椭圆柔性铰链柔顺机构的动力学建模与分析

以椭圆的离心角为积分变量,得到椭圆柔性铰链的转角计算的积分公式,推导出椭圆柔性铰链的刚度表达式.在此基础上针对一种应用广泛的含椭圆柔性铰链的柔顺机构,建立其动力学模型,得到该机构系统的固有频率计算公式.通过算例分析了该机构的各种参量对系统固有频率以及柔性铰链刚度的影响.     

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.     

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.     

Nonlinear modeling of compliant mechanisms incorporating circular flexure hinges with finite beam elements

Modeling of compliant mechanisms incorporating flexure hinges is mainly focused on linear methods. However, geometrically nonlinear effects cannot be ignored generally. This work shows that nonlinear behavior plays an important role in the deformation and stress analysis, which consequently impacts the design of compliant mechanisms. In this study a nonlinear higher order finite beam element based modeling approach is presented strongly reducing the computation time of nonlinear models. Planar deformation and mechanical stress of a single circular flexure hinge under a wide range of loads is modeled and computed with the proposed approach. A comparison with a 3D-nonlinear finite element model shows very good agreement and validates the beam model. It is shown that the linear and nonlinear deformation behavior of a single flexure hinge deviate marginally so that linear modeling approaches are sufficient. Furthermore a planar displacement amplification mechanism incorporating circular flexure hinges is studied by means of the same method highlighting the distinct deviation of the behavior of the geometrically nonlinear model from its linear prediction. In conclusion the nonlinear behavior at the system level can not longer be neglected. Finally, a study shows that different designs of the displacement amplification mechanism are achieved when linear or nonlinear modeling approaches are applied.     

Accurate low DOF modeling of a planar compliant mechanism with flexure hinges: the equivalent beam methodology

A methodology for accurate and efficient finite elements method (FEM) simulations of planar compliant mechanisms with flexure hinges is presented. First, using symmetry/antisymmetry boundary conditions and 3D elements, one-eighth of a single hinge is simulated to determine its true stress/stiffness characteristics. A set of fictitious beams is derived, which have the identical characteristics. This set is used in conjunction with other beams that model relatively stiff links to generate an equivalent model of an entire mechanism consisting of the beam elements only. The model has a low number of degrees-of-freedom (DOF) and appears to be more accurate than any 2D FEM models, even those with very large number of DOF. The methodology has been developed specifically for the right circular flexure hinge; however, it can be applied to all types of revolute flexure hinges.     

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...     

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.     

S形折叠式柔性铰链结构设计

为了减小柔性铰链的转动刚度,依据串并联关系,设计了S形折叠式柔性铰链。使用伪刚体法和能量法,建立了S形柔性铰链的刚度模型。利用ANSYS建立了该柔性铰链的有限元模型,对铰链进行了刚度和应力分析,并将其与理论值进行了比较,得到刚度误差约为3%,验证了刚度模型的准确性。当转角达到最大值±35°时,安全系数为4,符合设计要求。     

快速控制反射镜两轴柔性支撑平台刚度优化设计

基于椭圆弧柔性铰链兼顾了直梁型柔性铰链运动范围大和圆弧型柔性铰链运动精度高的特点,设计了基于椭圆弧柔性铰链的二维快速控制反射镜系统两轴柔性支撑平台。为使柔性支撑平台快速响应性好,即使其低阶固有频率最大化,对该柔性支撑平台进行了结构优化设计。理论推导了单个柔性铰链最大刚度与许用应力、转角和铰链参数的理论计算公式。然后,采用集总参数的分析方法,得出了两轴柔性支撑平台低阶最大固有频率的理论计算公式。由公式可知:在转动惯量一定的情况下,低阶固有频率最大化即为工作方向刚度最大化。最后,通过有限元仿真和实验检测验证了理论计算的准确性,得到的结果显示:柔性支撑平台的最大固有频率和最大应力的理论值与仿真值的相对误差小于5%,平台工作刚度的理论值与仿真值、实测值的相对误差分别为3.86%和5.75%。仿真和实验结果表明:利用本文推导的理论公式进行柔性支撑平台刚度优化设计,既可以满足工程设计要求,又能省去繁杂的有限元计算。     

