Topological and Shape Optimization of Flexure Hinges for Designing Compliant Mechanisms Using the Level Set Method

A flexure hinge is a major component in designing compliant mechanisms that o ers unique possibilities in a wide range of application fields in which high positioning accuracy is required. Although various flexure hinges with di erent configurations have been successively proposed, they are often designed based on designers' experiences and inspirations. This study presents a systematic method for topological optimization of flexure hinges by using the level set method. Optimization formulations are developed by considering the functional requirements and geometrical constraints of flexure hinges. The functional requirements are first constructed by maximizing the compliance in the desired direction while minimizing the compliances in the other directions. The weighting sum method is used to construct an objective function in which a self-adjust method is used to set the weighting factors. A constraint on the symmetry of the obtained configuration is developed. Several numerical examples are presented to demonstrate the validity of the proposed method. The obtained results reveal that the design of a flexure hinge starting from the topology level can yield more choices for compliant mechanism design and obtain better designs that achieve higher performance.

Optimizing the Qusai-static Folding and Deploying of Thin-Walled Tube Flexure Hinges with Double Slots

The thin-walled tube flexure（TWTF） hinges have important potential application value in the deployment mechanisms of satellite and solar array, but the optimal design of the TWTF hinges haven＇t been completely solved, which restricts their applications. An optimal design method for the qusai-static folding and deploying of TWTF hinges with double slots is presented based on the response surface theory. Firstly, the full factorial method is employed to design of the experiments. Then, the finite element models of the TWTF hinges with double slots are constructed to simulate the qusai-static folding and deploying non-linear analysis. What＇s more, the mathematical model of the TWTF flexure hinge quasi-static folding and deploying properties are derived by the response surface method. Considering of small mass and high stability, the peak moment of quasi-static folding and deploying as well as the lightless are set as the objectives to get the optimal performances. The relative errors of the objectives between the optimal design results and the FE analysis results are less than 7%, which demonstrates the precision of the surrogate models. Lastly, the parameter study shows that both the slots length and the slots width both have significant effects to the peak moment of quasi-static folding and deploying of TWTF hinges with double slots. However, the maximum Mises stress of quasi-static folding is more sensitive to the slots length than the slots width. The proposed research can be applied to optimize other thin-walled flexure hinges under quasi-static folding and deploying, which is of great importance to design of flexure hinges with high stability and low stress.

Kinematics modeling of a 6-PSS parallel mechanism with wide-range flexure hinges

A novel 6-PSS flexible parallel mechanism was presented,which employed wide-range flexure hinges as passive joints.The proposed mechanism features micron level positioning accuracy over cubic centimeter scale workspace.A three-layer back-propagation(BP) neural network was utilized to the kinematics analysis,in which learning samples containing 1 280 groups of data based on stiffness-matrix method were used to train the BP model.The kinematics performance was accurately calculated by using the constructed BP model with 19 hidden nodes.Compared with the stiffness model,the simulation and numerical results validate that BP model can achieve millisecond level computation time and micron level calculation accuracy.The concept and approach outlined can be extended to a variety of applications.

Analysis of the Micro-Rotation Compliant Mechanism Based on the Corner-Filleted Flexure Hinges

The purpose of this thesis is to derive the flexibility formula of the corner-filleted flexure hinge easily and conveniently and use it to design a micro-rotation compliant mechanism. Firstly,we get the corner-filleted flexure hinge flexibility formula by methods of symmetry transformation and coordinates translation. The correctness of this formula is validated on the basis of the finite element method and under the premise that the effects of shear stress are taken into consideration. Then a micro-rotation compliant mechanism is designed in accordance with the corner-filleted flexure hinge,and the deduction and analysis of its working moment/rigidity are conducted. Moreover,this theoretical formula is proved to be accurate and reliable through the finite element analysis and the experimental verification,based on which the structural design and optimization can be made on the rotating part of a micro adjustment device. The results illustrate that designing and optimizing the structures by the analysis model is convenient and reliable so that complicated 3D modeling and finite element analysis are not needed.

Reliability Analysis of Flexure Hinge Based on Kriging Method

The uncertainty widely exists in the engineering practice.Therefore,it is necessary to research the effect of uncertainty on the structural system. In this paper,the reliability and sensitivity of the flexure hinge, which is the key component of the compliant mechanisms,are investigated. The results of the reliability analysis can effectively guide the engineer to design and optimize the flexure hinge. In order to improve the calculating efficiency,the kriging method is introduced to estimate the failure probability and reliability sensitivity.

