静电梳微谐振子结构中的静力学问题

本文针对微机械领域中常用的静电梳微谐振子中存在的静力学问题 ,对其悬臂梁的两种结构——蟹脚型结构和直脚型结构的受力情况作了分析 ,推导出应力和位移的计算方法 ,并对蟹脚型结构的设计进行了优化 ,和国外文献进行了相比 ,它们更符合实际情况     

静电梳微谐振子蟹脚型结构的振动特性

运用梁的理论讨论了静电梳微谐振子常见结构———蟹脚型结构的振动特性 ,推导出计算蟹型结构谐振频率的计算公式 ,分析了各几何参量对结构谐振频率的影响 ,并和静电梳微谐振子的另一种常见结构———直脚型结构的振动特性进行了比较。得到的结论对静电梳微谐振子的设计具有指导意义     

静电梳微谐振子蟹脚型结构的振动特性

运用梁的理论讨论了静电梳微谐振子常见结构－蟹脚型结构的振动特性,推导出计算蟹型结构谐振频率的计算公式,分析各几何参量对结构谐振频率的影响,并和静电梳微谐振子的另一种常见结构－直脚型结构的振动特性进行了比较,得到的结论对静电梳微谐振子的设计具有设计具有指导意义。     

静电梳微谐振子直脚型结构的振动特征

静电梳微谐振子是微机械领域常用的直线型驱动装置。运用梁的理论讨论了一种常用的结构－直脚型结构的振动特性,提出了计算机结构谐振频率的实用算法。并探讨了影响谐振频率的几何参数,得到的结论对静电梳微谐振子的设计具有指导意义。     

静电梳微谐振子直脚型结构的振动特性

静电梳微谐振子是微机械领域常用的直线型驱动装置。运用梁的理论讨论了一种常见的结构———直脚型结构的振动特性 ,提出了计算结构谐振频率的实用算法。并探讨了影响谐振频率的几何参数 ,得到的结论对静电梳微谐振子的设计具有指导意义     

静电梳状硅微单侧直脚谐振器的力学性能

建立单侧支撑直脚型静电梳状硅微谐振器的三次超静定简化力学模型,给出该模型中谐振频率、弹性系数和横向最大位移的计算公式.与五次超静定系统的双侧支撑直脚型静电梳状硅微谐振器的各力学性能参数的计算公式对比发现它们有显著差别.分析表明,与双侧支撑直脚型静电梳状硅微谐振器显著不同,单侧支撑直脚型静电梳状硅微谐振器的谐振频率、弹性系数、横向最大位移会随两根支撑梁的间距变化而改变,并当此间距超过某一值后,上述三变量的变化均很小且趋向于一定值.同样,后者的谐振频率会随支撑梁厚度的变化而单调改变,这也是前者所没有的现象.为此从两者因为超静定次数不同而约束冗余度不同的角度,对此现象进行了物理意义上的解释.经与试验结果对比,单侧支撑直脚型静电梳状硅微谐振器横向谐振频率的理论值与实测值吻合较好,最大误差为12.07%.     

不同型式支撑的静电硅微谐振器的性能比较

针对直脚型、蟹脚型、之字型和弓型四种支撑梁结构型式的静电梳状谐振器,介绍了符合问题实质的五次超静定力学模型,给出了横向谐振频率、弹性系数和位移随谐振器结构参数和材料参数变化的函数关系。经与试验结果对比,各类谐振器横向谐振频率的理论值与实测值吻合较好,最大误差为11.62%。比较分析表明:在特征尺寸相同的情况下,直脚型、蟹脚型、之字型和弓型静电梳状谐振器的横向谐振频率依次减小,且都与谐振器的厚度无关;在特征尺寸和驱动电压相同的情况下,直脚型、蟹脚型、之字型和弓型静电梳状谐振器的横向位移输出能力依次增加;直脚型、蟹脚型、之字型和弓型静电梳状谐振器的横向弹性系数,均只与材料的杨氏模量和支撑梁的几何参数有关,而与横向位移无关。     

激光直写法制备仿刚毛微纳阵列的研究

提出一种采用激光直写技术制备微纳阵列的新方法来制备仿壁虎刚毛二级结构微阵列。该制备过程由计算机控制完成。实验制备出具有不同几何尺寸的一级结构阵列,并在此基础上探索制备二级结构微阵列的三种方案,其中,“自上而下”的方案通过对曝光时间和显影时间的控制使第二级结构扎根于第一级结构中,有效提高了两级结构间的连接强度。制备实验的同时,分析了曝光时间、显影时间等参数对阵列制备的影响。激光直写制备微纳阵列的方法具有高效率、低成本的优点。     