Spatial force-based non-prismatic beam element for static and dynamic analyses of circular flexure hinges in compliant mechanisms

This paper presents a spatial force-based non-prismatic beam element modeling approach for circular flexure hinges, which is capable of accurate and efficient modeling of both static and dynamic characteristics of flexure-based compliant mechanisms. The spatial force-based non-prismatic beam element is an improvement and extension of the existing beam elements by considering shear and torsional effects of circular flexure hinge. The new consistent mass matrix formulation was derived using the Unit Load method. A parallel-guided compliant mechanism was taken as an example to validate the efficiency and accuracy of the proposed approach through static and modal analyses with fewer non-prismatic beam elements, and the results are well agreed with ANSYS simulation results with massive 3D solid or 2D shell elements. The developed approach is also available to model arbitrarily shaped flexure hinges in compliant mechanisms.     

Design and analysis of flexure-hinge parameter in microgripper

In the precision engineering field, a large number of applications require precise and microlevel manipulations, and microgrippers are an essential device to achieve precise manipulations. Highly precise movements are, in general, hard to achieve using conventional joints due to manufacturing error and backlash. In this paper, a new two-dimensional, compliant, monolithic piezo-actuated microgripper using flexure hinges is reported. The microgripper is designed, and a comparison study on stress and displacement is done by varying the hinge parameters such as the hinge radius, web thickness, position of flexure hinge, and radius of curvature of hinges. Kinematics of the microgripper is analyzed based on input/output displacement for all the above hinge design variations using FEM, and a kinematic model is arrived at based on the hinge location.     

直圆椭圆复合型柔性铰链研究

提出一种新型的单轴柔性铰链结构型式——直圆椭圆复合柔性铰链,它由半个直圆柔性铰链和半个椭圆柔性铰链构成。给出了直圆椭圆复合柔性铰链的柔度设计计算公式,并通过有限元方法验证了此公式的正确性。分析计算了一组不同椭圆短半轴的复合铰链实例,结果表明直圆椭圆复合柔性铰链的性能高于直圆柔性铰链。设计的直圆椭圆复合柔性铰链非常适合于需要大位移、高精度传动的应用场合。     

A generalized analytical compliance model for transversely symmetric three-segment flexure hinges

This paper presents a generalized compliance model for a three-segment notch flexure hinge with transverse symmetry. This flexure hinge configuration is most frequently employed in planar-motion, small-displacement compliant mechanisms. The axial and bending compliances are derived for this flexure hinge based on the compliances of two flexure components. The derivation is generalized such that it can be applied to various segment geometries. Using this open-ended model, a three-segment right elliptical corner-filleted flexure hinge design was analyzed. This geometric configuration introduces additional geometric parameters, which can be used to optimize the compliance of the flexure hinge without modifying its gross dimensions. The results of the analysis were validated in part by modifying the geometric parameters of the center segment and elliptical corner fillets to form limiting cases corresponding to several previously investigated configurations, namely right elliptical, three-segment right circular corner-filleted, and right circular geometries. Finite element analysis simulation and experimental testing were used to further validate the three-segment right elliptical corner-filleted analytical model. Additional simulations based on the analytical model were performed to highlight the influence of geometric parameters on compliances and to investigate shear effects for short flexure hinges.     