Simulation optimal design of a compliant mechanism with circular notch flexure hinges based on the equivalent beam methodology

This paper presents an in-depth study of Equivalent beam model (EBM).Firstly three-dimensional (3D) finite element analysis (FEA) model for circular flexure hinge developed by Zettl et al.was verified by the comparison with Smith's experimental results and the 3D FEA model was feasible within 5.5% error.Then the accuracy of Timoshenko short-beam due to shear force was verified based on finite element method.The results showed that the EBM has good accuracy within 5% error for 1≤r/t≤3.Finally the EBM methodology was applied for the simulation optimal design of a bridge-type compliant mechanism.The results showed that the EBM methodology has very high numerical efficiency and satisfactory accuracy for simulation optimal design of planar compliant mechanism with flexure hinges.

A large workspace flexure hinge-based parallel manipulator system

Parallel manipulator systems as promising precision devices are used widely in current researches. A novel large workspace flexure parallel manipulator system utilizing wide-range flexure hinges as passive joints is proposed in this paper, which can attain sub-micron-scale precision over the cubic centimeter motion range. This paper introduces the mechanical system architecture based on the wide-range flexure hinges, analyzes the kinematics via stiffness matrices, presents the control system configuration and control strategy, and finally gives the system performance test results.

Design and Dynamic Modeling of a 2-DOF Decoupled Flexure-Based Mechanism

Flexure mechanisms with decoupled characteristics have been widely utilized in precision positioning applications.However,these mechanisms suffer from either slow response or low load capability.Furthermore,asymmetric design always leads to thermal error.In order to solve these issues,a novel 2-DOF decoupled mechanism is developed by monolithically manufacturing sets of statically indeterminate symmetric（SIS） flexure structures in parallel.Symmetric design helps to eliminate the thermal error and Finite Element Analysis（FEA） results show that the maximum coupling ratio between X and Y axes is below 0.25% when a maximum pretension force of 200 N is applied.By ignoring the mass effect,all the SIS flexure structures are simplified to ＂spring-damper＂ components,from which the static and dynamics model are derived.The relation between the first resonant frequency of the mechanism and the load is investigated by incorporating the load mass into the proposed dynamics model.Analytical results show that even with a load of 0.5 kg,the first resonant frequency is still higher than 300 Hz,indicating a high load capability.The mechanism＇s static and dynamic performances are experimentally examined.The linear stiffnesses of the mechanism at the working platform and at the driving point are measured to be 3.563 0 N·μm-1 and 3.362 1 N·μm-1,respectively.The corresponding estimation values from analytical models are 3.405 7 N·μm-1 and 3.381 7 N·μm-1,which correspond to estimation errors of-4.41% and 0.6%,respectively.With an additional load of 0.16 kg,the measured and estimated first resonant frequencies are 362 Hz and 365 Hz,respectively.The estimation error is only 0.55%.The analytical and experimental results show that the developed mechanism has good performances in both decoupling ability and load capability;its static and dynamic performance can be precisely estimated from corresponding analytical models.The proposed mechanism has wide potentials in precision positioning applications.

LOADS INFLUENCE ANALYSIS ON NOVEL HIGH PRECISION FLEXURE PARALLEL POSITIONER

A large workspace flexure parallel positioner system is developed, which can attain sub-micron scale accuracy over cubic centimeter motion range for utilizing novel wide-range flexure hinges instead of the conventional mechanism joints. Flexure hinges eliminate backlash and friction, but on the other hand their deformation caused by initial loads influences the positioning accuracy greatly, so discussions about loads＇ influence analysis on this flexure parallel positioner is very necessary. The stiffness model of the whole mechanism is presented via stiffness assembly method based on the stiffness model of individual flexure hinge, And the analysis results are validated by the finite element analysis （FEA） simulation and experiment tests, which provide essential data to the practical application of this positioner system.

