A Method for Isomorphism Identification of the Gear Train Kinematic Chains

2014 ◽  
Vol 11 (7) ◽  
pp. 2125-2134 ◽  
Author(s):  
Yanhuo Zou
Keyword(s):  
Gear Train ◽  
Kinematic Chains ◽  
Isomorphism Identification

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

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Yanhuo Zou ◽  
Peng He
Keyword(s):  
Equivalent Circuit Model ◽  
Gear Train ◽  
Analysis Method ◽  
Kinematic Chains ◽  
Mathematical Algorithm ◽  
Structure Synthesis ◽  
Mathematical Problems ◽  
Node Voltage ◽  
Isomorphism Identification ◽  
Weighted Adjacency Matrix

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.

Intelligent Design of Mechanism Kinematic Chains by Advanced Optimal Methods

2011 ◽  
Vol 201-203 ◽  
pp. 2182-2185
Author(s):  
Miao Zhang ◽  
Ning Bo Liao ◽  
Chen Zhou ◽  
Xi Tao
Keyword(s):  
Graph Theory ◽  
Intelligent Design ◽  
Kinematic Structure ◽  
Kinematic Chains ◽  
Complicated Problem ◽  
Optimal Methods ◽  
Advantages And Disadvantages ◽  
Mechanism Kinematic ◽  
Isomorphism Identification ◽  
Structure Enumeration

When using graph theory to conduct intelligent design for kinematic structure enumeration, the isomorphism identification of graphs is an important and complicated problem. In this paper, the methodology of transferring isomorphism identification into optimization issue was introduced. Then the recent development of applying advanced optimal methods for isomorphism identification was reviewed, the advantages and disadvantages of there methods were discussed.

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.

scholarly journals MEANS, STANDS AND MACHINES FOR TESTING GEAR WHEELS AND GEAR TRAINS OF HELICOPTER REDUCTION TRAINS

2021 ◽  
pp. 97-117
Author(s):  
O. Pilipenko ◽  
D. Kolesnik ◽  
A. Berezniak ◽  
V. Kohan ◽  
O. Pankul
Keyword(s):  
Vibration Signal ◽  
Technical Condition ◽  
Gear Train ◽  
Aviation Industry ◽  
High Tech ◽  
Kinematic Chains ◽  
Accurate Picture ◽  
Advanced Control ◽  
Gear Trains ◽  
Gear Wheels

The production and repair of such high-tech and important products as helicopters‟ reduction trains is impossible without comprehensive testing of these products, starting with the manufacture of their individual parts and assemblies and ending with the delivery of reduction trains to the customer. Various means for testing of gear wheels‟ rims and gear trains of helicopter‟s reduction trains, which have found application in testing equipment, are presented. Devices, testers, stands and machines for various tests are considered in order to control the characteristics of gear trains of aviation reduction trains after certain periods of their operation and repair, aimed at achieving better performance during further operation. The considered traditional metrological means of control of gear rims, gear measuring machines and complexes, some stands and machines for testing of reduction trains, pulse controllers and roll machines give an idea of various methods and means of control of gear wheels and gear trains of helicopters‟ reduction trains. The main method of experimental research of gear trains of reducers is stand tests both on movable gear wheels and on roll machines. Until recently, the most common method for monitoring and diagnosing gear trains has been vibrography, however, existing techniques do not give an accurate picture of the train condition, especially the contact surface of the teeth. During the operation of the gear train as a part of the helicopter‟s reduction train, signals from other sources (rotors, blades, shafts, bearings) are superimposed on the vibration signal generated by the gear train which significantly complicates the extraction and processing of the desired vibration signal. One of the most effective methods for monitoring and diagnosing the technical condition of kinematic chains of different complexity, which includes gear trains of helicopters„ reducers is kinematometry. The disadvantage of traditional kinematometry is the need to use high-precision sensors for the frequency and phase of the rotor rotation. Control of vibration from the early 1990s to the present time is the most advanced control, the means and methods of which are well developed in the aviation industry.

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

2021 ◽  
Vol 25 (21) ◽  
pp. 13263-13276
Author(s):  
Luchuan Yu ◽  
Chenxu Cai ◽  
Jianhua Zhang ◽  
Qinhe Zhang
Keyword(s):  
Efficient Method ◽  
Kinematic Chains ◽  
Isomorphism Identification

Similarity recognition and isomorphism identification of planar kinematic chains

2020 ◽  
Vol 145 ◽  
pp. 103678 ◽  
Author(s):  
Liang Sun ◽  
Rongjiang Cui ◽  
Zhizheng Ye ◽  
Yuzhu Zhou ◽  
Yadan Xu ◽  
...  
Keyword(s):  
Kinematic Chains ◽  
Isomorphism Identification

Topological invariant and definition method for detecting isomorphism in planar kinematic chains

2020 ◽  
pp. 095440622096078
Author(s):  
Rongjiang Cui ◽  
Zhizheng Ye ◽  
Liang Sun ◽  
Chuanyu Wu
Keyword(s):  
Planetary Gear ◽  
Topological Invariant ◽  
Detection Methods ◽  
Kinematic Chains ◽  
Essential Step ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Configuration Synthesis ◽  
Definition Of ◽  
Isomorphism Identification

Isomorphism identification is an essential step in mechanism configuration synthesis. Although various detection methods have been proposed, some of them can only effectively identify kinematic chains (KCs) within 10 links or complex programs that are needed to identify multilink KCs. In this study, a new isomorphism identification method is proposed based on the distance concept of graphs and the graph theory definition of isomorphism. In addition to two complex 21- and 28-link planar simple-joint KCs (PSKCs), the proposed algorithm is tested on the complete atlas of 8-link 1-DOF, 9-link 2-DOF, 10-link 1-DOF, 12-link 1-DOF, and 13-link 2-DOF PSKCs. The algorithm is also tested on 6-link 1-DOF and 7-link 1-DOF planetary gear trains (PGTs) to detect isomorphism. All results are in agreement with those of the existing literature. The method is fully automated via a computer program and has been verified to be reliable and efficient.

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.

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