面向构态切换稳定性的约束变胞机构可靠性优化设计方法

为获得稳定、可靠的构态切换能力而开展可靠性优化设计是降低约束变胞机构运动功能失效概率的关键。基于多构态欠驱动约束变胞源机构的组成原理建立了含变胞运动副的扩展Assur杆组的模块化受力分析模型。根据变胞运动副的等效阻力梯度模型，考虑系统内外部误差的随机性，利用可靠性理论建立了约束变胞机构构态切换能力的概率评估模型。基于可靠性评估及可靠性灵敏度分析，提出了面向约束变胞机构构态切换稳定性的可靠性优化设计方法，进而针对可靠性灵敏度较高的结构参数随机变量的公差进行优化设计，使优化后的设计方案同时满足可靠性和经济性要求。最后，以折纸变胞机构为例，验证了提出的可靠性优化设计方法的可行性和有效性。研究工作为开展面向高概率的构态切换重复执行能力的变胞机构可靠性优化设计奠定了基础，同时对推进变胞机构的工程应用具有理论和实际意义。     

基于杆组邻接矩阵的平面机构综合方法

为在平面机构综合中能够求解出包含R副和P副的全部运动链,给出一种基于杆组邻接矩阵的平面机构综合新方法。通过对前期研究提出的杆组邻接矩阵进行修正,构造改进的杆组邻接矩阵。基于改进的杆组邻接矩阵,求解给定杆组的所有装配方式,并同步辨识同构体,获取杆组装配关系的杆组邻接矩阵。根据提出的约束条件,采取逐级构造杆组邻接矩阵方法,求解杆组间的可行连接方式,并同步辨识同构体,从而获取全R副杆组间的连接关系的杆组邻接矩阵。将所有类型杆组代入求得的杆组连接关系矩阵,获取所有类型杆组可构成的全部机构构型,包含主动件和机架变换问题。以平面6杆机构为例,应用该方法首次求出包含R副和P副的所有机构构型为364种,验证了提出的综合方法的有效性和实用性。     

平面变胞间歇机构动力学分析及其仿真

在采用杆组法建立平面变胞间歇运动机构的运动学分析的数学模型之后,在运动学分析的基础上,对其进一步进行动力学的分析研究。根据已经确定的杆件负载,求出主动件所需的动力以及各约束的约束反力,为选定动力和构件的强度设计提供依据。利用ADAMS对机构进行动力学仿真,计算结果及仿真结果相互验证,证明了动态静力法分析结果的可靠性。     

Position analysis of higher-class Assur groups by virtual variable searching and its application in a multifunction domestic sewing machine

This paper presents a simple and effective method to solve the position of higher-class Assur groups by means of virtual variable searching. It transforms the higher-class Assur groups into a constraint link, Class II Assur group(s), and virtual driving link(s), defined by the virtual variable. The constraint link is reassembled by one-dimensional searching of the virtual variable, and the potential solutions of the position of the higher-class Assur group are achieved with rapid mathematic convergence. Detailed criteria are set up for complicated higher-class Assur groups, including how to select the virtual driving link and constraint Link, and how to decide the solving sequence of converted Class II Assur groups. A versatile visual program has been developed to simulate higher-class planar mechanisms. Finally, an example of the feeding mechanism of a multifunction domestic sewing machine demonstrates the new method.     

基于约束函数的变胞机构变胞方程

变胞机构拥有多个变换的稳态和变胞态,其拓扑构态描述与分析是变胞机构结构学的难点。采用数学分析方法,探索全面、简便而准确地描述和分析变胞机构构态拓扑结构的问题。根据运动副约束的特征,定义反映运动副类型、级别、自由度、方位、性质及其随时间变化情况等诸多特征信息的参数——运动副约束函数,采用矩阵法构建以约束函数为元素的机构变胞源运动链邻接矩阵。针对合并构件、分离构件、改变构件性质、新增运动副、消除运动副及改变运动副性质等六类机构变胞方式,分别定义相应的机构变胞函数和变胞矩阵,建立相邻稳态之间变胞态的机构变胞方程。应用实例表明,所定义的运动副约束函数、运动链邻接矩阵、变胞矩阵和变胞函数等概念能简便、广泛地描述变胞机构的构态特征,基于约束函数的机构变胞方程能准确地描述和分析机构相邻稳态之间变胞态的变换过程,为变胞机构的结构分析提供一种新的途径和方法,并为进一步的变胞机构运动学和动力学分析以及机构综合研究提供理论基础。     

