The Establishment of the Canonical Perimeter Topological Graph of Kinematic Chains and Isomorphism Identification

2006 ◽  
Vol 129 (9) ◽  
pp. 915-923 ◽  
Author(s):  
Huafeng Ding ◽  
Zhen Huang
Keyword(s):  
Adjacency Matrix ◽  
Degree Sequence ◽  
Topological Graph ◽  
Topological Graphs ◽  
Kinematic Chains ◽  
New Concepts ◽  
Element Number ◽  
One To One ◽  
Descriptive Method ◽  
Isomorphism Identification

Some new concepts, such as the perimeter loop, the maximum perimeter degree-sequence, and the perimeter topological graph, are first presented in this paper, and the method for obtaining the perimeter loop is also involved. Then, based on the perimeter topological graph and some rules for relabeling its vertices canonically, a one-to-one descriptive method, the canonical adjacency matrix set of kinematic chains, is proposed. Another very important characteristic of the descriptive method is that in the canonical adjacency matrix set the element number is reduced dramatically, usually to only one. After that, an effective method to identify isomorphism of kinematic chains is given. Finally, some typical examples of isomorphism identification including two 28-vertex topological graphs are presented in this paper.

The Novel Characteristic Representations of Kinematic Chains and Their Applications

2005 ◽  
Author(s):  
Z. Huang ◽  
H. F. Ding ◽  
Y. Cao
Keyword(s):  
Adjacency Matrix ◽  
Degree Sequence ◽  
Object Oriented ◽  
Kinematic Chain ◽  
Object Oriented Programming ◽  
The Novel ◽  
Topological Graphs ◽  
Kinematic Chains ◽  
Set Up ◽  
Oriented Programming Language

In this paper, based on perimeter topological graphs of kinematic chains, many novel topological concepts including the synthetic degree-sequence, the characteristic adjacency matrix and the characteristic representation code of kinematic chain are proposed. Both the characteristic adjacency matrix and the characteristic representation code are unique for any kinematic chain and easy to be set up. Therefore a quite effective isomorphism identification method is presented depending on the characteristic adjacency matrix. It high effectiveness is proved by many examples. With object-oriented programming language, a program which can sketch topological graphs of kinematic chains has been developed based on the characteristic representation code. Finally, an application software system establishing the atlas database of topological graphs is introduced. And some functions about the atlas database are also presented in this paper.

The Systemic Research on Loop Characteristics of Planar Kinematic Chains and Its Applications

2005 ◽  
Author(s):  
H. F. Ding ◽  
Z. Huang ◽  
Y. Cao
Keyword(s):  
Degree Sequence ◽  
Kinematic Chain ◽  
Loop Analysis ◽  
Topological Graph ◽  
Type Analysis ◽  
Kinematic Chains ◽  
Relationship Of ◽  
The Relationship ◽  
Basic Loop ◽  
Isomorphism Identification

Based on the array representation of loop in topological graph of kinematic chains, this paper proposes two basic loop operations. Their existent conditions and properties of the two operations are also researched. In further loop analysis we discuss the important concepts including the independent loop, canonical degree-sequence and perimeter topological graph. Two Theorems deal with the relationship of loops. Based on above basic theory some important applications are given, such as the isomorphism identification based on the loop set concept, the detection of the rigid sub-chains in a kinematic chain and the type analysis of freedom of kinematic chains.

The Establishment of Novel Structure Representation Models for Several Kinds of Mechanisms

2009 ◽  
Author(s):  
Huafeng Ding ◽  
Jing Zhao ◽  
Zhen Huang
Keyword(s):  
Topological Graph ◽  
Planar Mechanisms ◽  
Topological Graphs ◽  
Structure Representation ◽  
Joint Kinematic ◽  
Kinematic Chains ◽  
Mathematical Representations ◽  
Novel Structure ◽  
Structure Synthesis ◽  
Topological Models

This paper attempts to establish the unified topological models and corresponding mathematical representations for planar simple joint, multiple joint and geared (cam) kinematic chains. First, the conventional topological representation models of kinematic chains are introduced. Then new topological models of multiple joint and geared (cam) kinematic chains, which are derived from the topological graph of simple joint kinematic chains, are presented. The characteristics of the new topological graphs and their associations with the topological graph of simple joint kinematic chains are also addressed. The most important merit of the new topological graphs is that it makes it much easier to do unified structure synthesis and further establish conceptual design platform for various planar mechanisms of these kinds.

