Enumeration of 1-DOF Planetary Gear Train Graphs Based on Functional Constraints

2002 ◽  
Vol 124 (4) ◽  
pp. 723-732 ◽  
Author(s):  
Jose M. del Castillo
Keyword(s):  
Planetary Gear ◽  
Gear Train ◽  
Functional Constraints ◽  
Planetary Gear Train ◽  
Input Shaft ◽  
Single Output ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Single Input ◽  
Different Levels

A procedure for the enumeration of the graphs of 1-dof planetary gear trains is presented. The planetary gear trains enumerated have a single input shaft and a single output shaft. These gear trains should satisfy certain functional constraints that avoid the existence of idle links. These constraints are derived. The enumeration of the graphs exploits the resulting particular features of the structure of planetary gear trains by proceeding gradually through different levels of that structure. The procedure includes a check for isomorphism among the resulting graphs. Finally, the graphs of the planetary gear trains having up to 9 links are presented. Those graphs containing embedded structures are identified.

Conditions for Self-Locking in Planetary Gear Trains

2006 ◽  
Vol 129 (9) ◽  
pp. 960-968 ◽  
Author(s):  
David R. Salgado ◽  
J. M. del Castillo
Keyword(s):  
Planetary Gear ◽  
Degree Of Freedom ◽  
The Self ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Analytical Expression ◽  
Planetary Gear Trains ◽  
Input And Output ◽  
Approximate Relationship ◽  
Gear Trains

The objective of the present work is to determine the conditions that have to be satisfied for a planetary gear train of one degree of freedom to be self-locking. All planetary gear trains of up to six members are considered. As a result, we show the constructional solutions of planetary gear trains exhibiting self-locking. Unlike other studies, the self-locking conditions are obtained systematically from the analytical expression for the product of the efficiency of a given train by the efficiency of the train resulting from interchanging its input and output axes. Finally, a proof is given of an approximate relationship between these two efficiencies.

The Analysis of Planetary Gear Trains

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
Madhusudan Raghavan
Keyword(s):  
Planetary Gear ◽  
Gear Train ◽  
Compact Representation ◽  
Planetary Gear Train ◽  
Traditional Concept ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Large Families ◽  
Case Basis

The generalized lever is a new tool in gear train representation. It extends the traditional concept of a lever representation of a planetary gear set to 1 that includes negative lever ratios. This allows an exhaustive permutation of the nodes of a lever, thereby leading to all possible topological arrangements of a planetary gear train. Consequently, we achieve a compact representation of large families of planetary gear trains, which would otherwise have to be dealt with on a case-by-case basis.

The Kinematics of Eight-Speed Planetary Gear Hubs for Bicycles

2012 ◽  
Vol 232 ◽  
pp. 955-960 ◽  
Author(s):  
Long Chang Hsieh ◽  
Hsiu Chen Tang
Keyword(s):  
Design Methodology ◽  
Planetary Gear ◽  
Design Concept ◽  
Gear Train ◽  
Transmission Systems ◽  
Planetary Gear Train ◽  
Kinematic Design ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Internal Gear

Recently, bicycles are used as exercising machines and traffic vehicles. Planetary gear trains can be used as the transmission systems with multi-speed for bicycles. The purpose of this work is to propose a design methodology for the design of eight-speed internal gear hubs with planetary gear trains for bicycles. First, we propose a design concept for the design of eight-speed planetary gear hub. Then, based on this design concept and train value equation of planetary gear train, the kinematic design of eight-speed planetary gear hub is accomplished. One eight-speed planetary gear hub is synthesized to illustrate the design methodology. Based on the proposed design methodology, many eight-speed internal gear hubs with planetary gear trains can be synthesized.

scholarly journals Work of the planetary gear trains as differentials and their capabilities

2019 ◽  
Vol 287 ◽  
pp. 04001
Author(s):  
Kiril Arnaudov ◽  
Stefan Petrov ◽  
Emiliyan Hristov
Keyword(s):  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Gear Train ◽  
Motor Drive ◽  
Planetary Gear Train ◽  
Maximum Security ◽  
Single Carrier ◽  
Planetary Gear Trains ◽  
Gear Trains

Planetary gear trains can work differently, namely, with F=1 degree of freedom, i.e. as reducers or multipliers, and also with F=2 degrees of freedom, i.e. as differentials. Moreover, with a two-motor drive they work as a summation planetary gear train and with a one-motor drive, they work as a division planetary gear train. The most popular application of planetary gear trains is as a differential which is bevel and is produced globally in millions of pieces. Some of the cylindrical planetary gear trains can also be used as differentials. Although less often, they are used in heavy wheeled and chain vehicles such as trailer trucks, tractors and tanks. They are also very suitable for lifting machines with a two-motor drive which provides maximum security for the most responsible cranes, such as the metallurgical ones. Initially the paper presents some simple, i.e. single-carrier cylindrical planetary gear trains, both with external and internal meshing, driven by 2 motors. Their kinematic capabilities and velocity, respectively, are considered to realize the necessary gear ratio. Finally, the case of a compound two-carrier planetary gear train is considered, which is composed of 2 simple planetary gear trains. This shows that not only the simple planetary gear trains, i.e. the single-carrier ones, can work as differentials.