基于变胞铰链的并联机构结构设计与构型分析

为了拓展变胞机构的种类，提出了一种变胞运动单元，该变胞单元采用三个旋转关节，并且三个旋转关节可以通过位置调节形成等效球铰、虎克铰以及转动副。与传统的锁定运动副来实现变胞功能的变胞单元相比，此变胞单元三种构型的切换只需对轴线位置调整，无需额外增加关节锁死电机。通过研究由线矢量构成的螺旋系统的相关性，揭示了变胞运动单元构态变化的基本原理。提出了可用于构造新型变胞并联机构的支链构型设计方法，并基于螺旋的互易性分析了各支链构型所必须满足的几何约束条件。提出了两种变胞并联机构，通过不同的支链装配形式可将其从6自由度构型转换为3自由度构型，并对支链安装形式进行改进，构造出了具有3自由度平移模式和3自由度转动模式的并联机构。对变胞支链作为中心支链组装而成的并联机构的构型及对应的运动类型进行了分析，获得了六种不同构型的并联机构。     

基于球面五杆机构的变胞并联机构构型综合

提出一类基于球面五杆机构的变胞并联机构。基于具有解耦特性的球面五杆机构,应用螺旋理论综合出一类具有变胞特性的可重构混联支链,该混联支链由一个球面五杆机构和一个四自由度串联支链混联而成,应用三条相同的所述可重构混联支链构型出一类变胞并联机构。不同于现有利用约束奇异和支链奇异综合可重构并联机构的方法,提出利用球面五杆机构的解耦特性和关节锁死的方法来实现并联机构的可重构,因此该类变胞并联机构可有效避免重构过程中的约束奇异以及支链奇异。该类变胞并联机构可在一个广泛的范围内变换其工作模式和自由度,且伺服电动机均可安装在机构的固定平台。提到的方法可应用于其他基于解耦闭链的变胞并联机构构型综合。     

平面多杆机构杆组自动生成方法

阿苏尔杆组理论指出,通过对不同运动链选取不同的机架和原动件,能够得到各种可能的阿苏尔杆组与机构构型。基于这一理论提出一种阿苏尔杆组的自动生成方法。针对杆组的结构特点,提出简单易行的杆组同构判别方法,该判别方法也适用于平面多杆机构运动链的同构判别。联合应用运动链的邻接矩阵与关联矩阵,使得自动生成算法与计算机编程相结合,实现了平面多杆机构杆组的自动生成。该自动生成机构杆组的方法理论简单,编程可操作性强,能够实现多杆运动链在构成机构时杆组的准确快速的拆分。该方法将杆组的拆分过程与由杆组搭接形成机构的过程相联系,对拆分得到的所有杆组与机构构型进行同构判别,得到了六杆以内的13种杆组,以及由八杆运动链构成的153种机构。     

The method of cut-joint kinematic constraint: velocity propagations

Based on a recent formulation for parametric design of mechanical systems using kinematic analysis, we reported an approach to automated design by converting mechanical part geometry into a mechanism by breaking the part into sub-parts attached by higher pair joints. In order to evaluate the performance of a mechanism where a design change has been introduced into one of its links, we extend the formulation in this paper to address the propagation of this change and its effect on the velocity of other members. This analysis will limit itself to mechanisms. Velocity propagations due to modifications in the design of a mechanical part are analytically addressed using a proposed working coordinates formulation based on the cut-joint kinematic constraint method (presented earlier). Velocity vectors in state-vector notation are derived and treated as variables such that propagations of working coordinates of a link are obtained with respect to position and orientation. The underlying theory is presented and several planar and spatial mechanisms are treated.     

An algorithmic description of the structural synthesis of planar Assur groups

An algorithm for the structural synthesis of planar Assur groups is presented. A method for identifying structural groups is proposed that enables one to automatically identify and exclude structurally isomorphic groups. A technique for generating electronic catalogs of all Assur groups with a given number of links is described.     

