运动链拓扑胚图的同构判断

平面并联机构基于胚图的综合方法中,拓扑胚图的同构判断是关键的环节。针对不含二元杆的运动链拓扑胚图,解决它们之间的同构判断问题。运动链的拓扑胚图与拓扑图相比有着独特的个性,由于在支链上没有二元点,所以图的顶点之间的关系主要是顶点之间的相对位置。根据拓扑胚图的特性,从关于图的邻接矩阵的经典理论出发,建立图的任意顶点之间的路径数矩阵,将路径数矩阵的元素按照一定规则排列成路径数组。论证了拓扑胚图同构的条件。在度序列和一阶路径数组相等的前提下,利用二阶路径数组来判断拓扑胚图是否同构。举实例说明判断过程及具体应用。拓扑胚图同构判断问题的解决不仅为基于胚图的型综合奠定了基础,而且对于某些运动链拓扑图的同构判断也具有普遍意义。     

空间机构的结构描述

应用拓扑学理论,提出一种新的空间机构有级边拓扑描述方法,推导出有级边拓扑图的几个重要的矩阵:邻接矩阵,关联矩阵和环路矩阵。在此基础上,分析了矩阵的性质,空间机构运动副轴线位置关系对运动特性的影响,给出了空间机构的结构描述特征字符串。     

含复铰平面开链和拓扑对称性在型综合中的应用

提出了在运动链型综合组合法中应用的含复铰平面开链的有关概念 ,给出了构造平面开链的方法 ,以及六杆以下所有的开链型式。同时 ,讨论了平面闭式运动链和平面开链中铰链点拓扑对称性的判断问题 ,给出了判断方法及其在型综合中的应用方法。研究表明 ,利用拓扑对称性可以有效地减少同构运动链型的数量。     

平面机构统一拓扑描述模型的建立及同构判别

介绍平面单铰运动链、平面复铰运动链、齿轮(凸轮)运动链常规的拓扑表达模型.然后,以单铰运动链的拓扑图为基础,提出平面复铰运动链、齿轮(凸轮)运动链的新拓扑图模型,并分析新拓扑模型的特点,给出含复铰的运动链和齿轮(凸轮)运动链的拓扑模型与平面单铰运动链的联系.新拓扑模型的优点在于与平面单铰运动链的模型相统一,方便了基于计算机的机构运动链自动综合和同构判别,从而为实现运动链拓扑图的唯一数字化,机械概念设计的自动化、智能化和网络化创造了条件.给出这几类运动链的统一的同构判别方法.     

平面3-DOF混联机构构型综合及其同构分析

通过应用Assur杆组法及图论理论对平面3-DOF全转动副机构进行了构件分类和构件组合,得到了一种最基本的3条支链对称的运动链结构。然后运用拓扑胚图插点法画出了其拓扑胚图,对其支链进行分类并插入拓扑胚图中,再进行同构分析得到了6种运动链构型。最后,运用一种新的基于构件关系的图论描述方法推导出了此机构的混联构型,并对其进行了应用研究。这些为以后非全转动副平面3-DOF机构的研究打下了基础。同时,通过研究平面3-DOF机构也更加有利于空间少自由度机构的研究。     

邻接矩阵在平面机构分析中的应用

研究了邻接矩阵在平面机构自由度计算、同构识别和速度瞬心求解中的应用。揭示了邻接矩阵与机构自由度的关系。给出了同构运动链邻接矩阵的特征向量及特征值关系的充要条件 ,据此提出了识别机构运动链同构的方法。最后 ,提出了应用邻接矩阵自乘求解机构全部瞬心及求解给定瞬心最短路经的方法     

平面闭链机构的缩杆邻接矩阵变更研究

针对平面闭链机构运动特性集成的问题,对闭链机构的设计过程、闭链机构运动链数目综合过程、缩杆邻接矩阵表示、去同构链、去呆链等方面进行了研究,以此获得了各杆件不同自由度的缩杆邻接矩阵数目表。通过对各缩杆邻接矩阵的比较,提出了少杆与多杆机构局部同构的识别方法,建立了平面闭链少杆机构向多杆机构的过渡过程,在此基础上给出了平面闭链机构的缩杆邻接矩阵变更过程。最后,运用平面闭链机构缩杆邻接矩阵变更方法对现有的飞剪机构进行了改进,验证了该变更过程的可行性。研究结果表明:平面闭链多杆机构可以由少杆机构添加若干杆件及运动副获得。     

