Kinematic Chain Isomorphism Identification Research Articles

The Equivalent Mechanical Model of Topological Graphs and the Isomorphism Identification of Kinematic Chains

Abstract In type synthesis of mechanisms, isomorphic identification of kinematic chains is a key issue, which has been studied for many years. In this paper, a new topological invariant, a character array of edge is constructed based on a novel model called an equivalent mechanical model. This invariant is used as a necessary condition for recognizing the edges of two topological graphs. On this basis, a method of constructing mapping by closed loop is proposed. The constructed mapping is used as the adequacy of identification so as to accurately identify the isomorphism of two graphs. This method is sufficient and necessary, which has been successfully tested in the 10-vertex, 12-vertex, 15-vertex, 28-vertex topological graphs. This method is limited to planar mechanisms that consist of revolute joints.

Representation of planar kinematic chains with multiple joints based on a modified graph and isomorphism identification

The representation and isomorphism identification of kinematic chains (KCs) with multiple joints are crucial issues to be solved in mechanism research. In this paper, a modified graph—planar face graph (PF graph), is proposed. As a key concept, “face” has been put forward to represent the case that a single, specific relationship is incident with multiple incidents. Some other basic concepts relating to PF graph are also explained in detail. PF graph is used to represent KCs with multiple joints and it reflects the uniqueness of KCs and realizes the one-to-one correspondence between KCs and adjacency and incident matrices. It also establishes relationships with other methods for representing KCs and it is proved to be suitable for complex mechanical systems. Moreover, the sufficient and necessary condition of isomorphism are derived, and two properties of permutation similarity are analysed. Based on them, the modified eigenvalue eigenvector method and the maximum path method are proposed, and they are integrated to form a new algorithm. In addition, the reliability and efficiency of the algorithm are proved.

The Equivalent Mechanical Model of Topological Graphs and the Isomorphism Identification of Kinematic Chains

The Equivalent Mechanical Model of Topological Graphs and the Isomorphism Identification of Kinematic Chains

Numbering method for the kinematic chain isomorphism recognition of a planar mechanism

The kinematic chain isomorphism identification of a planar mechanism is an important part of the innovative design of kinematic chain regeneration. Based on the structural characteristics of the kinematic chain of a planar mechanism, a new method, i.e. the numbering method, is proposed for isomorphism identification. Firstly, the links of a kinematic chain are numbered according to certain rules, and they are normalized. Then, the normalized contracted link adjacency matrix is used to represent the connection of the kinematic chain graph. Based on whether the contracted link adjacency matrix of two kinematic chains is the same, we can judge whether the two links are similar.

Mechanism isomorphism identification based on artificial fish swarm algorithm

The aim of this paper is to propose a practical solution for mechanism kinematic chain isomorphism identification – an artificial fish swarm algorithm. The artificial fish model of mechanism isomorphism identification is established, and behavioral way of the artificial fish is designed. According to isomorphism identification features of topological graph, the process of mechanism isomorphism identification based on artificial fish swarm algorithm is confirmed. The rationality and reliability of artificial fish swarm algorithm on the isomorphic identification of mechanism have been illustrated by a specific example, which provides a new method for intelligent CAD system design of mechanism. It builds a basis for future work in isomorphism identification of mechanism with high efficiency. Isomorphic identification of mechanism will contribute to rational qualitative analysis of mechanism design, perfection of irrationality can be done timely, which is the key factor for mechanical manufacturing. In this paper, we introduce the mechanism kinematic chain firstly, then optimization of artificial fish swarm algorithm is illustrated, and it is shown that how fish swarm algorithm is applied to mechanism kinematic chain. Finally, the feasibility and efficiency of the method are verified by the example of 10 bars, and the complex mechanism can be identified by the example of 14 bars and 18 bars.

Identification of Isomorphism in Multistage Planetary Gear Trains

Isomorphism identification of kinematic chains occupies an important place in the field of mechanism structure synthesis. A method to identify the isomorphism of multistage planetary gear trains is proposed in this paper. Firstly, the structure topology model and the corresponding link-link adjacency matrix are presented, to describe the schematic diagram of multistage planetary gear trains. Then, based on the hamming number method, the hamming number matrix is obtained by the link-link adjacency matrix, and the hamming value of link, the hamming number and the hamming strings of multistage planetary gear trains are introduced, which can determine whether the multistage planetary gear trains is isomorphic or not. The study shows that this work is beneficial to the development of new multistage planetary gear trains.