基于柔性铰链结构的大口径压电快摆镜

为了解决压电作动器驱动的快速反射镜因压电作动器伸长量较小,导致快速反射镜偏转角过小的问题,该文提出了一款新型快速反射镜设计方案。采用三级杠杆式柔性铰链放大机构实现压电作动器位移的放大,采用柔性轴承作为快摆镜的运动关节实现快摆镜的大角度定轴偏转。通过理论推导和有限元仿真对快摆镜的最大偏转角度、等效应力、谐振频率以及振型进行分析。实验结果表明,所设计的快摆镜可以实现大于2 mrad的镜面偏转,满足大范围、高精度的光束定位要求。

差动驱动并联机器人设计与运动学分析

基于Stewart并联机器人构型和偏置柔性虎克铰链,利用双螺旋副差动传动的方案设计了一款低成本高精度6-RR-RP-RR构型的6-DOF并联机器人。首先,基于双螺旋副差动传动原理,分别提出了串联和并联两种差动驱动方案,并对柔性虎克铰链进行了设计,确定了最终的整机结构设计方案;其次,对柔性铰链的柔度进行了理论建模,并仿真验证了其柔度和强度设计的合理性;此外,对该并联机器人开展了逆运动学分析,建立了其运动学模型,并采用牛顿-拉普拉森数值迭代方法进行了求解;最后,分别利用多体动力学和Ansys仿真软件验证了整机运动学模型和求解的准确性。

基于柔性铰链微动平台的自抗扰控制方法

微动平台一般以柔性铰链为导向机构,由于系统固有频率低,会严重限制传统PID算法的控制带宽,影响定位精度。因此,设计自抗扰控制算法(ADRC)将系统未建模动态与外部未知扰动共同视作“总扰动”,通过扩张状态观测器(ESO)进行估计和补偿,提高系统的控制带宽。为了充分利用已知的模型信息,设计基于模型的ADRC算法,将柔性铰链标称模型输入到ESO中,进一步提升系统的控制性能。最后,通过10μm行程的点位运动实验进行验证。结果表明:因为控制带宽无法过大而导致PID难以响应,ADRC提高了控制系统带宽,实现了精密定位;模型ADRC进一步提升了响应速度与定位精度。相比ADRC,模型ADRC整定时间缩短了68.1%,最大跟踪误差降低了53.8%,定位精度提升了60.7%。

空间四自由度柔顺并联机构设计与仿真

设计了一种由压电陶瓷驱动的整体式空间四自由度柔顺并联定位平台,使用柔性铰链代替传统的运动副,消除了传统机构铰链配合的摩擦与间隙。建立了空间四自由度定位平台的运动学模型,使用三维建模软件建立几何模型。通过计算得到解析结果,并对空间四自由度柔顺并联定位平台进行有限元分析,得到其位移特性。比较理论计算和有限元仿真结果,得出误差在允许范围内,验证了设计的定位平台的可行性。

正交柔顺矢量测力系统的设计和性能分析

针对多分支正交柔顺矢量测力系统的设计难题,提出了梁连接单元模拟测力元件的方法;采用该方法建立了测力分支及矢量测力系统的有限元模型,并对6种分支形式和平面布局形式进行了结构特点分析。在此基础上,结合矢量测力系统案例,通过有限元模型进行参数详细设计,最终获得了结构紧凑且耦合较小的方案。对台架的3个载荷分量(轴向力、法向力、俯仰力矩)进行了校准试验,其中,校准的不确定度均在0.5%满量程(Full Scale,FS)左右。针对大载荷矢量测力系统加载精度对校准测量的影响较大的问题,提出了基于载荷与测量比值的性能评估方法,采用该方法,得到设计的矢量测力系统的3个分量的测量重复性在0.4%FS左右,大量程测量滞后性在0.7%FS以内。研究成果对于正交矢量测力系统的结构设计和性能分析具有一定的参考意义。

A simple compliance modeling method for flexure hinges

Various types of flexure hinges have been introduced and implemented in a variety of fields due to their superior performances.The Castigliano’s second theorem,the Euler–Bernoulli beam theory based direct integration method and the unit-load method have been employed to analytically describe the elastic behavior of flexure hinges.However,all these methods require prior-knowledge of the beam theory and need to execute laborious integration operations for each term of the compliance matrix,thus highly decreasing the modeling efficiency and blocking practical applications of the modeling methods.In this paper,a novel finite beam based matrix modeling(FBMM)method is proposed to numerically obtain compliance matrices of flexure hinges with various shapes.The main concept of the method is to treat flexure hinges as serial connections of finite micro-beams,and the shearing and torsion effects of the hinges are especially considered to enhance the modeling accuracy.By means of matrix calculations,complete compliance matrices of flexure hinges can be derived effectively in one calculation process.A large number of numerical calculations are conducted for various types of flexure hinges with different shapes,and the results are compared with the ones obtained by conventional modeling methods.It demonstrates that the proposed modeling method is not only efficient but also accurate,and it is a more universal and more robust tool for describing elastic behavior of flexure hinges.