变胞机构的构态变换矩阵与运动副方位变胞

针对邻接矩阵不能用于运动副方位变胞的问题,构建了一种描述变胞机构结构拓扑和构型演化的构态变换矩阵。该矩阵提供了运动链连接状况、运动副类型和运动副方位特征信息,使各类运动链都可应用该构态变换矩阵进行描述。给出了基于该构态变换矩阵的运动副方位变胞的基本原理和方法。首先构造平面运动链的构态变换矩阵,然后构造对应的带有消极自由度的平面运动链的构态变换矩阵,进而改变矩阵中某些运动副的轴线方位,构造出变胞后的运动链的构态变换矩阵,最后根据构态变换矩阵的拓扑信息,构造对应的机构结构简图,实现运动副方位变胞。实例表明,给出的构态变换矩阵结构简单,便于构造,信息量大;提出的变胞方法便捷可行。     

一种基于汉明矩阵和连杆邻接矩阵的运动链同构识别方法

在机械装置的创造性设计中,应淘汰同构运动链,为后续设计减少机构方案,提高机械装置的设计效率.基于汉明矩阵提出了一种新的运动链同构判别方法.首先,从连杆邻接矩阵中导出运动链汉明矩阵;接着,将汉明矩阵的平方阵与连杆邻接矩阵的立方阵求积,得到运动链积矩阵;然后,将积矩阵各行元素以降序排列得积矩阵行序列;最后,将行序列中各元素与本文中所定义的拓扑因子相乘并求总和,得出运动链的同构识别码,即IRC(Isomorphism recognition code).同构识别码不随构件标号的改变而改变,故若运动链的同构识别码相同,则它们为同构链,否则为异构链.大量实例证明了该方法的有效性.因其简洁、高效且利于计算机执行的特点,故可以考虑将其作为同构筛选的一种新的选择.     

杆件环路代码的运动链同构识别

针对平面机构运动链的特点,在研究了其结构不变量的基础上,基于杆件环路代码提出了新的运动链结构恒量,该恒量将杆件的级别、运动副数目以及各杆件的连接关系考虑在内。据此提出了利用该恒量对运动链进行同构识别的方法,该方法具有高效可靠、应用简便等特点。     

基于转化邻接矩阵的含复铰运动链描述与同构识别

针对机构分析与综合中复合铰链难以处理和含复铰运动链同构识别困难的问题,分析复合铰链的内部结构,提出引入Pin构件将复合铰链转化为多个并联单铰链的新方法,从而将含复铰运动链转化为只含单铰的简单运动链。定义运动链转换邻接矩阵,用于描述含复铰运动链,通过分析发现该矩阵的内涵性质丰富,方便运动链的分析。提出运用转换邻接矩阵的阶数、对角线元素矢量、矩阵特征值和特征矢量等参数识别判断含复铰运动链同构关系的方法,这些特征参数是含复铰运动链的不变量。实例证明,利用转化邻接矩阵可简单、方便、直观地描述含复铰运动链,其特征值和特征矢量用于识别含复铰运动链的同构关系,具有准确、高效和简便的特点。定义的转化邻接矩阵及其运用方法为复合铰链的处理以及含复铰运动链的识别提供了新的途径。     

平面运动链同构识别方法的研究

同构识别在机构类型综合中占有重要位置。本文在对含高副平面运动链分析的基础上，提出了含高副平面运动链支路码的概念，并提出了一种用计算机对含高副和不含高副的平面运动链均适用的同构识别方法。该方法不受运动链杆数和自由度数的限制，且速度快、计算量少。经大量实例计算，该方法行之有效     

Hierarchical clustering approach for determination of isomorphism among planar kinematic chains and their derived mechanisms

The problem of isomorphism among kinematic chains and their derived mechanism has been a hot area of research from last several years. The researchers so far have proposed many methods which are mainly based on characteristic polynomial and some code based methods to test the isomorphism among kinematic chains. In this present communication a hierarchical clustering based computerized method is proposed for the above said problem and it is tested for planar kinematic chains upto twelve links without any counter examples. In this method a hierarchical clustering algorithm is also developed for the identification of distinct mechanism derived from kinematic chains. In this method kinematic chains are represented in the form of weighted squared shortest path distance matrix and this matrix is further transformed in the form of tree or dendrogram with the help of hierarchical clustering algorithm. This algorithm directly gives the number of distinct mechanism derived from a given kinematic chain. The cophenetic correlation coefficient of dendrogram is used as an index for isomorphism identification among kinematic chains. The proposed method is efficient and accurate and only one matrix for a given kinematic chain is developed for the determination of distinct mechanisms. This method is successfully examined for one degree of freedom, 6, 8, 10, 12 links planar kinematic chains, 9 links two degree of freedom and 10 links three degree of freedom planar kinematic chains. The computer algorithm for the proposed method has been proposed which can easily be converted into a computer program. These results are useful for designers to detect isomorphism in mechanisms derived from kinematic chains and duplication among kinematic chains.     

