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.     

卫星天线臂结构优化设计的分级遗传算法

为满足刚度大、强度高、质量小的设计要求,本文针对卫星天线臂的结构优化设计提出了分级遗传算法。首先,依据设计与制造要求,将天线臂结构优化设计分解为拓扑构型与杆件尺寸两级优化问题。然后,将单元材料相对密度作为基因,整体结构的相对密度作为染色体,将刚度与质量转化为适应度函数,形成拓扑构型的遗传算法。其次,在保持拓扑构型不变的条件下,将组成拓扑构型的各杆件的剖面面积作为设计变量,杆件结构的质量作为目标函数,形成杆件尺寸优化模型,通过引入遗传算子,形成第二级遗传算法。最后,给出了某卫星天线臂结构优化设计实例,证实了本文分级遗传算法的有效性。     

基于参数化的机械产品尺寸变型设计研究与实现

在分析当前三维参数化设计技术的基础上，结合CAD系统、参数化思想和层次型数据表技术，提出了一种产品级的参数化变型设计方法。利用SolidEdge变量表、Acess数据库和VB语言，开发了基于SolidEdge的产品参数化变型设计系统。以注塑机的合模部件为例，演示了所提出的方法和开发系统的实际应用。     

基于子结构法的多层级结构拓扑优化

为避免多层级结构拓扑优化中的尺度分离问题,保证不同多孔结构之间的连接性,提出了一种基于子结构法的多层级结构拓扑优化方法。采用参数化水平集方法,将多孔结构拓扑优化分为两个层级,在细观层级优化多孔结构拓扑构型,在宏观层级优化多孔结构最优空间分布。采用子结构法建立宏细观结构之间的联系,将细观结构凝聚为超单元,凝聚的超单元又作为宏观结构分析和优化的基本单元。数值算例表明：所提方法可有效实现二维、三维多层级结构的拓扑优化;在多层级结构设计中考虑多种类型的多孔结构时,所提方法能有效保证不同多孔结构之间的连接性。     

航天器桁架结构快速设计方法研究

随着航天事业的发展,桁架作为航天器主承力结构应用越来越广泛,并呈现大型化复杂化的发展趋势。传统模式下航天器桁架结构设计效率低下,无法适应“快速响应约束,迭代更新高效”等应用要求,制约桁架结构的发展。针对这一现象,文中基于自顶向下(Top-Down)设计模式和参照柔性相关思想,提出了航天器桁架结构快速设计方法,并进行了验证。结果表明,航天器桁架结构快速设计方法逻辑关系明确,简便实用,能够实现结构元件自动创建和装配,快速响应外部约束并自适应更新,能确保设计状态的迭代有效可控,显著提升桁架结构设计效率,可推广应用于航天器桁架结构设计。     

基于Mathcad求弹性梁弯曲问题的数值解

提出一种求解受复杂载荷作用的弹性梁弯曲问题数值解的新方法。该方法利用奇异函数表示弹性梁的弯曲内力和弯曲变形方程,与梁的边界条件和连续条件联立,应用数学软件Mathcad中相应的求解块和绘图工具,可以快速获得弹性梁的支座约束力、任意截面的剪力和弯矩、挠度和转角等参数以及相应的曲线图。该方法无需编程,既适用于静定或超静定梁,也适用于等截面或变截面梁,为梁的强度和刚度校核以及优化设计等提供了新途径。     

基于虚拟构架模型分析手指包容抓取内力

在手指包容抓取物体时的内力分析中 ,基于虚拟构架模型来分析手指抓取内力 ,手指任一接触点处的内力通常能分解成该构架虚拟连接点两个 (二维平面 )或三个 (三维空间 )杆轴方向的分力 ,由虚拟构架内力 ,我们给出了二手指和三手指内力表达式。这种内力分析法为处理机器人手的抓力大小、操作规划与优化以及力控制设计等问题提供了理论基础     

The minimum weight structural configuration of pin-jointed truss cantilevers of given external shape

The minimum weight configuration of a statically determinate cantilever truss of known external shape is formulated as a non-linear mathematical programming problem which can be solved using Dynamic Programming. The recursive equations lead to a closed-form solution for equal permissible stresses in tension and compression, and weight comparisons with the thin webbed beam, the Warren truss, and the equivalent Michell structure are presented.When the design criteria are tensile yield or buckling under compressive load, numerical tabulations are required in the solution. But it is demonstrated, by way of an example, that many aspects of practical problems can be accommodated with relative ease using this approach.     