脚型解剖学标志点自动标识方法

针对现有标志点提取方法的不足,提出一种自动标识人体脚型解剖学标志点的有效方法,该方法以包含解剖学标志点的三维数字脚型作为变形模板.通过主成分分析(Principle component analysis,PCA)和迭代最近点(Iterative closest point, ICP)算法使目标脚型与模板脚型在最小二乘意义上对齐与配准,找出目标脚型与模板脚型之间的初始对应点集.采用以均匀采样和基于曲率分布的采样相结合的方法在模板脚型上获取采样点集,以采样点集在目标脚型上的对应点为位置约束,采用基于离散拉普拉斯的网格变形方法,使模板脚型逼近目标脚型.通过迭代,使模板脚型在误差范围内逼近目标脚型,这时模板脚型上的点与目标脚型上的对应点建立了映射关系,模板脚型上的解剖学标志点在目标脚型上的对应点即可视为目标脚型上的解剖学标志点.试验结果表明,基于模板的脚型解剖学标志点标识方法,自动化程度高,适应性强,能够应用于脚型的三维形态差异分析和基于脚型的鞋楦个性化定制系统.     

之字型支撑梁硅微谐振器机械性能分析

与相同几何尺寸的其他支撑形式相比,之字型支撑梁降低了硅微谐振器的谐振频率。通过对之字型支撑梁硅微谐振器的力学建模分析,发现其为5次超静定问题,在此基础上得出了谐振频率等重要的性能参数随几何参数的变化关系。分析结果表明,在保证支撑梁垂直长度不变的条件下,对固定的折弯次数n,谐振频率fx 随折弯角度φ的增大而增大;对固定的折弯角度φ,谐振频率fx 随折弯次数n的增大而趋于一个固定值;φ=90°时则等效于双侧直脚型微谐振器。     

Design and stiffness analysis of a compliant spherical chain with three degrees of freedom

This paper introduces and investigates a compliant spherical 3R open chain that is obtained by the in-series connection of three identical circularly-curved beam flexures with coincident centers of curvature and mutually orthogonal axes of maximum rotational compliance. The considered open chain is intended to be used directly as a spherical mechanism in pointing devices or as a complex spherical flexure for the development of spatial parallel manipulators. The compliance matrix of the proposed chain is first determined via an analytical procedure. After finite element validation, the obtained equations are used in a parametric study to assess the influence of circularly-curved beam flexure geometric parameters on the overall stiffness performances of the considered compliant spherical 3R open chain. In addition, comparison with an equivalent compliant spherical chain employing straight beam flexures is reported to highlight the added benefits of using circularly-curved beam flexures in terms of reduced parasitic motions.     

A spatial closed-form nonlinear stiffness model for sheet flexures based on a mixed variational principle including third-order effects

The sheet flexure is commonly used to provide support stiffness in flexure mechanisms for precision applications. While the sheet flexure is often analyzed in a simplified form, e.g. by assuming planar deformation or linearized stiffness, the deformation in practice is spatial and sufficiently large that nonlinear effects due to the geometric stiffness are significant.This paper presents a compact analytical model for the nonlinear stiffness characteristics of spatially deforming sheet flexures under general 3-D load conditions at moderate deformations. This model provides closed-form expressions in a mixed stiffness and compliance matrix format that is tailored to flexure mechanism analysis. The effects of bending, shear, elongation, torsion and warping deformation are taken into account, so that the stiffness in all directions, including the in-plane lateral support direction, is modeled accurately. The model is verified numerically against beam and shell-based finite elements. The approach for deriving closed-form solutions in a nonlinear context is detailed in this paper. The Hellinger–Reissner variational principle with a specific physically motivated set of low-order interpolation functions is shown to be well-suited to the geometrically nonlinear analysis of flexures.An extension of the derivation approach to the nonlinear closed-form analysis of general flexure mechanisms consisting of multiple sheet flexures connected in parallel is presented. This is demonstrated with the case of a spatially deforming parallelogram flexure mechanism and a cross-hinge flexure mechanism.     

Lattice flexures: Geometries for stiffness reduction of blade flexures

Reducing the motion-direction stiffness of compliant mechanisms reduces their actuation effort and simplifies associated static balancing mechanisms. This work introduces a flexure type called lattice flexures and evaluates some of their fundamental properties. Lattice flexures have a reduced bending stiffness when compared to traditional rectangular-section blade flexures of similar size. The motion-direction bending stiffness of two lattice flexure types, called X-type and V-type, are analytically derived, corroborated with finite element analysis, and validated with measurements of physical prototypes. The lattice flexure has the potential to reduce the bending stiffness of some compliant mechanisms by 60–80%, as demonstrated in devices manufactured using 3D printing technologies. It is shown that some lattice flexures exhibit a torsional/bending stiffness ratio as much as 1.7 times higher than an equal aspect-ratio blade flexure, and a transverse bending/motion-direction bending stiffness ratio up to 6.5 times higher than an equal aspect-ratio blade flexure.     

