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.     

Tractable model for concave flexure hinges

In this article we prove that approximate solutions previously developed by us, with inverse conformal mapping, for concave flexure notch hinges rotational compliance in correct applications are accurate enough in comparison with the more complicated "precision" solutions for the conic profiles based on the integration of differential equations, finite element model, and experimental data at uncertainty within 10% or less. This is also true with the developed, in this article, simple computer aided evaluation of the approximating circles and their shift to contiguity even without its analytical expression and estimation of the hinge rotation instantaneous center position on this basis.     

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.     

Parabolic and hyperbolic flexure hinges: flexibility, motion precision and stress characterization based on compliance closed-form equations

The parabolic and hyperbolic flexure hinges are introduced as new rotation joints to be utilized in two-dimensional monolithic mechanisms. Closed-form equations are formulated for compliances to characterize both the active rotation and all other in- and out-of-plane parasitic motions. The stress levels are also evaluated in terms of compliances. Checked against finite element analysis and experimental measurement data, the model predictions are within 8% error margins. Further simulation is performed to compare geometrically-equivalent parabolic and hyperbolic flexure hinges. The results indicate that the parabolic flexures are more rotation-compliant and induce less stress, while the hyperbolic flexures are less sensitive to parasitic effects.     

Three flexure hinges for compliant mechanism designs based on dimensionless graph analysis

This paper presents the dimensionless empirical equations and graph expressions of three flexure hinges for compliant mechanism designs. The in-plane and out-of-plane stiffnesses of the flexure hinges are developed. The rotational precision, denoted by the midpoint stiffness, is derived for the purpose of optimized geometric design. Based on the developed methodologies, the influences of the geometric parameters on the performance of the flexure hinges are investigated, and the performance comparisons among the flexure hinges are conducted to further understand the characteristics of these kinds of compliant mechanisms.     

三种形状柔性铰链转动刚度的计算与分析

本文针对3种形状的柔性铰链进行力学分析，推导出它们各自绕z轴的转动刚度计算公式；通过计算、比较和分析得出柔性铰链中外形、几何尺寸等设计参数对转动刚度的影响程度。根据分析结果确定3种形状柔性铰链各自的微制造工艺及适用场合，为MEMS中柔性铰链的设计与应用提供一定的依据。     

单轴柔性铰链柔度系数试验装置的设计

为了在空间光学遥感器大尺寸反射镜柔性支撑结构的试验研究过程中获得柔度特性试验数据,设计了一种结构紧蹙的单轴柔性铰链试验装置,采用该装置在材料拉伸试验机上同时实现了端部弯曲和纯弯曲试验功能.该装置利用杠杆原理实现纯弯曲加载,并采用由刚性辊子组成的约束通道对纯弯曲组件进行约束,从而降低了摩擦对载荷传递的影响.试验过程的模拟...     

直圆柔性球铰柔度矩阵的解析计算

基于线弹性和小变形假设理论,通过引入比例系数(直圆柔性球铰槽口间距与切割半径倍数之比)并利用其结构对称的特点,推导得到了形式较为简洁的直圆柔性球铰柔度矩阵各子元素的解析柔度计算公式。利用有限元仿真软件验证了所推公式的正确性,并绘制了相应的误差曲线。结果表明:当比例系数小于0.2时,直圆柔性球铰各柔度计算公式的相对误差限均在11%以内;随着比例系数的增加,除沿x向的拉压柔度C11误差较小外,其他柔度计算公式的误差均呈增加的趋势,最大误差为30%。实验结果显示理论分析与仿真结果基本趋于一致,验证了直圆柔性球铰各柔度解析式的正确性。本文的研究内容为直圆柔性球铰在实际应用中的结构设计和参数优化奠定了理论基础。     

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.     

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.     

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。     

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.     

A generalized self-consistent estimate for the effective elastic moduli of fiber-reinforced composite materials with multiple transversely isotropic inclusions

The effective elastic properties of a fiber-reinforced composite material with multiple transversely isotropic inclusions are estimated by the use of a generalized self-consistent method, which considers strong interactions between the inclusion and matrix as well as among inclusions. The accuracy of this method is established by comparing to the closed-form analytic solutions by Christensen when the matrix and inclusion are isotropic. Furthermore, current predictions from the generalized self-consistent method for a composite with multiple inclusions correspond well with the numerical results from finite element analysis. The generalized self-consistent method can be particularly useful in establishing micromechanics models of natural biological composite materials such as cortical bone to examine the dependence of the elastic properties of cortical bone on its porosity.     

