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.

scholarly journals Structural synthesis of plane kinematic chain inversions without detecting isomorphism

2021 ◽  
Vol 12 (2) ◽  
pp. 1061-1071
Author(s):  
Jinxi Chen ◽  
Jiejin Ding ◽  
Weiwei Hong ◽  
Rongjiang Cui
Keyword(s):  
Mechanism Design ◽  
Adjacency Matrix ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Synthesis Methods ◽  
Creative Design ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract. A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

Critical Review of Existing Degeneracy Testing and Mobility Type Identification Algorithms for Kinematic Chains

2005 ◽  
Author(s):  
Rajesh Pavan Sunkari ◽  
Linda C. Schmidt
Keyword(s):  
Critical Review ◽  
Kinematic Chain ◽  
Structural Studies ◽  
Mobility Analysis ◽  
Structural Synthesis ◽  
Common Error ◽  
Kinematic Chains ◽  
The Individual ◽  
Almost All ◽  
Mathematical Justification

Mobility analysis is one of the fundamental problems of structural studies of kinematic chains. Degeneracy testing, an important step in structural synthesis, can be considered as a part of the mobility analysis due to the similarity of the two problems. One common error in the algorithms for these two problems is the assumption that the graph of a planar kinematic chain is a planar graph. This work shows that almost all the mobility analysis algorithms, except that of Lee and Yoon, have this error. This work also critically reviews the two most efficient algorithms on degeneracy testing, those by Hwang and Hwang, and Lee and Yoon. It is shown that due to the errors in the Hwang and Hwang’s algorithm, it failed to identify some of the degenerate chains. Furthermore, the accuracy of the Lee and Yoon’s algorithms for mobility analysis and degeneracy testing is proved by providing the mathematical justification of the individual steps of the algorithms.

scholarly journals Improved high-order adjacent vertex assignment sequence for similarity vertices and isomorphism identification of planar kinematic chains

2020 ◽  
Author(s):  
Liang Sun ◽  
Zhizheng Ye ◽  
Fuwei Lu ◽  
Rongjiang Cui ◽  
Chuanyu Wu
Keyword(s):  
Structural Features ◽  
High Order ◽  
Adjacent Vertex ◽  
Innovative Design ◽  
Kinematic Chains ◽  
Adjacent Point ◽  
Sequence Method ◽  
Definition Of ◽  
Isomorphism Identification ◽  
Specific Definition

Abstract Isomorphism identification is fundamental to synthesis and innovative design of kinematic chains (KCs). The identification can be performed accurately by using the similarity of KCs. However, there are very few researches on isomorphism identification based on the properties of similarity vertices. In this paper, an improved high-order adjacent vertex assignment (IHAVS) sequence method is proposed to seek out the similarity vertices and identify the isomorphism of the planar KCs. First, the specific definition of IHAVS is described. Through the calculation of the IHAVS, the adjacent point value sequence reflecting the uniqueness of the structural features is established. Based on the value sequence, all possible similarity vertices, corresponding relations and isomorphism discrimination can be realized. By checking the topological diagrams of KCs of different number of links, the correctness of the proposed method are verified. Finally, the method is used to find the similarity vertices of all the 9-link 2-DOF(degree of freedom) planar KCs.

Topological Characteristics and Automatic Generation of Structural Synthesis of Spatial Mechanisms: Part II — Automatic Generation of Structural Types of Kinematic Chains

1992 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao
Keyword(s):  
Kinematic Chain ◽  
Automatic Generation ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Automatic Program ◽  
Spatial Mechanisms ◽  
Structural Types ◽  
Topological Characteristics ◽  
Linear Graphs ◽  
Independent Loops

Abstract Based on the single-opened chain constraints and the network topological characteristics of mechanisms, a powerful new method for structural synthesis of spatial kinematic chain with plane and nonplane linear graphs has been developed. This permits the development of a highly efficient and completely automatic program for the computer-generated enumeration of structural types of mechanisms. The method is illustrated by applying to the case of kinematic chains with up to six independent loops on a personal computer.

Innovative Design Based on Prototypes of the Main Mechanism of Table Lamp

2012 ◽  
Vol 198-199 ◽  
pp. 189-192
Author(s):  
Wan Chun Zhou ◽  
Jian Jun Lu
Keyword(s):  
Topological Structure ◽  
Kinematic Chain ◽  
Main Mechanism ◽  
Schematic Diagram ◽  
Design Constraints ◽  
Innovative Design ◽  
Kinematic Chains ◽  
Structure Characteristics ◽  
Practical Design ◽  
Number Synthesis

On the basis of analyzing the topological structure of an original mechanism, it leads to the generalized kinematic chain meeting the same topological structure characteristics of the original mechanism in accordance with the generalized principle of mechanism, number synthesis of kinematic chain and compound hings. Allocation of ground links and performing links in the kinematic chain can get all feasible specialized kinematic chains while considering practical design constraints. In the final step, concrete schematic diagram of mechanism being restored from specialized kinematic chains leads to a series of new mechanism different from the original one. Designers ascertain appropriate new mechanism after selection and analysis.