Metamorphic manipulating mechanism design for MCCB using index reduced iteration

The present research on moulded case circuit breaker(MCCB) focuses on the enhancement of current-limiting interrupting performance during short circuit, overload, under voltage and phase failure, involving electrics, magnetic, mechanics, thermal, material, friction, arc extinguishing, impact vibration, skin effect, etc. The rigid-flexible coupling of the parts and components of the metamorphic manipulating mechanism in multi-fields leads to the non-rigid, high frequency, high damping, singularity of the Euler-Lagrange equations which represents the multi-body dynamics. The small step iteration which is used for obtaining the instantaneous and short time critical interrupting performance of metamorphic mechanism appears inaccuracy. It is difficult to realize top-down design by existing CAD systems. Therefore, a metamorphic manipulating mechanism design method for MCCB using index reduced iteration(IRI) is put forward. The metamorphic manipulating mechanism of MCCB is decomposed into three mechanisms: main switch connector mechanism, electromagnet-drawbar-jump buckle mechanism, and bimetallic strip-drawbar mechanism, which is respectively described by electro-dynamic force, electromagnet force, and bimetallic strip force. The dummy part(virtual rigid) without moment of inertia and mass is employed as intermediate to join the flexible body and rigid body. The model of rigid-flexible coupling metamorphic mechanism multi-body dynamics is built. The differential algebraic equations(DAEs) of the multibody dynamics model are converted to pure ordinary differential equations(ODEs) by coordinate partition. Order reduced integration with multi-step and variable step-size is preceded based on IRI. The non-linear algebraic equations are solved in each integration step by Newton-Rapson iteration. There is no ill-condition and singularity of Jacobian matrix when step size reduces to zero. The independent prototype design system using ACIS R13, HOOPS V11.0 and Visual C++.NET 2003 has been developed, which verifies the effectiveness of the proposed method. The proposed method enhances the current-limiting interrupting performance of MCCB, and has reference significance for multi-body dynamics design for similar flexible metamorphic mechanisms in multi-fields.     

变胞机构理论与应用研究概述

阐述了变胞机构的特点及其结构学、运动学、动力学、控制、柔性建模及设计等若干理论问题。介绍了矢量法、矩阵法、指数积方法等几种运动分析方法,比较了Newton/Euler法、Lagrange方法、Kane方法、Roberson/W ittenburg方法、高斯最小约束原理法等几种动力学建模方法的优缺点,提出了变胞机构的几种控制方法和柔性变胞机构建模中存在的几个关键性的问题。最后概述了变胞机构的应用领域,展望了变胞机构的应用前景。     

变胞机构的基因建模理论与构态进化分析

变胞机构的英文首创是“Metamorphic mechanisms”。这一概念借用了生物学中“Metamorphosis”,即变形、变拓扑态、可生长并进化演化。基于这一基本概念,并结合机构的基本杆组组成原理,首次提出变胞机构具有生物特性的组成原理,定义变胞元与变胞基因,并基于变胞基本单元建立变胞机构生物特性结构模型,分析基因进化引导的构型综合思想。通过分析变胞机构的构态转化特点,讨论变胞源机构及生成方法与过程,得出变胞机构构态演变过程生物学进化特性。深入研究变胞机构在变胞进化生长过程中构型要素的转化方式与蜕化方法,建立变胞机构学具有生物演变特征的机构组成原理及进化构态建模理论。在此基础上结合传统基本机构进化生成变胞机构构型给出分析示例,并基于工作阶段子机构之间进化为变胞机构过程中不同的自由度跃迁结果,对变胞源机构的进化计算分别进行讨论。     

Structural Synthesis of Compliant Metamorphic Mechanisms Based on Adjacency Matrix Operations

A compliant metamorphic mechanism attributes to a new type of metamorphic mechanisms evolved from rigid metamorphic mechanisms. The structural characteristics and representations of a compliant metamorphic mechanism are different from its rigid counterparts, so does the structural synthesis method. In order to carry out its structural synthesis, a constraint graph representation for topological structure of compliant metamorphic mechanisms is introduced, which can not only represent the structure of a compliant metamorphic mechanism, but also describe the characteristics of its links and kinematic pairs. An adjacency matrix representation of the link relationships in a compliant metamorphic mechanism is presented according to the constraint graph. Then, a method for structural synthesis of compliant metamorphic mechanisms is proposed based on the adjacency matrix operations. The operation rules and the operation procedures of adjacency matrices are described through synthesis of the initial configurations composed of s+1 links from an s-link mechanism (the final configuration). The method is demonstrated by synthesizing all the possible four-link compliant metamorphic mechanisms that can transform into a three-link mechanism through combining two of its links. Sixty-five adjacency matrices are obtained in the synthesis, each of which corresponds to a compliant metamorphic mechanism having four links. Therefore, the effectiveness of the method is validated by a specific compliant metamorphic mechanism corresponding to one of the sixty-five adjacency matrices. The structural synthesis method is put into practice as a fully compliant metamorphic hand is presented based on the synthesis results. The synthesis method has the advantages of simple operation rules, clear geometric meanings, ease of programming with matrix operation, and provides an effective method for structural synthesis of compliant metamorphic mechanisms and can be used in the design of new compliant metamorphic mechanisms.     