A Method for the Identification of Displacement Isomorphism of Planetary Gear Trains

1992 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Kin-Tak Lam
Keyword(s):  
Planetary Gear ◽  
Gear Train ◽  
Mathematical Representation ◽  
Automatic Identification ◽  
Planetary Gear Train ◽  
Rotational Displacement ◽  
Interactive Computer Program ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Structural Code

Abstract The purpose of this paper is to present an efficient method for the identification of the displacement isomorphism of planetary gear trains. For every planetary gear train, the kinematic structure is characterized by its displacement graph and rotation graph. A mathematical representation, called the Structural Code, is introduced to represent the topological structure of the displacement graph and rotation graph of a planetary gear train. Based on the Structural Codes of displacement graphs and rotation graphs, the linear and rotational displacement isomorphism of planetary gear trains can be identified in an unambiguous way. Finally, an interactive computer program is developed for the automatic identification of the displacement isomorphism of planetary gear trains.

On the Kinematic and Meshing Efficiency Analysis of Planetary Gear Reducer with Two Ring Gears

2014 ◽  
Vol 575 ◽  
pp. 395-399
Author(s):  
Long Chang Hsieh ◽  
Teu Hsia Chen ◽  
Hsiu Chen Tang
Keyword(s):  
Planetary Gear ◽  
Efficiency Analysis ◽  
Reduction Ratio ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Ratio Equation ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
High Reduction

Planetary gear trains can be used as the gear reducers with high reduction ratio. This paper focused on the kinematic and meshing efficiency analysis of planetary simple gear reducer with two ring gears. First, the planetary simple gear train with two ring gears is proposed by using different shift coefficients. Then, by referring to the train value equation, the reduction-ratio equation is derived for the design the planetary gear reducer with two ring gears. According to reduction-ratio equation, the planetary gear reducers with two ring gears and having reduction ratios (20, 50, and 100) are synthesized. Then, based on the latent power theorem, the meshing efficiency equation of planetary gear train with two ring gears is derived. According to the meshing efficiency equation, the meshing efficiencies of planetary gear trains with two ring gears are analyzed. In this paper, we conclude: (1) Larger reduction ratio makes less meshing efficiency, and (2) The meshing efficiency of planetary gear reducer with two ring gears is not good.

On the Design of Planetary Gear Reducer with Simple Planet Gears

2013 ◽  
Vol 284-287 ◽  
pp. 867-871
Author(s):  
Long Chang Hsieh ◽  
Tzu Hsia Chen
Keyword(s):  
Engineering Design ◽  
Planetary Gear ◽  
Reduction Ratio ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Ratio Equation ◽  
Planetary Gear Trains ◽  
Compact Size ◽  
Gear Trains ◽  
High Reduction

Planetary gear trains are commonly used in various transmissions due to the following reasons: compact size, light weight, and multi-degrees of freedom. For example, planetary gear trains can be designed for following functions: gear reducers for power machinery, internal gear hubs for bicycle, gear increasers for wind generator, gear reducers for robot. In general, the reduction of non-coupled planetary gear train is less than 10. The purpose of this paper is to introduce the planetary gear train with high reduction ratio. Coupled planetary gear train can be designed to has high reduction ratio. Hence, this paper focuses on innovative, kinematic, and engineering design of coupled planetary gear train with high reduction ratio. The coupled planetary gear train synthesized in this paper is a planetary gear train with simple planet gears. It can be used as the gear reducer for a robot. Refer to the train value equation, the reduction-ratio equation of coupled planetary gear train is derived for the design purpose. Then, the coupled planetary coupled gear train with simple planet gears is synthesized based on the above reduction-ratio equation. Finally, the corresponding engineering design drawing is accomplished.

scholarly journals The Trajectory Analysis of Bevel Planetary Gear Trains

1993 ◽  
Vol 115 (1) ◽  
pp. 164-170 ◽  
Author(s):  
Chen-Chou Lin ◽  
Lung-Wen Tsai
Keyword(s):  
Trajectory Analysis ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Point Of View ◽  
Gear Train ◽  
Geometric Description ◽  
Planetary Gear Train ◽  
Planetary Gear Trains ◽  
Gear Trains

In this paper, the trajectory of bevel planetary gear trains has been studied. The parametric equations of trajectory are derived. It is shown that the trajectory generated by a tracer point on the planet of a bevel planetary gear train is analogous to that of a spur planetary gear train. Two cases, gear ratio equal to one and two, are presented in detail including the geometric description, plane of symmetry, extent of trajectory, number of nodes (cusps) and their locations. The criteria for the existence of cusps are verified algebraically, and interpreted from geometrical point of view.

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.

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