椭圆导角混合柔性铰链的设计计算与性能分析

为满足柔顺机构的大柔度要求,设计了一类新型椭圆导角混合柔性铰链。首先,以卡氏第二定理为基础推导了柔度和回转精度的计算公式,在参数的极限条件下,椭圆导角结构演化出其他三种铰链形式：直圆导角、椭圆直圆和直圆柔性铰链,使得多种柔性铰链的柔度和回转精度的计算公式合并在一组方程中,通过有限元分析验证了计算公式的正确性。其次,讨论了结构参数对柔度、回转精度和柔度精度比的影响趋势,分析结果表明,柔度与回转精度随参数的变化趋势具有相反性,且减小最小厚度是提高柔度的最佳方式。再次,比较了所提四种柔性铰链的性能,椭圆导角混合柔性铰链具有最大的柔度但回转精度较低,而直圆柔性铰链具有较高的回转精度且综合性能也较优越,但柔度最小。最后,对椭圆导角和直圆柔性铰链进行了应用研究,研究结果表明,椭圆导角混合柔性铰链在回转能力和应力水平方面具有显著优势。     

基于柔度比优化设计杠杆式柔性铰链放大机构

分析与研究了柔性铰链的柔度特性,用于柔性放大机构的优化设计。提出了一个通用的柔度比参数λ,探讨了具有不同柔度比λ的柔性铰链主要输出位移形式的灵敏度,分析了它对常用柔性铰链的柔度特性的影响规律。然后,以柔性铰链的柔度比λ为基本参数,在考虑柔性铰链转动中心偏移量的基础上,推导了二级杠杆式柔性铰链放大机构放大率的理论计算方法,并依据柔性铰链的柔度比特性提出了柔性放大机构的优化设计方法。开展了有限元仿真和实验研究。结果显示,优化后的柔性放大机构的放大率比优化前的放大率分别提高了0.234和0.23。实验表明,依据柔性铰链的柔度比λ对柔性放大机构进行优化设计能够有效地提高柔性放大机构的位移放大率与工作行程,进而提高放大机构的末端运动及定位精度。     

微位移放大机构的分析与计算

基于力学理论提出一种通用的柔性铰链柔度的计算方法,适用于各种切口形状的单轴和多轴柔性铰链的设计计算。推导出直圆柔性铰链在平面受力状态下的柔度计算公式,并分析了直圆柔性铰链结构参数与性能的关系。分析一种微位移放大机构的结构与工作原理,推导出微位移放大机构获得较大输出位移时,机构中两直圆柔性铰链结构参数应满足的关系,计算结果表明本文方法正确有效。     

Design and analysis of a multi-notched flexure hinge for compliant mechanisms

This article presents a new multi-notched flexure hinge, which consists of two right circular and two parabolic notches, for positioning stages based on compliant mechanisms. First, the configuration of the presented multi-notched hinge is obtained using topology optimization, and the final shape is proposed based on post-processing. Second, the dimensionless empirical equations for the stiffness, rotational precision and stress levels of the flexure hinges are developed using finite element analysis (FEA). Third, based on the established equations, the influences of the geometric parameters on the performance of the flexure hinge are investigated. Finally, to further understand the characteristics of this type of flexure hinge, comparisons with flexure hinges of various shapes are performed in terms of stiffness, rotational precision and stress levels.     

混合型柔性铰链构型设计与柔度建模

通过将对称型柔性铰链进行分段和命名,提出一种基于柔性铰链基段和镜像段串联组合的混合型柔性铰链构型设计方法。基于卡式第二定理,将基段柔度建模转化成与其槽口形状函数有关的定积分问题。推导得到镜像段与其基段间的柔度映射和多段基段的柔度矩阵,进而构建出形式统一的两段混合型柔性铰链通用柔度和精度模型。选取圆锥曲线、矩形梁和棱台型基段类型,基于组合设计共获得96种新型混合型柔性铰链。结合具体算例和借助有限元验证理论模型的正确性,并对所设计和现有的柔性铰链构型性能统一进行评价分析。研究工作可为柔性铰链构型优选和特性评价提供理论指导。     

基于挠曲线方程的柔性铰链转动柔度公式推导

利用材料力学和微积分的理论推导出了常用直圆柔性铰链转动柔度的计算公式,与至今一直沿用由J.M.PAROS给出的精确柔度计算公式相比,更简洁准确,更有利于直圆柔性铰链的设计和分析。并分析了直圆柔性铰链的结构参数对其柔度的影响,为直圆柔性铰链在压电微位移放大中的应用提供了一定的理论基础。     