An Improved Genetic Algorithm Approach on Mechanism Kinematic Structure Enumeration with Intelligent Manufacturing

During the process of mechanism kinematic structure enumeration, isomorphism identification of graphs is an important and complicated problem. The problem is known to be a NP-complete problem. In this paper, according to the mechanism kinematic chain isomorphism identification criteria, a highly efficient hybrid genetic algorithm model is proposed for isomorphism identification. The model method is coupled with genetic algorithm, optimal choice, and optimal crossover operation. It shows a quick convergence rate of the late operation and can avoid convergence to local optimum. Simulation results show that the hybrid algorithm is more rapid and effective compared with simple genetic algorithm and the improved neural network algorithm.

An Algorithm for Identifying the Isomorphism of Planar Multiple Joint and Gear Train Kinematic Chains

Isomorphism identification of kinematic chains is one of the most important and challenging mathematical problems in the field of mechanism structure synthesis. In this paper, a new algorithm to identify the isomorphism of planar multiple joint and gear train kinematic chains has been presented. Firstly, the topological model (TM) and the corresponding weighted adjacency matrix (WAM) are introduced to describe the two types of kinematic chains, respectively. Then, the equivalent circuit model (ECM) of TM is established and solved by using circuit analysis method. The solved node voltage sequence (NVS) is used to determine the correspondence of vertices in two isomorphism identification kinematic chains, so an algorithm to identify two specific types of isomorphic kinematic chains has been obtained. Lastly, some typical examples are carried out to prove that it is an accurate, efficient, and easy mathematical algorithm to be realized by computer.

An improved hybrid immune algorithm for mechanism kinematic chain isomorphism identification in intelligent design

In intelligent mechanism design, isomorphism identification of mechanism kinematic chains (IIMKC) is aimed at avoiding repeated mechanism design and is proved to be an NP-complete problem. In this paper, kinematic chains are represented by graphs. An improved hybrid immune algorithm, which integrates the clonal selection immune algorithm with genetic algorithm and the local search algorithm, is proposed to solve IIMKC problem. Moreover, the novel saving and updating operator is proposed to save the best antibodies and maintain a diverse repertoire of antibodies for improving performance of clonal selection. In addition, the pseudo-crossover operator is introduced to enhance the efficiency of genetic algorithm. Simulation results validate the high efficiency and robustness of the hybrid immune algorithm.

A fast algorithm for kinematic chain isomorphism identification based on dividing and matching vertices

Kinematic chain isomorphism identification is a crucial issue in mechanism topology and an important application of Graph Isomorphism to mechanisms. In this paper, a kinematic chain is uniquely represented by a graph, and a fast deterministic algorithm called the Dividing and Matching Algorithm (DMA) is proposed. First, the vertices of each graph are divided by the degree. Then, vertex connection properties in a sub-graph and between sub-graphs are explored. Accordingly the expanded square degree and the correlation degree are proposed, based on which, the Dividing Vertex Algorithm (DVA) is developed to divide vertices into sets. Moreover, it is proved that only the vertices from the corresponding sets between two graphs are possible to be bijective or matched, which avoids exhaustive search. Eventually, a backtracking procedure is employed to match the vertices between corresponding sets by calling up DVA repeatedly. DMA detects whether the adjacency matrices of two graphs can be adjusted to be equivalent by changing the orders of vertices. Justifications for the reliability of each part of DMA are provided. The experiments and comparisons with existing algorithms show the effectiveness and efficiency of DMA.

Isomorphism Identification of Planar Kinematic Chains Based on Characteristic Arrays and Computation

At present, the research of isomorphism identification of planar kinematic chains has reached a great improvement, however, most of the methods are proved so complex, inefficient as well as unreliable that the research is hindered and restricted a lot. At the same time, especially with the appearance of the planar kinematic chains with multiple joints, there is less research about the methods. Hence, in the paper, based on the method of kinematic chains with characteristic arrays, one method of isomorphism identification of kinematic chains with single joint as well as multiple joints is proposed presently. What is more, a software based on this new method proposed is developed with Visual Basic. In the end of the paper, an example is analysed in detail with hand computation and this software, through which the method is proved simple, efficient as well as reliable.

Research on Kinematic Chain Isomorphism Identification Method Based on the Standardization Adjacent Matrix

In order to solve a baffling problem of kinematic chain isomorphism identification, proceeded from the isomorphism’s principles of graph theory, a new method for detecting isomorphism among planar kinematic chains using the standardization adjacent matrix is presented in this paper. The general course of adjacent matrix standardization processing and numbering principle of node are introduced, the implementation of this new method is illustrated with an example, it is showed that this new method can be accurately and effectively performed.