A closed-form nonlinear model for spatial Timoshenko beam flexure hinge with circular cross-section

Beam flexure hinges can achieve accurate motion and force control through the elastic deformation. This paper presents a nonlinear model for uniform and circular cross-section spatial beam flexure hinges which are commonly employed in compliant parallel mechanisms. The proposed beam model takes shear deformations into consideration and hence is applicable to both slender and thick beam flexure hinges. Starting from the first principles, the nonlinear strain measure is derived using beam kinematics and expressed in terms of translational displacements and rotational angles. Second-order approximation is employed in order to make the nonlinear strain within acceptable accuracy. The natural boundary conditions and nonlinear governing equations are derived in terms of rotational Euler angles and subsequently solved for combined end loads. The resulting end load-displacement model, which is compact and closed-form, is proved to be accurate for both slender and thick beam flexure using nonlinear finite element analysis. This beam model can provide designers with more design insight of the spatial beam flexure and thus will benefit the structural design and optimization of compliant manipulators.

基于轴承和柔性铰链的布拉格光纤光栅加速度计

为实现中高频振动信号的测量,本文设计了一种基于轴承和柔性铰链结构的光纤布拉格光栅加速度传感器。首先,基于理论力学模型推导出其固有频率、灵敏度与结构参数的数学模型,然后进行结构优化设计,并制作了传感器实物。在此基础上,对所设计传感器动态特性进行有限元仿真和实验测试。研究结果表明:传感器工作频率为10~1200 Hz,加速度灵敏度达17.25 pm/g,测量误差小于0.3 g,线性度大于0.99,重复性误差为2.33%,且能实现温度补偿。

刚柔耦合关节SCARA机器人的双柔性动力学模型

针对电子装配机器人高速高精要求,提出一种能够利用柔性铰链变形补偿轴承摩擦死区,实现高精度定位运动的刚柔耦合关节SCARA机器人的概念设计,并建立考虑柔性铰链变形与机械臂一阶弹性变形的双柔性动力学模型。首先,设计一种刚柔耦合轴承的结构,通过轴承中柔性铰链的变形量主动补偿摩擦死区引起的定位误差;在每个关节处引入两个扭转弹簧,分别模拟柔性铰链和机械臂的弹性变形;其次,建立关节的摩擦模型以模拟关节摩擦环境;然后,使用拉格朗日动力学方法建立包含摩擦信息与振动信息的动力学模型。设计开环和闭环的数值仿真进行验证,结果表明该模型理论分析的有效性。

二维并联跨尺度压电精密位移驱动平台研制

多自由度跨尺度精密位移驱动平台在光学计量检测、半导体制造、生物医学工程等诸多领域具有广泛的应用需求。针对串联多自由度压电驱动平台结构厚重的问题,结合压电柔性铰链机构和冲击驱动原理,研制了一款结构紧凑的二维并联跨尺度压电精密位移驱动平台。通过有限元仿真和实验测试验证其性能,结果表明:压电柔性铰链定子的静态位移为7.95μm,固有频率为11.80 kHz。低频步进位移和高频平滑运动测试表明:原理样机的步进位移分辨力为100 nm,平滑运动速度为4.96 mm/s,负载力达到100 mN以上。原理样机基本满足多自由度跨尺度精密位移驱动的技术要求,在微纳光学检测等系统中具有良好的应用价值。

空心板桥加固技术及效果评估

某高速公路30 m多跨简支空心板桥运营多年后,桥面铺装层、空心板底板及腹板出现较多裂缝,部分铰缝出现破损。为确保桥梁结构承载能力、正常使用功能及耐久性,需对该桥进行维修加固。针对桥梁结构抗弯、抗剪及横向整体加固技术进行研究,经比选分析,确定在空心板底板粘贴碳纤维板提升抗弯承载力,增大空心板板端部截面提升抗剪承载力,在空心板顶、底板锚粘横向钢板条带提升横向整体性能。采用MIDAS Civil软件建立空心板桥整体有限元模型,评估总体加固效果,并分析铰缝总体损伤程度对空心板桥横向整体性能的影响。结果表明:上述加固方法能够有效提升空心板桥承载力及横向整体性能,其中抗弯承载力提高6%,抗剪承载力提高75%;在铰缝总体损伤不大于90%时,加固后的空心板桥具有较好的横向整体性能。