Aeroelastic stability analysis of hingeless rotor blades with composite flexures

The flap-lag-torsion coupled aeroelastic behavior of a hingeless rotor blade with composite flexures in hovering flight has been investigated by using the finite element method. The quasi-steady strip theory with dynamic inflow effects is used to obtain the aerodynamic loads acting on the blade. The governing differential equations of motion undergoing moderately large displacements and rotations are derived using the Hamilton’s principle. The flexures used in the present model are composed of two composite plates which are rigidly attached together. The lead-lag flexure is located inboard of the flap flexure. A mixed warping model that combines the St. Venant torsion and the Vlasov torsion is developed to describe the twist behavior of the composite flexure. Numerical simulations are carried out to correlate the present results with experimental test data and also to identify the effects of structural couplings of the composite flexures on the aeroelastic stability of the blade. The prediction results agree well with other experimental data. The effects of elastic coupling such as pitch-flap, pitch-lag, and flap-lag couplings on the stability behavior of the composite blades are also investigated.     

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.     

A novel flexure beam module with low stiffness loss in compliant mechanisms

Flexure mechanisms provide guided motion via elastic deformation of thin beams. Due to the employment of compliant elements, these mechanisms cannot sufficiently maintain acceptable constraint stiffness level in the entire range of motion. The stiffness deterioration afflicts the performance of flexure mechanisms in terms of motion range, accuracy and constraint characteristics. This paper presents a novel flexure beam module with improved constraint behavior in beam-based flexure mechanisms. The proposed module alleviates the problem of stiffness loss in large displacements and provides a better motion performance. The mathematical model governing the static behavior of the module is developed using the principle of virtual work. The geometric nonlinearity associated with large midplane stretching is taken into account. Closed-form solutions are derived for load-displacement relationships, providing a powerful design tool for the novel flexure. Also a nonlinear expression is obtained for the strain energy of the flexure in terms of end displacements. The functionality of the presented module is exploited in a multi-beam parallelogram mechanism. The constraint behavior of the parallelogram is analytically quantified and considerable improvements in stiffnesses and error motions are observed. The analytical results provided in this paper are verified via finite element simulations. The proposed novel module can be used as the building block of more complex flexures to improve their stiffness characteristics, diminish their error motions and widen their stability region.     

新型六足爬行机器人设计

采用了仿哺乳类的腿部结构,并针对这种腿部结构设计了六足的行走方式,通过对12个步进电机的控制,采用三角步态,实现了六足机器人的直行功能.仿真及试验证明,这种结构能较好地维持六足机器人自身的平衡,并且对今后更深入地研究六足机器人抬腿行走姿态及可行性,具有较高的参考价值.     

Combining cross-pivot flexures to generate improved kinematically equivalent flexure systems

We show that new kinematic equivalents with improved performance of standard flexure elements can be systematically synthesized by combination of cross-pivot flexures. Cross-pivot flexures provide a unique feature of kinematic stability under both high loading and large displacement conditions which can be exploited to synthesize a range of kinematic equivalents to standard flexure elements which retain much greater stiffness, load capacity and range capacity than the traditional elements. Cross-pivot synthetic elements provide a means to expand the performance of a large range of flexure-based structures including motion stages, manufacturing equipment and optical systems. This could result in better data collection, smaller systems, and less distortion in operation.     

Compound joints: Behavior and benefits of flexure arrays

Because compliant mechanisms achieve their motion through deflection of flexible members, they have a limited range of motion and finite stiffness. Many common flexure geometries also suffer from a non-stationary center of rotation. These properties can be obstacles to their adoption in applications that require large displacements, low stiffness, or stationary centers of rotation. This work presents the concept of compound flexures: by assembling arrays of flexures, we can increase range of motion, decrease stiffness, and reduce center shift. We first develop the theory behind some of the basic behavior of compound joints. Then finite element analysis is used to explore other aspects of compound joint behavior such as off-axis stiffness and quantifying the center shift for two flexure types when used in compound joints of various configurations. It is shown in an example that range of motion can be doubled with no appreciable loss in off-axis stiffness, while the desired stiffness κ_θz remains unchanged. A method is presented to achieve zero center shift for a specified rotational displacement. Compound joints are shown to exhibit greater ranges of motion, higher off-axis stiffness, and reduced center shift compared to traditional joints.     

Experimental measurement of the bearing characteristics of straight-line flexure mechanisms

In this paper, we present an experimental set-up and procedure to accurately measure the bearing characteristics of any single Degree of Freedom (DoF) straight-line flexure mechanism. Bearing characteristics include stiffness in the bearing and motion directions, and error motions in the bearing directions. In particular, we present this characterization for the traditional paired double parallelogram (DP-DP) flexure and its recently-reported improved variation, the clamped paired double parallelogram (C-DP-DP) flexure. Of particular interest is the bearing direction stiffness and its variation with motion direction displacement. While the bearing stiffness for both mechanisms has been extensively predicted via analysis and its consequences have been observed in experiments, its direct measurement poses several challenges and is not found in the literature. This paper presents an experimental set-up that is reconfigurable to accommodate both the above two flexures, comprises a novel virtual pulley concept, and employs carefully selected ground mounting and sensor locations, among other features that enable the desired measurements. The experimental results agree well with analytical predictions and generate insight into the importance of ground mounting, finite compliance of mechanism features that are generally assumed to be rigid, and manufacturing tolerances.