基于三角原理的压电驱动微位移定位机构的设计与分析

设计了一种基于三角原理的精密柔性定位机构,机构由压电叠堆作为驱动元件,经由柔顺机构输出缩小的位移。首先说明了机构的设计原理,然后设计了柔顺机构的结构,进行了理论计算和有限元分析,最后在试制的样机上进行了静态特性的实验,结果表明该柔顺机构可以实现预期的运动。     

Topology optimization of flexure hinges with a prescribed compliance matrix based on the adaptive spring model and stress constraint

This paper focuses on the configuration design of flexure hinges with a prescribed compliance matrix and preset rotational center position. A new method for the topology optimization of flexure hinges is proposed based on the adaptive spring model and stress constraint. The hinge optimization model is formulated by maximizing the bending displacement with a spring while optimizing the compliance matrix to a prescribed value. To avoid numerical instability, an artificial spring is used as an auxiliary calculation, and a new strategy is developed for adaptively adjusting the spring stiffness according to the prescribed compliance matrix. The maximum stress of flexure hinge is limited by using a normalized P-norm of the effective von Mises stress, and a position constraint of rotational center is proposed to predetermine the position of the rotational center. In addition, to reduce the error of the stress measurement, a simple but effective filtering method is presented to obtain a complete black-and-white design. Numerical examples are used to verify the proposed method. Topology results show that the obtained flexure hinges have the prescribed compliance matrix and preset rotational center position while also meeting the stress requirements.     

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.     

Two general solutions of torsional compliance for variable rectangular cross-section hinges in compliant mechanisms

Several approaches exist for calculating the torsional compliance of rectangular cross-section beams, but most depend on the relative magnitude of the cross-section thickness and width, which might be changing during the design phase (especially for design optimization) or is variant for variable cross-section beams such as circular flexure hinges and tapered bars. After summarizing current equations and analyzing their computational accuracy, two new equations are proposed, which are thickness-to-width ratio independent, and suitable for variable cross-section beams and optimization design of torsional elements in compliant mechanisms. The closed-form equations for the torsional compliance of elliptical and circular flexure hinges are derived by using the new equations.     

柔性铰链转动刚度计算公式的推导

柔性铰链作为无摩擦的支点有着成千上万的应用，以力学的基本公式和微积分为基础，给出了一般柔性铰链转动刚度计算公式的推导过程。在此基础上，得出了常用的直圆柔性铰链的设计计算公式，计算公式是精确的推导结果，且在表达上较迄今沿用的Paros给出的柔性铰链精确设计计算公式来得简洁，有利于柔性铰链及其机构的计算和分析。当直圆柔性铰链的切割半径与最小厚度相当时，Paros给出的简化公式存在一定的误差，这里的计算公式尤其适用于该类直圆柔性铰链。     

A modified post-processing technique to design a compliant based microgripper with a plunger using topological optimization

The precision of microobject manipulation is predominantly based on the appropriate design of micromanipulation devices such as microgrippers. A compliant mechanism-based microgripper is an appropriate choice to achieve a highly precise and controlled motion. This research article proposes a refined technique to design a compliant-based microgripper with a plunger. The topological optimization technique has been adopted in this research work to develop the conceptual design of the mechanism. Flexure hinges are introduced in the topologically optimized design to overcome the senseless regions developed during the optimization process which is highly complicated to manufacture. Various flexure hinge contours such as rectangular, circular, and elliptical are introduced in the conceptual design domain, and their effects are investigated. Various parameters of flexure hinges are considered; the stress, the displacements, and the strain energy stored in the mechanism are studied through finite element analysis (FEA). In addition to FEA, experimental verification of the design was also performed. Both results are convincing about the structural performance of the microgripper design. In general, microdevices possess higher surface forces than volumetric forces; hence, this design is introduced with a plunger segment which is used to push the microobject for an active release during micromanipulation.     

A novel analytical model for flexure-based proportion compliant mechanisms

This paper proposes a novel analytical model for flexure-based proportion compliant mechanisms. The displacement and stiffness calculations of such flexure-based compliant mechanisms are formulated based on the principle of virtual work and pseudo rigid body model (PRBM). According to the theory and method, a set of closed-form equations are deduced in this paper, which incorporate the stiffness characteristics of each flexure hinge, together with the other geometric and material properties of the compliant mechanism. The rotation center point for a corner-filleted flexure hinge is investigated based on the finite element analysis (FEA) and PRBM. An empirical equation for the rotational angle is fitted in this paper in order to calculate accurately the position of the end-point of the flexure hinge. The displacement proportion equation for such mechanisms is derived according to the new approach. Combining the new proposed design equation and the existed stiffness equation, a new proportion compliant mechanism with corner-filleted flexure hinges is designed by means of the least squares optimization. The designed models are verified by finite element analysis.     