Generation of Planar Kinematic Chains With One Multiple Joint

2013 ◽  
Author(s):  
Huafeng Ding ◽  
Weijuan Yang ◽  
Peng Huang ◽  
Li Ma ◽  
Andrés Kecskeméthy
Keyword(s):  
Conceptual Design ◽  
Degrees Of Freedom ◽  
Characteristic Number ◽  
Automatic Method ◽  
Topological Graph ◽  
Topological Graphs ◽  
Systematic Method ◽  
Joint Kinematic ◽  
Kinematic Chains ◽  
First Time

It is very important to synthesize as many feasible kinematic structures of mechanisms as possible in the conceptual design of mechanisms. Besides simple joint mechanisms, multiple joint mechanisms are also widely used in various mechanical systems. This paper proposes an automatic method for the synthesis of planar multiple joint kinematic chains which are seldom addressed in literature. The bicolor topological graph and the bicolor contracted graph are adopted to represent the topological structures of multiple joint kinematic chains. The characteristic number string of bicolor topological graphs is proposed and used to detect efficiently isomorphism in the synthesis progress. A systematic method for the synthesis of kinematic chains with one multiple joint is proposed, and the whole families of multiple joint kinematic chains with up to 16 links and all possible degrees of freedom are obtained for the first time.

Automatic Structural Synthesis of Planar Multiple Joint Kinematic Chains

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Huafeng Ding ◽  
Weijuan Yang ◽  
Peng Huang ◽  
Andrés Kecskeméthy
Keyword(s):  
Degrees Of Freedom ◽  
Characteristic Number ◽  
Structural Synthesis ◽  
Topological Graph ◽  
Topological Graphs ◽  
Systematic Method ◽  
Joint Kinematic ◽  
Kinematic Chains ◽  
Mechanical Products ◽  
First Time

It is of great importance in the conceptual creative design of mechanical systems to synthesize as many feasible kinematic structures of mechanisms as possible. However, the methods for the structural synthesis of multiple joint kinematic chains are seldom addressed in literature even though they are widely used in various mechanical products. This paper proposes an automatic method to synthesize planar multiple joint kinematic chains. First, the bicolor topological graph and the bicolor contracted graph are introduced to represent the topological structures of multiple joint kinematic chains. Then, the characteristic number string of bicolor topological graphs is proposed and used to efficiently detect isomorphism in the synthesis progress. Finally, a systematic method for the synthesis of kinematic chains with one multiple joint is proposed, and the whole families of multiple joint kinematic chains with up to 16 links and all possible degrees of freedom are synthesized for the first time.

Unified Topological Representation Models of Planar Kinematic Chains

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
Huafeng Ding ◽  
Jing Zhao ◽  
Zhen Huang
Keyword(s):  
Conceptual Design ◽  
Topological Representation ◽  
Topological Graph ◽  
Planar Mechanisms ◽  
Topological Graphs ◽  
Joint Kinematic ◽  
Kinematic Chains ◽  
Mathematical Representations ◽  
Structure Synthesis ◽  
Topological Models

This paper attempts to establish unified topological models and corresponding mathematical representations for planar simple joint, multiple joint, and geared (cam) kinematic chains. First, the conventional topological representation models of kinematic chains are introduced. Then, new topological models of multiple joint and geared (cam) kinematic chains, which are derived from the topological model of simple joint kinematic chains, are presented. The characteristics of the new topological graphs and their associations with the topological graph of simple joint kinematic chains are also addressed. The most important merit of the new topological graphs is that it makes it much easier to undertake unified structure synthesis and further to establish conceptual design platform for various planar mechanisms. Synthesis examples of both multiple joint and geared chains are given, which show the effectiveness of the unified topological models.

