基于胚图的运动链拓扑图同构判断

运动链拓扑图的同构判断是机构型综合的关键环节,也是极难解决的研究热点。针对该问题创造性地提出了基于胚图的运动链拓扑图同构判断方法,首先,将拓扑图中的二元杆移除,从而得到拓扑图的胚图,利用路径数组来判断胚图的同构。然后,在胚图同构的前提下,利用特征数组来判断运动链拓扑图同构。并且举例说明该方法简洁高效。     

运动链拓扑图的特征数组表示及同构判断

运动链拓扑图同构判断是一个世界性的难题,为解决它提出新的方法。基于运动链拓扑图的特点,用特征数组来描述运动链的拓扑图。将运动链拓扑图支链上的二元杆数按照多元杆进行分组排列,组内的各支链顺序可变,组外的各多元杆的顺序可变,从而形成特征数组。用特征数组来描述拓扑图的特征,这一描述方式直观简洁且不受拓扑图画法形式和标号方式变化的影响。借用字符串的概念定义特征数组的同构,用Visual Basic编程,给出程序实现原理。建立判断矩阵来判断同构的特征数组,只有当判断矩阵的每行和、每列和同时为非零值时,两拓扑图是同构的。最后通过实例证明该方法准确、简单、高效且易于在计算机上实现。同构判断问题的解决为机构型综合奠定了基础。     

机器人运动链拓扑胚图的特征字符串描述

在机构基于胚图的综合方法中,判别拓扑胚图的同构关系是一个难题。提出特征字符串的概念,用于描述含较多基本连杆的拓扑胚图。基于运动链拓扑胚图支链上不含二度点的特性,制定相关规则,用特征字符串准确描述代表基本连杆的顶点的相对位置,引出拓扑胚图。制定判别同构拓扑胚图的相关准则,论证了拓扑胚图同构的条件。举实例对同一特征字符串和不同特征字符串描述的拓扑胚图进行了同构判断。通过与邻接矩阵方法比较,证明特征字符串法简单、有效。     

含复铰和环路的Assur杆组拓扑描述

为综合得到含复铰的Assur杆组构型综合,提出了一种含复铰杆组特征值的构型方法。分析此杆组特征值,得到了杆组中构件数、复铰数、环路数以及外接运动副之间的关系。进一步的通过含复铰杆组特征值组合以环路数为依据得出了拓扑胚图的生成方法。在拓扑胚图的基础上总结出了二元构件的分配原则以及归纳了二元构件的约束条件,由此确定二元构件的分配,得到杆组拓扑图。避免了拓扑图的同构判别,丰富了含复铰杆组的构型综合,同时为实现计算机的自动绘制奠定了基础。     

基于环路特性的运动链拓扑图及特征描述的自动生成

基于运动链拓扑图环路的数组描述及环路数组之间的相互运算,给出通过基本环数组之间的相互运算构成组合环的算法及其条件,并给出运动链的唯一数字特征描述.然后,以 Windows 为平台,以VC 6.0为工具,利用面向对象的程序设计方法,开发了一套集运动链拓扑图绘图及唯一数字特征描述--特征邻接矩阵和特征描述代码自动生成的计算机程序.此程序的最大特点是不管运动链拓扑图的画法形式如何改变,项点标号方式如何改变,计算机都能自动生成其唯一数字描述,从而实现运动链拓扑图的唯一数字化,并为机械概念设计的自动化、智能化和网络化创造了条件.结果表明,提出的程序解决了机械概念设计过程中运动链拓扑图的唯一数字描述方式难以计算机自动实现问题.     

赋权无向图的顶点素数分类与同构判别

运动链拓扑胚图一般是含自环和赋权的无向图,拓扑胚图的同构判别是类型综合的关键。提出了一种适用于赋权无向图顶点分类方法,将顶点度、赋权、自环分别用不同的素数区分,然后利用三者素数乘积形成顶点素数度,将素数度序列按相同元素分组,将每组元素与素数重新建立映射,该映射关系下的素数可作为赋权无向图顶点的唯一标识,最后对邻接矩阵动态修改法进行改进,并用于运动链拓扑胚图和一般赋权无向图的同构判别,判别实例表明该方法的有效性。     

含复合铰机构运动链的拓扑图表示与同构判别

提出一种适用于含任意复合铰个数的机构运动链拓扑图表示新方法,该方法在对含复合铰运动链转化为拓扑图时,在拓扑图顶点上标以顶点号和顶点对应的构件运动副数,与复合铰相连接的所有构件被看作是相互邻接的构件,该拓扑图完整表示了含复合铰机构运动链的信息,且不增加拓扑图顶点数规模。在拓扑图表示基础上,将邻接矩阵动态修改法应用到含复合铰运动链的同构判别,判别实例表明邻接矩阵动态修改法能有效对含复合铰机构运动链进行同构判别。     

基于运动副替代的周转轮系创新综合方法

提出了将单铰运动链用于轮系创新综合必须满足的基本结构条件,利用运动链的无向双色拓扑图及拓扑胚图,在运动链构件数与自由度数一定的情况下,用胚图插点法获得了所有可能的基于该复铰运动链的满足轮系创新综合要求的运动链结构型。应用本文提出的方法不仅可以得到各种工程实际中常用的轮系结构型,而且也能够获得许多我们过去不曾见过的结构型,为轮系的创新综合开辟了一条新的途径。     

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.     