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.

Identification of Isomorphism in Kinematic Chains Using Hamming Method

2014 ◽  
Vol 592-594 ◽  
pp. 2723-2727
Author(s):  
Indu Saini ◽  
Vijay Pal Singh
Keyword(s):  
Reliable Method ◽  
Kinematic Chain ◽  
Difficult Problem ◽  
Satisfactory Solution ◽  
Sewing Machine ◽  
Kinematic Chains ◽  
Straight Line ◽  
And Inversion ◽  
Isomorphism Identification

Isomorphism identification is a difficult problem in kinematic chains. There is number of method given by many researchers to detect the isomorphism and inversion of kinematic chain but each has its own shortcomings. Purpose of this paper is to give an efficient and reliable method. An attempt has been made to provide satisfactory solution to detection of isomorphism by using hamming method. The method is implemented on sewing machine, break drum; straight line motion mechanisms have six links kinematic chain.

A More Direct Method for Structural Synthesis of Simple-Jointed Planar Kinematic Chains

1994 ◽  
Author(s):  
Varada Raju Dharanipragada ◽  
Nagaraja Kumar Yenugadhati ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Computer Program ◽  
Reliable Method ◽  
Direct Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Structural Synthesis ◽  
Indirect Methods ◽  
Kinematic Chains ◽  
A Chain

Abstract Structural synthesis of kinematic chains leans heavily on indirect methods, most of them based on Graph Theory, mainly because reliable isomorphism tests are not available. Recently however, the first and third authors have established the Secondary Hamming String of a kinematic chain as an excellent indicator of its isomorphism. In the present paper this Hamming String method was applied with slight modifications for synthesizing on a PC-386, distinct kinematic chains with given number of links and family description. The computer program, written in Pascal, generated both the six-bar and all 16 eight-bar chains as well as one sample family (2008) of ten-bar chains, verifying previously established results. Hence this paper presents a direct, quick and reliable method to synthesize planar simple-jointed chains, open or closed, with single- or multi-degree of freedom, containing any number of links. A spin-off of this paper is a simple, concise and unambiguous notation for representing a chain.

scholarly journals Innovative design method of the metamorphic hand

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141775415 ◽  
Author(s):  
Wei Sun ◽  
Jianyi Kong ◽  
Xingdong Wang ◽  
Huaiguang Liu
Keyword(s):  
Design Method ◽  
Kinematic Chain ◽  
Theoretical Method ◽  
Combination Method ◽  
Structural Synthesis ◽  
Innovative Design ◽  
Automated Production ◽  
Metamorphic Mechanism ◽  
Physical Experiments ◽  
Number Synthesis

In order to solve the last centimeter problem of automated production, it is necessary to innovative design of flexible fixture. This article presents a metamorphic hand design method through the principle of metamorphic mechanism. Firstly, kinematic chain satisfying the requirements is obtained by number synthesis and structural synthesis. Then, the kinematic chain becomes a mechanism that meets the requirements using regeneration design rules. And the holographic matrix description method is used to describe the configuration transformation of the metamorphic mechanism. Furthermore, through the combination method of kinematic chain, the metamorphic clamp increases the two joint fingers into a metamorphic hand. Finally, the validity of the theoretical method is verified by physical experiments.

Innovative Design Based on Topological Analysis of Rope-Type Long-Link Grippers

2010 ◽  
Vol 29-32 ◽  
pp. 1274-1278
Author(s):  
Wan Chun Zhou ◽  
Tong Zhou
Keyword(s):  
Topological Analysis ◽  
Kinematic Chain ◽  
Structural Type ◽  
Similar Function ◽  
Specific Design ◽  
Topological Map ◽  
Design Constraints ◽  
Innovative Design ◽  
Kinematic Chains ◽  
Chain Maps

In this thesis, the author first analyzed the topological structure of the original mechanism. On this basis, the topological map and a series of kinematic chain maps which meet the requirements have been constructed with graph theory. Then the types of various components were designated based on specific design constraints, and generalized kinematic chains were turned into the new mechanism having the same or similar function with the original mechanism. Designers can value them comprehensively and screen out the good structural type. The method is regarded as a workable and efficient method for development and design of new products.

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