STUDY ON ISOMORPHISM OF PLANAR KINEMATIC CHAINS

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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。     

利用邻接矩阵的幂序列进行运动链和机构的同构判定

从同构的图论意义出发,提出了一个新的运动链结构不变量,进而提出了利用邻接矩阵的幂序列进行运动链同构判定的方法。它与现有的其他方法相比,具有直观、简便和显明图论依据的特点,且该方法不仅可以实现运动链的同构判定,而且可以成功地判定一般图的同构。在此基础上,本文最后给出了从同一运动链中识别出不同机构的两个方法。     

ADJACENT MARTIX METHOD OF IDENTIFYING ISOMORPHISM TO PLANAR KINEMATIC CHAIN WITH MULTIPLE JOINTS AND HIGHER PAIRS

The adjacent matrix method for identifying isomorphism to planar kinematic chain with multiple joints and higher pairs is presented. The topological invariants of the planar kinematic chain can be calculated and compared by adjacent matrix. The quantity of calculation can be reduced effectively using the several divisions of bars and the reconfiguration of the adjacent matrix. As two structural characteristics of adjacent matrix, the number of division and division code are presented. It can be identified that two kinematic chains are isomorphic or not by comparing the structural characteristics of their adjacent matrixes using a method called matching row-to-row. This method may be applied to the planar linkage chain too. So, the methods of identifying isomorphism are unified in the planar kinematic chain that has or hasn't higher pairs with or without multiple joints. And it has some characters such as visual, simple and convenient for processing by computer, and so on.     

平面运动链同构识别的距离和序列法

对平面机构运动链结构组成进行探讨后,研究了运动链中的结构不变量,并基于缩杆邻接矩阵提出了4个新的运动链结构恒量序列,这些恒量序列将杆的级别、运动副数目以及各杆的连接关系考虑在内。以此为基础,提出了对运动链进行同构识别的距离和序列法。该方法实质上是对运动链进行分类同构识别,因此具有操作简单、可靠性好、识别效率高等特点,已成功应用于12杆以下机构运动链型综合时的同构识别     

Synthesis of a complete set of contracted graphs for planar non-fractionated simple-jointed kinematic chains with all possible DOFs

The contracted graph shows the primary topological structure of kinematic chains and is the foundation for constructing kinematic structures of mechanisms. In this paper, a fully-automatic method is proposed to synthesize a complete set of contracted graphs for planar non-fractionated simple-jointed kinematic chains with all possible degrees of freedom. First, based on the 4-parameter index and link assortment array, the relationships of link assortment arrays and non-fractionated contracted graphs for different types of kinematic chains are revealed. Then, the general steps to generate the adjacency matrices of contracted graphs from the synthesis equation set are given. Efficient methods to detect fractionated structures and isomorphism are also addressed. Finally, a human-machine interactive synthesis program is developed, and the complete list of both contracted graphs and valid contracted graphs for planar non-fractionated simple-jointed kinematic chains with up to 19 links and all possible degrees of freedom is presented for the first time.     

In quest of a reliable and efficient computational test for detection of isomorphism in kinematic chains

The test based on comparison of the characteristic coefficients of the adjancency matrices of the corresponding graphs for detection of isomorphism in kinematic chains has been shown to fail in the case of two pairs of ten-link, simple-jointed chains, one pair corresponding to single-freedom chains and the other pair corresponding to three-freedom chains. An assessment of the merits and demerits of available methods for detection of isomorphism in graphs and kinematic chains is presented, keeping in view the suitability of the methods for use in computerized structural synthesis of kinematic chains. A new test based on the characteristic coefficients of the “degree” matrix of the corresponding graph is proposed for detection of isomorphism in kinematic chains. The new test is found to be successful in the case of a number of examples of graphs where the test based on characteristic coefficients of adjancency matrix fails. It has also been found to be successful in distinguishing the structures of all known simple-jointed kinematic chains in the categories of (a) single-freedom chains with up to 10 links, (b) two-freedom chains with up to 9 links and (c) three-freedom chains with up to 10 links.