康复机器人下肢运动促动机构的拓扑结构分析及创新设计

对原始机构进行了拓扑结构分析,构造出了机构的拓扑胚图,再将代表二副杆的点插入拓扑胚图中,得到满足要求的所有运动链的拓扑图。按照图与机构的一一对应关系,把拓扑图转化为一般化运动链图谱。指定各构件类型后,可将一般化运动链图转化为特定化链,并具体化为与原始机构具有相同或相似功能的新型机构。在此基础上,设计者可对其进行综合评价,筛选出好的结构类型。该方法可提高机构创新设计的效率和质量,具有较强的可操作性。     

基于拉普拉斯矩阵特征向量的运动链规范排序

基于代数图论的理论，提出根据图的拉普拉斯矩阵第二和最大特征向量对运动链规范排序的方法和对运动链进行编码的方法，讨论了这种排序方法的应用，提出了一种新的识别运动链同构的方法。     

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。     

闭环机构关联杆组中基本连杆排列组合的确定

针对含冗余约束和被动自由度的闭环机构,解决其关联杆组中基本连杆的排列组合问题。采用Matlab程序,求解关联杆组中基本连杆的数目,确定基本连杆的组合形式。该方法与决策树方法相比,避免了数据的遗漏。同一关联杆组中基本连杆排列方式同构,推导出的拓扑胚图同构。提出选择性插入方法解决基本连杆的同构排列问题,通过程序实现,证明该方法能减少运算量,节省运算时间。举实例说明程序自动生成有效基本连杆排列方式的应用过程。结果表明,所提出的运算方法能在进行闭环机构拓扑胚图综合之前,清除同构的基本连杆排列方式,保证后续推导的拓扑胚图的有效性,同时便于在计算机上实现,提高自动化程度。     

A mixed isomorphism approach for kinematic structure enumeration graphs based on intelligent design and manufacturing

When using graph theory for kinematic structure enumeration, the isomorphism identification of graphs is an important and complicated problem. The problem is known to be an NP-complete problem. This paper presents a mixed algorithm based on a mapping property, a genetic algorithm, and a simulated annealing algorithm for the isomorphism identification problem. A validity encoding scheme was developed by considering the mapping relationship between two graphs, and some reset measures for the crossover and mutation operators were developed based on the characteristics in which the encoding cell could not be reiterated. A simulated annealing algorithm was introduced into the mixed algorithm to prevent premature convergence in resolution, and some other measures were developed for improving the efficiency, based on the parameter selection. An example shows that the mixed algorithm is a valid algorithm for the isomorphism identification of kinematic structure graphs in mechanism design. It will be a reliable isomorphism identification algorithm for intelligent computer-aided design (CAD) and manufacturing (CAM).     

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.     

Similar Vertices and Isomorphism Detection for Planar Kinematic Chains Based on Ameliorated Multi-Order Adjacent Vertex Assignment Sequence

Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains(KCs).The detec-tion can be performed accurately by using the similarity of KCs.However,there are very few works on isomorphism detection based on the properties of similar vertices.In this paper,an ameliorated multi-order adjacent vertex assign-ment sequence(AMAVS)method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs.First,the specific definition of AMAVS is described.Through the calculation of the AMAVS,the adjacent vertex value sequence reflecting the uniqueness of the topology features is established.Based on the value sequence,all possible similar vertices,corresponding relations,and isomorphism discrimination can be realized.By checking the topological graph of KCs with a different number of links,the effectiveness and efficiency of the proposed method are verified.Finally,the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-DOF(degree of freedom)planar KCs.     

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.     

Derivation and isomorphism identification of valid topological graphs for 1-, 2-DOF planar closed mechanisms by characteristic strings

A characteristic string approach is presented for derivation and isomorphism identification of valid topological graphs (TGs) for some 1, 2-DOF (degree of freedom) planar closed mechanisms from the contracted graphs (CGs). First, topological graph (TG) is simplified by the topology graph with digits (DTG) for the 1-, 2-DOF planar closed mechanisms. Second, the equivalent conditions between the characteristic string and DTG are determined and verified by some created simulation mechanisms of valid TGs, a complicated derivation of TG is transformed into an easy derivation of the characteristic string. Third, the valid characteristic strings are derived corresponding to non-isomorphic TGs, and the invalid characteristic strings corresponding to the isomorphic and invalid TGs are determined using the characteristic string. Finally, many valid characteristic strings for the 2-DOF planar mechanisms are derived from some valid characteristic strings for the 1-DOF planar mechanisms.     

基于图论和拓扑结构分析的机械式无级变速器的创新设计

归纳了原始机构的拓扑构造特性,运用图论理论得到了原始机构的拓扑缩图.通过对机构的原始拓朴缩图进行二度点的分配,消去同构方案后,即可综合出符合条件的拓扑全图和一系列相时应的运动链图谱.在此基础上指定各构件和运动副的类型,得到与原始机构具有相同或相似功能的新型机构.设计者可根据功能要求和具体的设计环境,从中筛选出好的结构.