并联机器人机构构型创新设计研究

提出一种并联机器人机构构型创新设计新方法——桁架推演法,该方法包括三个主要步骤：根据具体设计需求选择自由度为0的并联机构桁架,并选择适当的推演规则;在一定的约束条件下对桁架进行推演;对推演结果分析、判断和决策,得到新并联机构构型。最后举例说明了桁架和推演规则等对并联机器人机构构型创新设计具有决定性影响的关键技术问题。     

Dispersive equations for high resolution imaging and lattice fringe artifacts

The imaging equations for high resolution electron microscopy are analysed using an approach based upon expanding the electron wave as positionally modulated diffraction beams. A high-order semi-linear approximation is derived which includes the leading non-linear effects of a reciprocal space integration and can be conveniently expressed in real space. This allows a direct visualisation of imaging effects in real space using a conventional wave dispersion approach. Based on this, the primary sources of lattice fringe artifacts and errors in the 2$\text{1}\text{2}$D technique are briefly discussed, and an experimental technique for guarding against them employing dark field imaging is described.     

一种9杆巴氏衍架的装配形态研究

选定其中的一个 5元构件为固定构件 ,对一种 9杆巴氏衍架装配形态进行了分析。如果将该固定构件去掉 ,这一问题等同于一个平面 8杆 12副阿苏尔杆组的位置分析。采用复数矢量法 ,先列出用于装配形态分析的含 4个角位移变量的 4个独立矢量方程 ,然后将它们转化为复数形式的代数方程组 ,直接采用结式消元方法对上述方程组进行消元 ,得到了一个单变量的 5 4次代数方程 ,表明该种 9杆巴氏衍架可能存在 5 4种装配形态。对该代数方程直接进行求解 ,然后利用辗转相除法求出其它 3个未知变量的值 ,最后利用复数的三角变换 ,求出了 5 4组对应于该巴氏衍架装配形态的 4个角位移值 ,从而完成了它的装配形态分析     

大型天线的俯仰架结构

为了研究俯仰架结构在大型天线结构设计中的作用,文中阐述了俯仰架结构的传力途径和工作原理,以及其对大型天线主面精度和保型效果的影响,并通过应用实例验证了俯仰架结构中的伞形支撑在大型天线保型设计中发挥的作用。文中列举出几种典型的俯仰架结构形式,总结了各自的优缺点,提出了大型天线俯仰架的一般设计原则,对大型天线的结构设计具有一定的参考意义。     

八面体变几何桁架机器人工作空间分析的解析法

提出了八面体变几何桁架机器人工作空间分析的解析方法,得到了八面体变几何桁架机器人工作空间边界曲面的解析方程,并在此基础上纵出了工作空间边界曲面的图形。分析计算结果表明,八面体变几何桁架机器人的工作空间是由30张曲面片包围而成的闭包。     

装配式钢桁架桥振动模态分析与试验研究

桥梁结构的动力学特性是其结构分析与优化设计的基础,以某型装配式钢桁架桥为研究对象,利用有限元软件ANSYS建立了该桥的三维空间有限元分析模型,并采用分块兰索斯法对其进行了模态分析,得到了桥梁的10阶固有频率和振型,而后基于环境激励的工作模态试验方法开展试验研究,通过试验数据的对比,验证了该分析方法的可靠性,为该型钢桁架桥的动力特性分析提供了直接的数据支持。     

Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms

There are several design equations available for calculating the torsional compliance and the maximum torsion stress of a rectangular cross-section beam, but most depend on the relative magnitude of the two dimensions of the crosssection(i.e., the thickness and the width). After reviewing the available equations, two thickness-to-width ratio Independent equations that are symmetric with respect to the two dimensions are obtained for evaluating the maximum torsion stress of rectangular cross-section beams. Based on the resulting equations, outside lamina emergent torsional joints are analyzed and some useful design Insights are obtained. These equations, together with the previous work on symmetric equations for calculating torsional compliance, provide a convenient and effective way for designing and optimizing torsional beams in compliant mechanisms.     

Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method

The present study is concerned with the vibration analysis of cross-ply laminated beams subjected to different sets of boundary conditions. The analysis is based on a three-degree-of-freedom shear deformable beam theory. The continuity conditions between layers of symmetric cross-ply laminated beams are satisfied by the use of the shape function incorporated into the theory which also unifies the 1D shear deformable beam theories developed previously. The governing equations are obtained by means of Hamilton's principle. Six different combinations of free, clamped and simply supported edge boundary conditions are considered. The free vibration frequencies are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results obtained for different length-to-thickness ratios and lay-ups are presented and compared with results available in the literature.     

桁架式支撑臂模态分析与振动主动控制研究

建立了一维大型空间可展开桁架式支撑臂的动力学模型,计算了支撑臂各阶模态的频率和振型,以及在各阶模态下的杆件模态应变能。基于杆件模态应变能对压电陶瓷作动杆的位置进行了优化设计。基于独立模态空间方法运用二次型最优控制理论,对支撑臂进行振动主动控制研究。对含有主动构件的空间桁架式支撑臂的振动主动控制进行了仿真,比较了控制前后支撑臂振动幅值的变化。仿真结果表明,该控制策略具有较好的振动控制效果。     

Nonlinear forced vibrations and static deformations of 3D beams with rectangular cross section: The influence of warping, shear deformation and longitudinal displacements

The geometrically nonlinear vibrations of beams with rectangular cross section, which may experience longitudinal, torsional and bending deformations, in any plane, are investigated by the p-version finite element method. Two main models are used: one of them is based on Bernoulli-Euler theory for beam bending and the other is based on Timoshenko theory; both models assume that the cross section rotates as a rigid body and is free to warp in longitudinal direction, as in Saint-Venants’s theory for torsion. The geometrical nonlinearity is taken into account by considering Green’s strain tensor and the importance of the longitudinal displacements of quadratic order, which are most often neglected in the strain-displacement relation, is here examined. Generalized Hooke’s law is used and the equation of motion is derived by the principle of virtual work. The importance of the warping function is analysed for different rectangular cross sections, and it is shown that its consideration can be fundamental to obtain correct results. Then, it is shown that the linearization of the trigonometric functions related with the twist angle, which is usually applied in the displacement field in models based on Saint-Venant’s hypothesis, should be done in the strain-displacement relations. Comparisons of the models for 3D beams based on Bernoulli-Euler’s and Timoshenko’s theories is presented. It is shown that if the rotations along the transverse axes are directly approximated by the respective derivatives of the transverse displacement functions, as is assumed in the model presented here that is based on Bernoulli-Euler’s theory, the additional shear stresses that appear when the bending and torsion motions are coupled, lead to wrong results. Finally, taking into account accuracy and simplicity, a model is chosen and employed to investigate the nonlinear forced vibrations of beams using direct integration of the equations of motion in the time domain. Examples of bending-torsion couplings due to the nonlinear terms are presented in dynamical problems.     

基于避障准则的双臂手移动机器人桁架内运动规划

针对桁架内移动的避障要求,研究双臂手移动机器人桁架内运动的规划方法。基于状态空间模型提出直角坐标空间下的六面心、八边心和八顶点搜索算法,避免了C空间内复杂度呈几何级数增长的问题,实现了末端无碰撞路径搜索。建立双臂手移动机器人三节臂的平面内避障准则,解决了机器人在桁架内运动时机器人臂与桁架杆的碰撞问题。根据平面内避障准则和臂形标志,求得了各个关节角的解析解,解决了数值解的不封闭问题。每个时刻末端姿态由通用旋转变换公式线性插值得到,在Matlab中仿真双臂手移动机器人桁架内的运动,验证了双臂手移动机器人在桁架内运动时避障方法的可行性。     

9杆巴氏桁架的位置分析

以非平面基本运动链(9杆巴氏桁架)为研究对象,对其数学模型和消元过程进行了研究。使用复数向量法对9杆巴氏桁架4个回路建立几何关系,列出矢量方程组并转化成为复指数形式。使用Sylvester结式对4个多项式方程依次两两消元,得到一个一元50次的多项式方程,求解后使用辗转相除法求其他3个变量,完成位置分析。最后通过一个算例,验证了这种巴氏桁架的解析解的数目为50。