Isomorphism Identification of Graphs of Kinematic Chains

2007 ◽  
Author(s):  
Huafeng Ding ◽  
Zhen Huang
Keyword(s):  
Computational Complexity ◽  
Computer Science ◽  
Adjacency Matrix ◽  
Complexity Analysis ◽  
Unique Representation ◽  
Kinematic Chains ◽  
Adjacency Matrices ◽  
Isomorphism Identification

Isomorphism identification of graphs is one of the most important and challenging problems in the fields of mathematics, computer science and mechanisms. This paper attempts to solve the problem by finding a unique representation of graphs. First, the perimeter loop of a graph is identified from all the loops of the graph obtained through a new algorithm. From the perimeter loop a corresponding perimeter graph is derived, which renders the forms of the graph canonical. Then, by relabelling the perimeter graph, the canonical perimeter graph is obtained, reducing the adjacency matrices of a graph from hundreds of thousands to several or even just one. On the basis of canonical adjacency matrix set, the unique representation of the graph, the characteristic adjacency matrix, is obtained. In such a way, isomorphism identification, sketching, and establishment of the database of common graphs, including the graphs of kinematic chains, all become easy to realize. Computational complexity analysis shows that, in the field of kinematic chains the approach is much more efficient than McKay’s algorithm which is considered the fastest so far. Our algorithm remains efficient even when the links of kinematic chains increase into the thirties.

A simple and efficient method for isomorphism identification of planar kinematic chains

2021 ◽  
Author(s):  
Luchuan Yu ◽  
Chenxu Cai ◽  
Jianhua Zhang ◽  
Qinhe Zhang
Keyword(s):  
Structural Design ◽  
Kinematic Chain ◽  
Structural Synthesis ◽  
Topological Graphs ◽  
Innovative Design ◽  
Kinematic Chains ◽  
Solid Foundation ◽  
Programming Software ◽  
Chain Links ◽  
Isomorphism Identification

Abstract Isomorphism identification plays an important role in structural design and innovative design. Based on the adjacency matrix and loop theory, a new method is proposed in this paper to identify the isomorphic kinematic chains. It enriches the application of loop-based theory for isomorphism identification. In the kinematic chain, links and joints are connected alternatively and every link corresponds to a fixed link degree. Due to the inherent characteristics, the labeled sequence of links can be random, which does not affect the result of isomorphism identification. By the programming software MATLAB, some examples with 6-, 8-, 10-, 11-, 12-link kinematic chains, and 15-vertex topological graphs are presented. Results show that the proposed method applies to topology graphs and kinematic chains with one or multiple joints. Compared with other methods, the proposed method is confirmed correctly. And there is no counterexample. It lays a solid foundation for structural synthesis in the future.

Studying the Optimal Layout of Topological Graphs to Facilitate the Automatic Sketching of Kinematic Chains

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Wenjian Yang ◽  
Huafeng Ding ◽  
Yong He ◽  
Min Wu
Keyword(s):  
Conceptual Design ◽  
Low Complexity ◽  
New Method ◽  
Computer Language ◽  
Optimal Layout ◽  
Topological Graph ◽  
Topological Graphs ◽  
Kinematic Chains ◽  
Two Parameters

The sketching of kinematic chains is important in the conceptual design of mechanisms. In general, the process of sketching kinematic chains can be divided into two steps, namely sketching topological graphs and converting them into the corresponding kinematic chains. This paper proposes a new method to automatically sketch topological graphs including both planar and nonplanar graphs. First, two parameters called moving sign (MS) and moving sign string (MSS) are defined, based on which a new algorithm is proposed to acquire all feasible layouts of the contracted graph by moving inner edges. All topological graphs synthesized from the same contracted graph are identified to have the shared feasible layouts, and another algorithm is proposed to determine the optimal layout for each topological graph. Then, topological graphs are sketched automatically by determining the location of vertices. The method has low complexity and is easy to be programmed using computer language.

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