Improved analytical chip thickness model for milling

In this paper an analytic expression for chip thickness in milling was formulated while considering the cycloidal motion of the teeth, runout, and uneven teeth spacing. In order to generalize the equation, the cutting parameters associated with milling (linear feed, tool rotational speed, and radius) were combined into a single, non-dimensional parameter. The new parameter allowed abstraction of the milling process and enabled selection of the maximum possible chip thickness in milling. Equations for entry and exit angles of a cut were also developed. The chip thickness values given by the new model were compared to prior models and showed lower error levels.     

An analytical model for predicting battery lifetime

We used an analytical high-level battery model to estimate the battery lifetime for a given load.The experimental results show that this model to predict battery lifetime under variable loads is more appropriate than that under constant loads.     

A generalized mathematical model for the production and digitization of radiographic images

A generalized mathematical model has been developed for the production of a radiographic shadow image of a tested object followed by its conversion into a digital image using a specialized optical scanner. The model takes the staged transformation of the radiographic shadow image of the tested object into account.     

A constitutive model for transversely isotropic foams, and its application to the indentation of balsa wood

An elastic-plastic constitutive model for transversely isotropic compressible solids (foams) has been developed. A quadratic yield surface with four parameters and one hardening function is proposed. Associated plastic flow is assumed and the yield surface evolves in a self-similar manner calibrated by the uniaxial compressive (or tensile) response of the cellular solid in the axial direction. All material constants in the model (elastic and plastic) can be determined from a combination of a total of four uniaxial and shear tests. The model is used to predict the indentation response of balsa wood to a conical indenter. For the three cone angles considered in this study, very good agreement is found between the experimental measurements and the finite element (FE) predictions of the transversely isotropic cellular solid model. On the other hand, an isotropic foam model is shown to be inadequate to capture the indentation response.     

A hybrid analytical model for the transverse vibration response of a micro-end mill

As a result of its detrimental effect on tool life and product quality, vibration analyses are crucial if the full potential of micro-milling operation is to be attained. In this paper, a hybrid analytical model (HAM) developed for estimating the transverse response of a micro-end mill is presented. The HAM is a combination of discrete and distributed structural elements. The discrete elements account for the stiffness and damping coefficients of the machining system, while the distributed elements idealize the geometrical representation of the micro-end mill with a novel model of the micro-flute. A number of slot micro-end milling operations, carefully designed with the Taguchi method of design of experiments, are carried out to examine the accuracy of the HAM. The comparison of the response profile from the experiment and the developed model shows reasonably close similarity. The influence of the helix angle is found to be far greater on the response of the micro-end mill than the other geometric variables. By making use of the root mean square of the response, it is further observed that the representation of the micro-flute of the micro-end mill with a less accurate model deteriorates the prediction of the HAM.     

A disturbance observer-based adaptive control approach for flexure beam nano manipulators

This paper presents a systematic modeling and control methodology for a two-dimensional flexure beam-based servo stage supporting micro/nano manipulations. Compared with conventional mechatronic systems, such systems have major control challenges including cross-axis coupling, dynamical uncertainties, as well as input saturations, which may have adverse effects on system performance unless effectively eliminated. A novel disturbance observer-based adaptive backstepping-like control approach is developed for high precision servo manipulation purposes, which effectively accommodates model uncertainties and coupling dynamics. An auxiliary system is also introduced, on top of the proposed control scheme, to compensate the input saturations. The proposed control architecture is deployed on a customized-designed nano manipulating system featured with a flexure beam structure and voice coil actuators (VCA). Real time experiments on various manipulating tasks, such as trajectory/contour tracking, demonstrate precision errors of less than 1%.     

A dynamic model of humanoid robots using the analytical method

This paper presents a new approach to analyzing dynamic models of humanoid robots. This new approach is divided into an unconstrained system that applies the principle of Lagrangian dynamics and a constrained system that applies Gauss’ principle. Constrained motion is important in the design and analysis of humanoid robots. In this paper, the central issue in the determination of the constrained system is considered to be the determination of this constraint factor. Using the fundamental equation described by the proposed approach, the constraint equation can easily be generated. Based upon the fundamental equation, the dynamic model of the humanoid robot is explained as divided by the sagittal and frontal planes. The suggested approach simplifies designing dynamic models of humanoid robots which will obey the constrained system whether or not they are constrained, holonomic, or open chain.