Kinematic Chain Isomorphism Identification Based on Loop-Code

A new method approach is presented to solve isomorphism identification of kinematic chain topology graphs. Kinematic chain topology graphs are depicted with loop-code based on the characteristic of kinematic chain topology graphs. The number of binary links in the limbs of topology graphs is arranged in group according to links with multi points of connection．Although the order of limbs in the groups and the order of links with multi points of connection outside the groups can change, the planar message of topology graphs can not change. Thereby forming loop-code.This representation is straightforward and not affected when drawing modes and labeling ways change in topology graphs．

A New Multivalued Neural Network for Isomorphism Identification of Kinematic Chains

A lot of methods have been proposed for the kinematic chain isomorphism problem. However, the tool is still needed in building intelligent systems for product design and manufacturing. In this paper, we design a novel multivalued neural network that enables a simplified formulation of the graph isomorphism problem. In order to improve the performance of the model, an additional constraint on the degree of paired vertices is imposed. The resulting discrete neural algorithm converges rapidly under any set of initial conditions and does not need parameter tuning. Simulation results show that the proposed multivalued neural network performs better than other recently presented approaches.

An improved artificial immune algorithm for mechanism kinematic chain isomorphism identification

An improved clonal selection artificial immune algorithm is presented to identify the isomorphism of the mechanism kinematic chains. The principles of isomorphism identification are based on the graph theory that adjacency matrices of two isomorphic graphs can interconvert. The clonal selection artificial immune algorithm is improved by adding a process named saving and updating operator after the process of refreshing. The high efficiency and robustness of this improved algorithm is proved by comparing it with simple clonal selection algorithm. The simulation results show that the improved algorithm can identify isomorphic kinematic chains successfully and rapidly.

Improving Neural Networks for Mechanism Kinematic Chain Isomorphism Identification

Detection of isomorphism among kinematic chains is essential in mechanical design, but difficult and computationally expensive. It has been shown that both traditional methods and previously presented neural networks still have a lot to be desired in aspects such as simplifying procedure of identification and adapting automatic computation. Therefore, a new algorithm based on a competitive Hopfield network is developed for automatic computation in the kinematic chain isomorphism problem. The neural approach provides directly interpretable solutions and does not demand tuning of parameters. We have tested the algorithm by solving problems reported in the recent mechanical literature. Simulation results show the effectiveness of the network that rapidly identifies isomorphic kinematic chains.

Isomorphism Identification of Kinematic Chains Using Novel Evolutionary Approaches

This paper presents a new method to isomorphism identification based on two novel evolutionary approaches—ant algorithm (AA) and artificial immune system (AIS). Salient features of the two evolutionary approaches are their efficient, robust and general-purpose algorithms for isomorphism identification despite its nondeterministic polynomial (NP) hard nature. First, based on the rearrangement of the vertexes in kinematic chains, the isomorphism identification of kinematic chains is transformed into a degree-reducible traveling salesman problem (TSP), so that the dimension and complexity can be largely decreased. Then AA and AIS algorithms are adopted to solve the transformed TSP. At last, characteristics of the two evolutionary approaches are discussed based on case studies.

Comments on mechanism kinematic chain isomorphism identification using adjacent matrices

A number of theories on the relationship between adjacent matrices of isomorphic mechanism kinematic chains have been investigated. A particular published theory about mechanism kinematic chain isomorphism using adjacent matrices has been revised, after errors in the original theory were discovered. Subsequently, the necessary and sufficient conditions of the eigenvalues and eigenvectors of adjacent matrices for isomorphic kinematic chains have been proven rigorously. A new procedure to identify isomorphic chains has been developed and presented. With this new procedure it is only necessary to compare eigenvalues and several eigenvectors of adjacent matrices of isomorphic kinematic chains to identify the isomorphic chains. Some examples have been provided to demonstrate how to use the theory.

A new method to mechanism kinematic chain isomorphism identification

A new method based on eigenvectors and eigenvalues is developed in this paper to identify isomorphism of mechanics kinematic chain. Kinematic chains are firstly represented by adjacent matrices. By comparing the eigenvalues and corresponding eigenvectors of adjacent matrices, the isomorphism of mechanism kinematics chain can easily be identified. The relationships in the mechanisms can also be obtained. A proof on this method is given in this paper. Some examples are provided to demonstrate the effectiveness of this method.

An artificial neural network approach to mechanism kinematic chain isomorphism identification

A new method based on an artificial neural network (ANN) technique is presented in this paper to identify the isomorphism of the mechanism kinematic chain. The mechanism kinematic chain is represented by a graph. The Hopfield–Tank ANN model for the graph isomorphism identification is developed, which includes the construction of an energy function and a dynamic equation. A case study is provided to demonstrate the preliminary success of the approach. An important motivation of this study is based on an observation that existing methods have not provided robust solutions, because of the NP hard nature of this problem.