［6］设计了一个以高平行度 的双四边形机构为提升平台的 LEMs 机构，文献［7］设