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-seale 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.

Higher mode effects in hinged wall with BRBsin base-frame structures using distributed parameter models

To investigate the effect of higher modes on the displacement and inner forces in HWBB(hinged wall with buckling-restrained braces in base)-frame structure,distributed parameter models for both the HWBB-hinged frame structure and the HWBB-MRF(moment resisting frame)structure are built.The hinged wall is simplified as a flexural beam.BRBs(bucking-restrained braces)are simplified to a rotational spring.MRF is simplified to a shear beam.Vibration equations of distributed parameter models are derived.Natural periods,natural modes of vibration,inner forces and displacements of the distributed parameter models are derived based on the vibration equations using numerical methods.The effect of the relative stiffness ratio and the rotational stiffness ratio on the higher mode effects is investigated.For elastic structures,the global displacement and shear in MRF are predominantly controlled by the first mode,while the shear and bending moment in the wall are significantly affected by higher mode effects.The effect of the yielding of BRB on the inner forces distribution in the HWBB-hinged frame is investigated.The results indicate that the first mode will no longer contribute to the inner forces and the contribution from higher modes to inner forces increases after the BRBs yield.Displacement is not sensitive to higher mode effects and it is controlled by the first mode after the BRBs yield.Parameter analysis demonstrates that the displacement amplitudes are reduced with the increase in the flexural stiffness of the wall before the flexural stiffness reaches a certain value.The first three periods decrease with the increase in the rotational stiffness.With the increase in the rotational stiffness ratio,the contribution from the first mode decreases while contributions from both the second mode and third mode increase.

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.

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。

考虑变墩高效应的小半径曲线梁桥地震易损性研究

为分析墩高变化形式对小半径曲线梁桥地震易损性的影响,以某互通式立交匝道桥第2联为背景,设计渐变型、凹岛型、凸岛型3种墩高变化形式曲线梁桥进行地震易损性研究。在提出的压弯剪扭耦合作用破坏的基础上,采用集中铰-纤维模型的桥墩建模方法,通过SeismoStruct有限元软件建立3种墩高变化形式曲线梁桥模型;选取符合Ⅲ类场地特性的50条地震波,利用能力需求比法,以位移延性比为损伤指标,研究不同变墩高形式下桥墩与支座的地震易损性。结果表明:当小半径曲线梁桥采用3种墩高变化形式时,以弯曲受力为主的中、高墩在地震作用下发生完全破坏概率较低,以弯剪或剪切受力为主的矮墩在强震作用下发生完全破坏概率较大,变墩高曲线梁桥可以适当提高矮墩的抗震能力;凹岛型墩高变化形式会增加矮墩的损伤概率,在抗震设计中应避免选择该墩高变化形式或尽可能优化墩梁连接方式;墩高变化形式对于支座的易损性影响小于对桥墩的影响。

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。

面向软材料搓动夹持的微夹钳设计与分析

为实现软材料在微纳尺度的夹持与搓动等操作,提出了一种基于压电驱动的具有搓动夹持功能的微夹钳装置。基于桥式放大器和杠杆机构的联合放大作用,增大了压电陶瓷驱动器输出端有限行程。通过正交布置的柔性铰链机构,实现搓动与夹持两自由度方向上的运动解耦。对机构的放大倍数和刚度等参数,建立了理论建模,并进行了有限元分析,验证了设计的合理性。夹持方向和搓动方向的位移放大倍数分别为11.30和8.11,行程分别达到了225,162μm,第一阶固有频率为164.81 Hz。

考虑弯剪耦合变形的矩形空心墩等效塑性铰模型

矩形空心墩因截面挖空导致抗剪性能削弱,塑性铰区弯剪裂缝显著,而既有等效塑性铰模型和等效塑性铰长度公式较少涉及弯剪耦合变形。为此,文章提出考虑弯矩梯度、拉伸漂移、应变渗透效应以及剪切变形的矩形空心墩曲率分布假定和墩顶位移计算方法,基于墩底塑性转角相等原则推导包含弯矩梯度、拉伸漂移和应变渗透效应的等效塑性铰长度理论公式和经验公式,并通过64个矩形空心墩试验数据对上述公式进行标定和验证。结果表明:规准等效塑性铰长度(L_(p)/h)随剪跨比、纵筋率及材料特性参数(f_(ul)/f_(yl)、f_(y1)d_(b)/√f'_(c))的增加而增大,与建议等效塑性铰长度经验公式的预测一致;规范和王震公式均高估了扣除剪切位移后的等效塑性铰长度,且会高估墩顶极限位移能力,使抗震设计偏于不安全;Berry公式计算的等效塑性铰长度略微保守,且能较准确地预测矩形空心墩的极限位移;而基于建议等效塑性铰长度经验公式和剪切位移占比系数经验公式的等效塑性铰模型,对矩形空心墩位移能力评估具有较高的计算精度和更小的离散性。

基于弥散裂缝理念的墩柱塑性铰区抗剪强度模型

为避免强震作用下钢筋混凝土墩柱发生弯剪破坏,需准确量化墩柱塑性铰区抗剪强度。然而,现行规范和既有文献的抗剪模型普遍假定斜截面箍筋初始全部屈服、箍筋抗剪贡献随配箍率线性增大并与混凝土抗剪贡献直接相加,且对纵筋抗剪贡献重视不够,与实际弯剪损伤演化和试验规律不符。为此,借助弥散裂缝理念将钢筋混凝土视作一种新型均质材料,基于莫尔应力圆推导一种符合弯剪损伤演化且考虑混凝土、箍筋、轴力、纵筋、剪跨比及位移延性系数等因素的抗剪强度模型,并通过139个矩形墩柱试验数据进行标定和验证。结果表明:Eurocode 8模型过高估计了墩柱抗剪强度,Caltrans模型抗剪计算结果略微保守,而《公路桥梁抗震设计规范》(JTG/T 2231-01-2020)模型的抗剪计算值与试验值较接近;相比规范模型,建议抗剪强度模型具有更高的计算精度和更小的离散性,抗剪强度折减系数取0.85时的安全保证率达85%,可用于矩形墩柱塑性铰区的抗剪能力评估。

基于椭圆形柔性铰链微克级单体式称量机构性能分析与优化

为了提高单体式称量机构的灵敏度,对微克级的单体式称量机构进行性能分析与优化,建立了基于椭圆形柔性铰链称量机构的数学模型;以称量机构的横梁末端位移来评价称量机构的灵敏度,通过在不同部分改变铰链厚度,分别验证椭圆形和圆弧形铰链对称量机构灵敏度的影响。结合Ansys Workbench有限元仿真软件对模型的准确确度进行了验证,给出了针对柔性铰链划分网格时的评价依据,结果表明:模型的最小误差为1.8%;且在1μg载荷下,椭圆形铰链相比于圆弧形增加了0.39 nm的末端位移。

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%。