构态变换有碰撞的变胞机构动力学性能分析

在许多变胞机构构态变换的方式中均伴随有构件之间的碰撞。碰撞势必在机构中产生振动。以一个平面五杆变胞机构为例,利用拉格朗日方程和碰撞动力分析方程建立了构态发生变化时有碰撞的情况的动力分析方法。研究表明:在变胞机构的构态转变过程中,由于碰撞的存在则机构中将会产生一定的振动。施加于机构上外力的大小对机构是否能够顺利实现构态变换及机构在构态变换时机构振动的时间有比较明显的影响。     

基于吴方法的一种7杆巴氏桁架位移分析研究

将吴方法运用到平面基本运动链的位移分析中,完成了一种7杆巴氏桁架的位移分析。结合矢量法和复数法建立3个几何约束方程式,将其扩展为12个多项式方程,同时变量个数由3个增加到12个。这12个方程式中6个为线性方程,剩下6个是简单的非线性方程,并且各多项式的初式中最多有一个变元。使用吴方法经过6次循环得到特征列,其中第一个多项式的最高次数为18次。通过数字实例对结果进行了验证,得到18组无增无漏的解;计算结果表明,与同一巴氏桁架相关的所有Assur组的解的数目是相等的,装配构形完全相同,与我们的预期是一致的。吴方法在这一问题上应用,为求解其他机构学问题提供了新思路。     

复数法求解平面杆组运动分析问题

提出了阿苏尔组运动分析的复数法,即根据平面杆组各杆的矢量关系式建立复数形式的输入输出方程,然后直接对该复数方程求解。文中采用实例验证了结果的正确性。     

[学科发展]机构学中机构重构的理论难点与研究进展——变胞机构演变内涵、分岔机理、设计综合及其应用

生产力发展与工程技术革新要求机构具备可自重组与可重构及“一机多用”的功能，以满足复杂工况需求。可重构机构具有可变活动度和可变构态，可以满足多任务、多工况与多功能的要求，然而，决定其设计方法的演变内涵与分岔机理的研究目前仍不为学者们充分了解。从变胞机构的演变与分岔机理的角度，以旋量理论、李群与李代数及微分流形为主要工具，揭示了机构演变内涵及运动与约束空间的内在关联关系；探究了机构演变中的分岔机理与可控奇异位形，回顾了变胞机构与折纸及折展机构的历史渊源，综述了变胞机构的构型设计、性能综合与新型设计理念及其创新应用。     

Configuration Analysis of Metamorphic Mechanisms Based on Extended Adjacency Matrix Operations

The adjacency matrix operations,which connect with configuration transformation correspondingly,can be used for analysis of configuration transformation of metamorphic mechanisms and the corresponding algorithm can easily be simulated by computer.But the adjacency matrix based on monochrome topological graph is not suitable for the topological representation of mechanisms with multiple joints.The method of adjacency matrix operations has its own limitations for analysis of configuration transformation of me...     

一种平面闭链腿式机构的尺度参数优化设计

以Theo Jansen机构输出的足端轨迹为目标,对一种新型平面闭链腿式机构的尺度参数进行优化。利用基本杆组法建立了该新型机构的运动学模型,根据新型机构和Theo Jansen机构的结构特点,利用曲柄摇杆机构的极限位置条件,将设计变量数目减少为一个;以两机构的足端轨迹偏差最小为目标,以各尺度参数间的几何关系为约束,建立了单目标优化问题,并利用一维搜索法得到优化结果。在此基础上,设计了一种八足移动机器人并搭建实验样机,验证了设计结果的可行性。