Compound Topological Invariant Based Method for Detecting Isomorphism in Planar Kinematic Chains

2020 ◽  
Vol 12 (5) ◽  
Author(s):  
Liang Sun ◽  
Zhizheng Ye ◽  
Rongjiang Cui ◽  
Wenjian Yang ◽  
Chuanyu Wu
Keyword(s):  
Detection Method ◽  
Planetary Gear ◽  
Topological Invariant ◽  
Detection Methods ◽  
Fourth Power ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Planetary Gear Trains ◽  
Simple Detection ◽  
Gear Trains

Abstract An important step in the structural synthesis of kinematic chains (KCs) or mechanisms is the detection of isomorphic structures. Although many detection methods have been proposed, most of them require complex computations and have poor versatility. In this study, a simple detection method is proposed based on a compound topological invariant (CTI), which comprises the fourth power of adjacency matrix and eigenvalues. Besides two complex 15- and 28-link planar simple-joint KCs (PSKCs), the method is tested on the complete atlas of contracted graphs with up to six independent loops, PSKCs with up to 13 links, 8-link 1-degree-of-freedom (DOF) planar multiple-joint KCs (PMKCs), and 6-link 1-DOF planetary gear trains (PGTs). All the results are in agreement with the reported results in the literature. Our method possesses good versatility and has been verified as being reliable and efficient.

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.

The Perimeter Loop-Based Method for the Automatic Isomorphism Detection in Planetary Gear Trains

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Wenjian Yang ◽  
Huafeng Ding
Keyword(s):  
Computer Program ◽  
Present Method ◽  
Planetary Gear ◽  
Previous Method ◽  
Important Process ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Planetary Gear Trains ◽  
The Future ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in transmission systems. The structural synthesis of PGTs is an effective way to create novel and excellent transmissions. In the structural synthesis of PGTs, the isomorphism detection (ID) is an essential and especially important process. The ID aims to avoid duplication and guarantee the uniqueness of each PGT. The reliability of the ID method directly determines the accuracy of the synthesis result. Unfortunately, when the existing ID methods are used to synthesize PGTs, the synthesis results are not consistent with each other. A very important reason is that the ID methods fail to work in some cases. This fact gives rise to the need of an extremely reliable ID method, which may resolve the contradiction in the existing synthesis results in the future. In this paper, our previous perimeter loop-based ID method, which is applicable for linkage kinematic chains and has been proved to be reliable and efficient, is improved to detect isomorphic PGTs. The improvements relative to our previous method are discussed in detail. The present method is fully automated with the aid of a computer program, and verified by the atlas of PGTs with up to six links, as well as some PGTs with seven, eight, and ten links.

Automatic Detection of Embedded Structure in Planetary Gear Trains

1997 ◽  
Vol 119 (2) ◽  
pp. 315-318 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Yi-Chang Wu
Keyword(s):  
Computer Program ◽  
Automatic Detection ◽  
Planetary Gear ◽  
Gear Train ◽  
Graph Representation ◽  
Structural Synthesis ◽  
Planetary Gear Train ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Embedded Structure

The detection of embedded structure is one of important steps in the structural synthesis of planetary gear trains. The purpose of this paper is to develop a computer program for the automatic detection of embedded structure in planetary gear trains. First, the graph representation of a planetary gear train is used to clarify the kinematic structure. Next, the concept of fundamental circuit is applied to derive an algorithm for the detection of embedded structure in a planetary gear train. Using the notation of adjacency matrix, an interactive computer program has been developed such that embedded structure in a planetary gear train can be automatically analyzed by only entering the corresponding graph.

The Detection of Embedded Structure in Planetary Gear Trains

1996 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Jin-Juh Hsu ◽  
Yi-Chang Wu
Keyword(s):  
Computer Program ◽  
Planetary Gear ◽  
Gear Train ◽  
Graph Representation ◽  
Structural Synthesis ◽  
Planetary Gear Train ◽  
Interactive Computer Program ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Embedded Structure

Abstract The detection of embedded structure is one of important steps in the structural synthesis of planetary gear trains. The purpose of this paper is to develop a computer program for the automatic detection of embedded structure in planetary gear trains. First, the graph representation of planetary gear trains are used to clarify the kinematic structure. Next, a method which is based on the concept of fundamental circuits for the detection of embedded structure in a planetary gear train. Using the notation of adjacency matrix, an interactive computer program has been developed such that embedded structure in a planetary gear train can be automatically analyzed by only entering the corresponding graph.

scholarly journals A new method for isomorphism identification of planetary gear trains

2021 ◽  
Vol 12 (1) ◽  
pp. 193-202
Author(s):  
Wei Sun ◽  
Ronghe Li ◽  
Jianyi Kong ◽  
Anming Li
Keyword(s):  
Detection Method ◽  
Planetary Gear ◽  
Distance Matrix ◽  
New Method ◽  
Topological Graph ◽  
Weighted Distance ◽  
Planetary Gear Trains ◽  
The Matrix ◽  
Gear Trains ◽  
Isomorphism Identification

Abstract. Planetary gear trains (PGTs) are widely used in machinery such as vehicles, pulley blocks, wrist watches, machine tools, and robots. During the process of structural synthesis of PGTs using graph theory, isomorphism identification of graphs is an important and complicated problem. The reliability of the isomorphism detection method directly determines the accuracy of the synthesis result. In this paper, a novel isomorphism identification method for PGTs is proposed. First, a new weighted adjacent matrix is presented to describe the topological graph of PGTs, which has is unique in describing the structure of PGTs. Then, the weighted distance matrix is proposed and the sum of the matrix is obtained, which can determine whether the planetary gear trains is isomorphic or not. Eventually, the examples demonstrate that this new method can be accurately and effectively performed.

