Automatic Structural Synthesis of Epicyclic Gear Trains With One Main Shaft

2015 ◽  
Author(s):  
Huafeng Ding ◽  
Shuai Liu ◽  
Peng Huang ◽  
Changwang Cai ◽  
Zhen Huang
Keyword(s):  
Automobile Industry ◽  
Structural Characteristics ◽  
Graph Representation ◽  
Synthesis Process ◽  
Automatic Method ◽  
Main Shaft ◽  
Topological Graphs ◽  
Epicyclic Gear ◽  
Adjacency Matrices ◽  
Gear Trains

Design of automatic gear boxes with better performance is a pursuit goal of the modern automobile industry. In order to develop CAD method for the creative design of automatic gear boxes, this paper proposes an automatic method for the structure synthesis of one degree of freedom (DOF) epicyclic gear trains (EGTs) with one main shaft which serve as the key mechanisms in automatic gear boxes. First, based on the graph representation of EGTs, the canonical perimeter graphs and the corresponding canonical adjacency matrices are obtained. Then, based on the canonical adjacency matrices, the characteristic number strings are obtained and used to identify isomorphism in the synthesis process. Third, an automatic method is proposed to generate the basic graphs of the topological graphs of EGTs, and the basic graphs up to 9 links are synthesized. After that, based on the structural characteristics for the graphs of EGTs, an automatic method is proposed to synthesize the topological graphs of EGTs from the basic graphs, and an algorithm for the detection of rigid subchains in EGTs is also presented. Finally, a program is developed, and 1-DOF EGTs having one main shaft with up to 9 links are synthesized.

scholarly journals Patent Analysis and Structural Synthesis of Epicyclic Gear Trains Used in Automatic Transmissions

2019 ◽  
Vol 10 (1) ◽  
pp. 82 ◽  
Author(s):  
Huafeng Ding ◽  
Changwang Cai
Keyword(s):  
Structural Characteristics ◽  
Main Shaft ◽  
Structural Synthesis ◽  
New Approach ◽  
Automatic Transmissions ◽  
Epicyclic Gear ◽  
Transformation Relation ◽  
Gear Trains ◽  
Basic Graph ◽  
Patent Survey

A patent survey is conducted to investigate the application status of epicyclic gear trains (EGTs) used in automatic transmissions (ATs). In this regard, 673 AT patents are investigated firstly, and 274 different EGTs are obtained after the patent processing. EGTs are presented by corresponding double bicolor graphs (DBGs) and they are sorted into 13 groups in accordance with the degree of freedom (DOF) of DBGs and the degree of hollow vertices. Then, structural characteristics of obtained EGTs, which are used to detect whether the EGTs obtained in the future can be used in ATs, are analyzed and summarized. Finally, a new approach is proposed to obtain new configurations of the EGTs with one main shaft based on the transformation relation between DBG and the basic graph. Several examples are presented to illustrate the validity of the proposed approach.

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.

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.

scholarly journals Kinematic Analysis of Tendon-Driven Robotic Mechanisms Using Graph Theory

1989 ◽  
Vol 111 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Lung-Wen Tsai ◽  
Jyh-Jone Lee
Keyword(s):  
Graph Theory ◽  
Kinematic Analysis ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Robotic Devices

The kinematic structure of tendon-driven robotic mechanisms has been investigated with the aid of graph theory. The correspondence between the graph representation of the kinematic structure and the mechanism has been established. We have shown that the kinematic structure of tendon-driven kinematic chains is similar to that of epicyclic gear trains. We also have shown that, using the concept of fundamental circuits, the displacement equations of tendon-driven robotic mechanisms can be systematically derived from the kinematic structure. The theory has been demonstrated by the kinematic analysis of three articulated robotic devices.

A Combinatorial Approach for the Automatic Sketching of Planar Kinematic Chains and Epicyclic Gear Trains

1990 ◽  
Vol 112 (1) ◽  
pp. 6-15 ◽  
Author(s):  
Wei-Hua Chieng ◽  
D. A. Hoeltzel
Keyword(s):  
Graph Representation ◽  
Combinatorial Approach ◽  
New Approach ◽  
Kinematic Chains ◽  
Constrained Problem ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Automatic Mechanism ◽  
Diagram Representation ◽  
Number Of Authors

Automatic mechanism sketching can be considered to be a computational approach for converting the graph representation of a mechanism into its skeleton diagram representation, subject to the constraint of the avoidance of crossing links. The purpose of sketching is to obtain a clearer understanding of the topological and functional characteristics of a mechanism. Since the avoidance of link crossing alone cannot provide control over the numerical solution to the sketching problem, the graph-to-mechanism conversion process, subject to the constraint of link crossing avoidance, can be classified as an ill-constrained problem. The application of heuristics and semi-algorithmic methods have been applied by a number of authors in an attempt to overcome this numerical barrier. This paper introduces a new computational model, based on a combinatorial approach, for algorithmically solving the numerically continuous mechanism sketching problem as a discrete domain problem. This new approach can systematically generate explicit, concrete sketching constraints, thereby providing a well defined methodology for mechanism sketching.