Design and fabrication of miniature compliant hinges for multi-material compliant mechanisms

Multi-material molding (MMM) enables the creation of multi-material mechanisms that combine compliant hinges, serving as revolute joints, and rigid links in a single part. There are three important challenges in creating these structures: (1) bonding between the materials used, (2) the ability of the hinge to transfer the required loads in the mechanism while allowing for the prescribed degree(s) of freedom, and (3) incorporating the process-specific requirements in the design stage. This paper presents the approach for design and fabrication of miniature compliant hinges in multi-material compliant mechanisms. The methodology described in this paper allows for the concurrent design of the part and the manufacturing process. For the first challenge, mechanical interlocking strategies are presented. For the second challenge, the development of a simulation-based optimization model of the hinge is presented, involving functional and manufacturing constrains. For the third challenge, the development of hinge positioning features and gate positioning constraints is presented. The developed MMM process is described, along with the main constraints and performance measures. This includes the process sequence, the mold cavity design, gate selection, and runner system development. A case study is presented to demonstrate the feasibility of creating multi-material mechanisms with miniature hinges serving as joints through MMM process. The approach described in this paper was utilized to design a drive mechanism for a flapping wing micro air vehicle. The methods described in this paper are applicable to any lightweight, load-bearing compliant mechanism manufactured using multi-material injection molding.     

柔性铰链的计算和分析

针对常用的直圆柔性铰链进行力学分析,与迄令一直沿用由J.M.PAROS给出的柔性铰链绕z轴的转动刚度(柔度)计算公式相比,提出了更为简洁、精确的转动刚度计算公式,使其有利于柔性铰链的设计和分析。对直圆柔性铰链所能承受的最大力矩和最大角位移进行了分析,给出了它们在不考虑应力集中影响下的计算公式。讨论了直圆柔性铰链各个参数对其性能的影响。为柔性铰链在精密定位系统中的应用提供了一定的理论基础。     

椭圆弧柔性铰链刚度简化计算及优化设计

本文主要研究了椭圆弧柔性铰链刚度的优化设计方法。首无,针对椭圆弧柔性铰链刚度计算公式过于复杂的问题,采用幂函数非线性曲线拟合的方法,推导了椭圆弧柔性铰链刚度的近似理论计算公式。然后,基于近似理论计算公式,分析了柔性铰链的精度特性及工作时的最大应力;采用GlobalSearch全域优化指令和Fmincon局域优化指令对椭圆弧柔性铰链工作方向的最大刚度进行了优化设计。最后,采用有限元仿真和实验验证的方法证实近似理论计算公式的适用性和优化结果的可靠性。验证显示:实验结果与近似理论计算结果的相对误差小于5%,表明提出的方法不仅省去了繁杂的有限元模型建立以及计算和修改的过程,大大提高了设计效率;而且通过优化计算可以得到椭圆弧柔性铰链的最大刚度。     

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。     

柔顺铰链的精度特性分析

以椭圆型铰链为基础,推导了单轴柔性铰链的几何中心偏移和转角计算公式,提出了将柔性铰链几何中心转角与偏移之比为精度系数这一概念,为定量地比较或设计柔性铰链提供了依据。通过椭圆型铰链结构参数变化算例,系统地比较了柔性铰链精度系数与其结构参数的关系,结果表明圆型铰链具有相对运动精度高的特性。     

传递矩阵法分析平面柔顺机构的振动特性

为了分析柔顺机构的动态性能和力学传递关系,提出一种新型的基于传递矩阵法的振动力学模型。柔顺机构由若干个柔性铰链与杆件顺序联接而成,采用传递矩阵法描述其力学状态量的传递关系。将柔性铰链视为拉伸和弯曲变形的弹性梁,应用材料力学理论建立反映其自振性能的传递矩阵。将杆件视为刚体,采用动量矩定理建立其动力学模型,得到描述振动刚体的传递矩阵。按照柔顺机构的联接形式,将每个元件的传递矩阵进行拼装,得到系统总传递矩阵。总传递方程以柔顺机构的边界点状态矢量为未知变量,矩阵中的元素为机构结构参数和频率的函数。应用边界条件,可得柔顺机构的特征方程,通过求解方程可得系统的固有频率和振型。将外力纳入传递矩阵,建立反映外力激励与系统的关系的扩展传递矩阵以求解系统的频率响应。通过2种常用平面柔顺机构的动态性能分析,结果表明所建立模型的正确性,能精确描述柔顺机构力学传递关系。     

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。