Topological Analysis of Single-Degree-of-Freedom Planetary Gear Trains

1991 ◽  
Vol 113 (1) ◽  
pp. 10-16 ◽  
Author(s):  
D. G. Olson ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Topological Analysis ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Graph Representation ◽  
Straightforward Manner ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Planetary Gear Trains ◽  
Input And Output ◽  
Gear Trains

Graph theory has been demonstrated by many researchers to be useful during the conceptual phase of mechanism design. For the particular class of mechanisms known as planetary gear trains, the graph representation has been used primarily for “topological synthesis,” the enumeration of kinematic chains satisfying the requirements for planetary gear trains. The subsequent “topological analysis” steps resulting in the specification of ground, input, and output links, have received very little attention in the literature, perhaps because the conventional graph representation for topological analysis, and utilizes a new graph representation which enables these steps to be performed in a straightforward manner. It is shown that among the thirteen distinct displacement graphs representing planetary geared kinematic chains with five links and one degree-of-freedom, only four distinct planetary gear trains result after assigning the ground, input, and output links subject to meaningful topological requirements.

An Application of Graph Theory for the Detection of Degenerate Structures in Planetary Gear Trains

2021 ◽  
Author(s):  
Essam L. Esmail ◽  
Anahed H. Juber
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Connectivity Matrix ◽  
Structural Synthesis ◽  
Multiple Degrees Of Freedom ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Straightforward Approach

Abstract One of the most important steps in the structural synthesis of planetary gear trains is to eliminate degenerate structures. First, the graph theory is used to represent planetary gear trains (PGTs). Second, a procedure is developed to identify fundamental geared entities (FGEs). Further, the single-planet FGEs are shown to have one-DOF and, therefore, cannot constitute a degenerate structure. It is this that allows a significant reduction in the calculation in relation to other methods of diagnosing degenerate structures. Third, using the concepts of FGEs and the notation of the associated adjacency matrix, an algorithm is developed for the detection of degenerate structures in PGTs. The algorithm is based on the fact that any degenerate structure is a PGT formed by two fundamental geared entities with common edges and/or vertices equal to or more than 3. Forth, the concept of connectivity between single-planet FGEs is introduced and a simple, straightforward approach for deducting the connectivity matrix from the adjacency matrix is developed. The new vertex-edge mobility criterion does not require combinatorial analysis. Besides, the method is applicable to one and multiple degrees of freedom PGTs, it is also applicable to multi-planet PGTs and complex PGTs, including contrary examples found in the literature.

Detection of Degenerate Structure in Single Degree-of-Freedom Planetary Gear Trains

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
Graph Theory ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Structural Synthesis ◽  
Drastic Reduction ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Planetary Gear Trains ◽  
Gear Trains

Graph theory is a powerful tool in structural synthesis and analysis of planetary gear trains (PGTs). In this paper, a new algorithm has been developed for detecting degenerate structure in planetary gear trains. The proposed algorithm is based on the concept of fundamental circuits' rotation graphs. Detection of degeneracy is entirely based on finding one key element. The key element or link that makes planetary gear train into two groups is found in this work. The main advantage of the proposed method lies in the drastic reduction in the required combinatorial analysis compared to other methods available.

scholarly journals Recognition of Bimolecular Logic Operation Pattern Based on a Solid-State Nanopore

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 33
Author(s):  
Han Yan ◽  
Zhen Zhang ◽  
Ting Weng ◽  
Libo Zhu ◽  
Pang Zhang ◽  
...  
Keyword(s):  
Self Assembly ◽  
Detection Method ◽  
Logic Gate ◽  
Detection Methods ◽  
Label Free ◽  
Recognition Method ◽  
Operation Pattern ◽  
Simple Detection ◽  
Dna Tetrahedron ◽  
Marker Molecule

Nanopores have a unique advantage for detecting biomolecules in a label-free fashion, such as DNA that can be synthesized into specific structures to perform computations. This method has been considered for the detection of diseased molecules. Here, we propose a novel marker molecule detection method based on DNA logic gate by deciphering a variable DNA tetrahedron structure using a nanopore. We designed two types of probes containing a tetrahedron and a single-strand DNA tail which paired with different parts of the target molecule. In the presence of the target, the two probes formed a double tetrahedron structure. As translocation of the single and the double tetrahedron structures under bias voltage produced different blockage signals, the events could be assigned into four different operations, i.e., (0, 0), (0, 1), (1, 0), (1, 1), according to the predefined structure by logic gate. The pattern signal produced by the AND operation is obviously different from the signal of the other three operations. This pattern recognition method has been differentiated from simple detection methods based on DNA self-assembly and nanopore technologies.

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