New Graph Representation for Planetary Gear Trains

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Wenjian Yang ◽  
Huafeng Ding ◽  
Bin Zi ◽  
Dan Zhang
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Planetary Gear ◽  
Graph Representation ◽  
Synthesis Process ◽  
Planetary Gear Trains ◽  
Computer Aided ◽  
Gear Trains ◽  
Isomorphic Graphs ◽  
Canonical Rotation

Planetary gear trains (PGTs) are widely used in machinery to transmit angular velocity ratios or torque ratios. The graph theory has been proved to be an effective tool to synthesize and analyze PGTs. This paper aims to propose a new graph model, which has some merits relative to the existing ones, to represent the structure of PGTs. First, the rotation graph and canonical rotation graph of PGTs are defined. Then, by considering the edge levels in the rotation graph, the displacement graph and canonical displacement graph are defined. Each displacement graph corresponds to a PGT having the specified functional characteristics. The synthesis of five-link one degree-of-freedom (1DOF) PGTs is used as an example to interpret and demonstrate the applicability of the present graph representation in the synthesis process. The present graph representation can completely avoid the generation of pseudo-isomorphic graphs and can be used in the computer-aided synthesis and analysis of PGTs.

A New Technique Based on Loops to Investigate Displacement Isomorphism in Planetary Gear Trains

2002 ◽  
Vol 124 (4) ◽  
pp. 662-675 ◽  
Author(s):  
V. V. N. R. Prasad Raju Pathapati ◽  
A. C. Rao
Keyword(s):  
Graph Isomorphism ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Graph Representations ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
A New Technique

The most important step in the structural synthesis of planetary gear trains (PGTs) requires the identification of isomorphism (rotational as well as displacement) between the graphs which represent the kinematic structure of planetary gear train. Previously used methods for identifying graph isomorphism yielded incorrect results. Literature review in this area shows there is inconsistency in results from six link, one degree-of-freedom onwards. The purpose of this paper is to present an efficient methodology through the use of Loop concept and Hamming number concept to detect displacement and rotational isomorphism in PGTs in an unambiguous way. New invariants for rotational graphs and displacement graphs called geared chain hamming strings and geared chain loop hamming strings are developed respectively to identify rotational and displacement isomorphism. This paper also presents a procedure to redraw conventional graph representation that not only clarifies the kinematic structure of a PGT but also averts the problem of pseudo isomorphism. Finally a thorough analysis of existing methods is carried out using the proposed technique and the results in the category of six links one degree-of-freedom are established and an Atlas comprises of graph representations in conventional form as well as in new form is presented.

Study on the Method of Planetary Gear Trains Based on Topological Theory

2013 ◽  
Vol 568 ◽  
pp. 169-175 ◽  
Author(s):  
Ya Feng He ◽  
You Ming Wang
Keyword(s):  
Planetary Gear ◽  
Basic Structure ◽  
Graph Representation ◽  
Topological Graphs ◽  
Topological Theory ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
New System

The method research of planetary gear trains (PGTs) by applying topological theory is very significance in searching for innovative planetary trains. A new graph representation and stratification standard are introduced firstly. Then three topological graphs of basic structure of PGTs are established as the basis of synthesis theory. Next several kinds of planetary trains with small teeth difference and method of isomorphic determination are presented, thus built up the procedure of PGTs by graphs and example. Finally a new system of classification and synthesis for PGTs is put forward according to the feature of loops in topological theory.

Generation of Epicyclic Gear Trains of One Degree of Freedom

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Y. V. D. Rao ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Planetary Gear Trains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Hamming Matrix

New planetary gear trains (PGTs) are generated using graph theory. A geared kinematic chain is converted to a graph and a graph in turn is algebraically represented by a vertex-vertex adjacency matrix. Checking for isomorphism needs to be an integral part of the enumeration process of PGTs. Hamming matrix is written from the adjacency matrix, using a set of rules, which is adequate to detect isomorphism in PGTs. The present work presents the twin objectives of testing for isomorphism and compactness using the Hamming matrices and moment matrices.