A review of graph theory application research in gears

2015 ◽  
Vol 230 (10) ◽  
pp. 1697-1714 ◽  
Author(s):  
Hui-Ling Xue ◽  
Geng Liu ◽  
Xiao-Hui Yang
Keyword(s):  
Graph Theory ◽  
Power Flow ◽  
Planetary Gear ◽  
Mechanical Efficiency ◽  
Gear Train ◽  
Synthesis Process ◽  
Epicyclic Gear ◽  
Analysis And Synthesis ◽  
Theory Application ◽  
Gear Trains

Graph theory has been applied to gear train analysis and synthesis for many years, and it is an effective and systematic modeling approach in the design process of gear transmission. Based on more than 100 references listed in this paper, a review about the graph-based method for kinematic and static force analysis, power flow, and mechanical efficiency computation is presented. The method is based on the concept of fundamental circuit corresponding to a basic epicyclic gear train. A 1-dof epicyclic gear train and a two-stage planetary gear train are used to illustrate the application of this method. Besides, isomorphism identification in the synthesis process and enumeration of 1-dof epicyclic gear train graphs are surveyed particularly. Also, the computerized methods for detection of redundant gears and degenerate structures in epicyclic gear trains are reviewed, respectively.

Epicyclic gear trains for automotive automatic transmissions

2000 ◽  
Vol 214 (5) ◽  
pp. 523-532 ◽  
Author(s):  
C-H Hsu ◽  
J-J Hsu
Keyword(s):  
Adjacency Matrix ◽  
Gear Train ◽  
Graph Representation ◽  
Structural Synthesis ◽  
Automatic Transmissions ◽  
Epicyclic Gear ◽  
Systematic Methodology ◽  
Gear Trains ◽  
Configuration Synthesis ◽  
Admissible Graph

Epicyclic gear trains, which contain at least four coaxial links, are widely used in automatic transmissions. This paper presents a systematic methodology for the synthesis of epicyclic gear trains for automotive automatic transmissions. The graph representation of epicyclic gear trains is applied to develop an approach for the structural synthesis of the graphs of admissible epicyclic gear trains. Next, for each admissible graph the adjacency matrix of an epicyclic gear train is defined to develop an algorithm for the configuration synthesis of epicyclic gear trains. Using the proposed algorithm, all possible epicyclic gear trains for automotive automatic transmissions are systematically synthesized. In this paper, admissible epicyclic gear trains with up to ten links have been successfully synthesized. The results of work will lead to the creation of new multispeed automotive automatic transmissions.

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.

Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
High Velocity ◽  
Mechanical Energy ◽  
Gear Train ◽  
Recursive Method ◽  
Gear Pair ◽  
Simple Method ◽  
Epicyclic Gear ◽  
Thick Line ◽  
Gear Trains ◽  
Isomorphic Graphs

Epicyclic gear trains (EGTs) are used in the mechanical energy transmission systems where high velocity ratios are needed in a compact space. It is necessary to eliminate duplicate structures in the initial stages of enumeration. In this paper, a novel and simple method is proposed using a parameter, Vertex Incidence Polynomial (VIP), to synthesize epicyclic gear trains up to six links eliminating all isomorphic gear trains. Each epicyclic gear train is represented as a graph by denoting gear pair with thick line and transfer pair with thin line. All the permissible graphs of epicyclic gear trains from the fundamental principles are generated by the recursive method. Isomorphic graphs are identified by calculating VIP. Another parameter “Rotation Index” (RI) is proposed to detect rotational isomorphism. It is found that there are six nonisomorphic rotation graphs for five-link one degree-of-freedom (1-DOF) and 26 graphs for six-link 1-DOF EGTs from which all the nonisomorphic displacement graphs can be derived by adding the transfer vertices for each combination. The proposed method proved to be successful in clustering all the isomorphic structures into a group, which in turn checked for rotational isomorphism. This method is very easy to understand and allows performing isomorphism test in epicyclic gear trains.

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