Modeling and analysis of an over-constrained flexure-based compliant mechanism

Bridge-type micro-displacement amplifier with flexure hinges is a classic displacement amplification mechanism. Existing theoretic models cannot predict its amplification ratio and input stiffness accurately and make it very difficult to confirm the amplifier’s performance and error compensation by means of these models, which is very significant in ultra-precision positioning. This paper focuses on the development of design equations that can accurately calculate the ideal displacement amplification ratio and input stiffness of the amplifier based on the thought of statically indeterminate structure. Force Method, Maxwell–Mohr Method, principle of superposition and deformation compatibility are used together to establish uncanonical linear homogeneous equations. The analytical results are verified by FEA simulations. The influence of the geometric parameters on the amplifier performance is investigated. It is noted that amplifier performance is more sensitive to the longitudinal distance of flexure hinges. Besides, two same-sized amplifiers with the opposite output directions can be clearly differentiated by these equations.     

NANO-BEARING： THE DESIGN OF A NEW TYPE OF AIR BEARING WITH FLEXURE STRUCTURE

A new type of air bearing with flexure structure is introduced. The new bearing is designed for precision mechanical engineering devices such as mechanical watch movement. The new design uses the flexure structure to provide 3D damping to absorb shocks from all directions. Two designs are presented: one has 12 T-shape slots in the radian direction while the other has 8 spiral slots in the radian direction. Both designs have flexure mountings on the axial directions. Based on the finite element analysis (FEA), the new bearing can reduce the vibration (displacement) by as much as 8.37% and hence, can better protect the shafts.     

另一类椭圆柔性铰链

本文提出了一类椭圆柔性铰链——深切口椭圆柔性铰链,其切口的宽度为椭圆的短轴,而切口的深度为椭圆的长半轴。基于材料力学中的变截面梁的弯曲理论,通过引入离心角作为积分变量,推导了计算这类柔性铰链柔度、转动精度和最大应力的计算公式,这些公式具有简洁、规范等特点,非常有利于工程设计中的计算和分析。最后,用有限元分析软件ANSYS分析了多个不同尺寸的椭圆柔性铰链。有限元方法分析结果与此解析计算公式的计算结果与吻合得很好,说明了这些解析计算公式的正确性。研究表明,这类铰链非常适合于要求高精度传动的应用场合。     

Note: Rotational compliance and instantaneous center of rotation in segmented and V-shaped notch hinges

This note shows a technique for the calculation of rotational compliance (stiffness) and develops a generalized mathematical model for the virtual center of rotation position in concave, segmented, and V-shaped notch hinges using Chebyshev's polynomials. The calculational results are in a good agreement with experimental data and finite element model verified output with estimated differences of less than 10%. This agreement shows that our tractable model is a general one for rotational compliance and the evaluation of a virtual center of rotation position in any type of concave flexure notch hinges.     

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.     

Note: Bending compliances of generalized symmetric notch flexure hinges

The bending compliances of generalized notch flexure hinges with transverse or transverse-and-axial symmetry are studied in two particular reference frames. For an end-point reference frame, the cross compliance and the rotary compliance are proportional. When the reference frame is placed at the flexure's midpoint, the cross compliance is zero. The translatory and rotary compliances of only half the flexure hinge are sufficient to calculate the overall compliances of a transverse-symmetry flexure configuration. Similarly, the overall bending compliances of a flexure hinge with transverse-and-axial symmetry require prior calculation of the translatory and rotary compliances of a quarter flexure solely.     

椭圆柔性铰链的柔度计算

基于材料力学中的变断面梁的弯曲理论,通过引入椭圆离心角作为积分变量,直观地得到椭圆柔性铰链的系列柔度计算公式。通过定义中间参数,推导出较为简洁的解析计算公式,从而避免费时的数值积分,便于柔性铰链柔度的计算和分析。当椭圆切口的长轴和短轴长度相等时,椭圆柔性铰链变成直圆柔性铰链,这些计算公式即退化为直圆柔性铰链的柔度计算公式。运用有限元软件ANSYS分析多个不同形状的椭圆柔性铰链,有限元法分析结果与这些柔度计算公式的计算结果吻合得很好,证明了公式的正确性。