Design of Multiple Operating Degrees-of-Freedom Planetary Gear Trains With Variable Structure

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Zeng-Xiong Peng ◽  
Ji-Bin Hu ◽  
Tian-Li Xie ◽  
Chun-Wang Liu
Keyword(s):  
Power Flow ◽  
Degrees Of Freedom ◽  
Flow Analysis ◽  
Graph Model ◽  
Planetary Gear ◽  
Variable Structure ◽  
Planetary Gear Trains ◽  
Planetary Gear Sets ◽  
Gear Trains ◽  
Synthesis Methodology

To obtain multiple speed ratios, a synthesis methodology of planetary gear trains (PGTs) with multiple operating degrees-of-freedom (DOFs) is proposed based on the variable structure method. Variable structure of PGT is accomplished by changing the fixed interconnection edge. First, PGTs with two operating DOFs are synthesized with a deduction method based on the relationship between the number of planetary gear sets (PGSs) and number of fixed interconnection edges. Next, connection characteristics of fixed interconnection edges are defined as frequency of utilization to construct original speed ratios of the two operating DOFs schemes. The connection characteristics are then obtained based on the power flow analysis. PGT graph model with connection characteristic is built to provide guidance in the design of varying structure. Finally, multispeed PGTs with multiple operating DOFs are synthesized based on the graph model and lever analogy. A design example for three-PGS PGTs is considered to highlight capabilities of the variable structure method.

Kinematic Analysis of Planetary Gear Trains Based on Topology

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Ming-Fei Gao ◽  
Ji-Bin Hu
Keyword(s):  
Automatic Transmission ◽  
Planetary Gear ◽  
Graph Representation ◽  
Speed Ratio ◽  
Topological Graph ◽  
Planetary Gear Trains ◽  
And Topology ◽  
Conceptual Design Phase ◽  
Gear Trains ◽  
The Relationship

Planetary gear trains (PGTs) are used in automatic transmission to achieve any desired speed ratios. At present, the study on the relationship between speed ratio and topology is not significant. Therefore, this paper focuses on studying the speed ratio based on topology. For this purpose, the graph theory is used to represent PGTs, and a concept of the speed topological graph is introduced. Based on the proposed graph representation, the relationship between the speed ratio and topology is studied. Three types of topological graphs are analyzed, which includes path, tree, and unicyclic graph, and necessary results are presented. The results reveal the relationship between speed ratio and topology, which helps in understanding the PGTs further. The result can help engineers to arrange the clutches and brakes to achieve desired speed ratio during the conceptual design phase, which can greatly improve the design efficiency of PGTs. The presented kinematics analysis method can be extended to analyze multi-input and multi-output planetary transmission.

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.

An Algorithm for Automatic Sketching of Planar Kinematic Chains

1985 ◽  
Vol 107 (1) ◽  
pp. 106-111 ◽  
Author(s):  
D. G. Olson ◽  
T. R. Thompson ◽  
D. R. Riley ◽  
A. G. Erdman
Keyword(s):  
Graph Theory ◽  
Line Graph ◽  
Kinematic Chain ◽  
Graph Representation ◽  
Synthesis Process ◽  
Line Graphs ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Synthesis Of Mechanisms ◽  
Computer Aided

One of the problems encountered in attempting to computerize type synthesis of mechanisms is that of automatically generating a computer graphics display of candidate kinematic chains or mechanisms. This paper presents the development of a computer algorithm for automatic sketching of kinematic chains as part of the computer-aided type synthesis process. Utilizing concepts from graph theory, it can be shown that a sketch of a kinematic chain can be obtained from its graph representation by simply transforming the graph into its line graph, and then sketching the line graph. The fundamentals of graph theory as they relate to the study of mechanisms are reviewed. Some new observations are made relating to graphs and their corresponding line graphs, and a novel procedure for transforming the graph into its line graph is presented. This is the basis of a sketching algorithm which is illustrated by computer-generated examples.

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