Automatic Analysis of Kinematic Structure of Planetary Gear Trains

1993 ◽  
Vol 115 (3) ◽  
pp. 631-638 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Kin-Tak Lam
Keyword(s):  
Computer Program ◽  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Automatic Analysis ◽  
Kinematic Structure ◽  
Identification Number ◽  
Interactive Computer Program ◽  
Planetary Gear Trains ◽  
Gear Trains

This paper presents a systematic algorithm for the automatic analysis of the kinematic structure of planetary gear trains with any number of degrees of freedom. The canonical displacement graphs and rotation graphs are introduced to represent the kinematic structure of planetary gear trains. Next, a single identification number method is presented to identify the displacement isomorphism of planetary gear trains. Then, nonfractionated multi-DOF planetary gear trains can be identified from their rotation graphs. Finally, an interactive computer program is developed for the automatic analysis of the kinematic structure of planetary gear trains. The result of this work is beneficial to the development of the new planetary gear trains.

A New Graph Representation for the Automatic Kinematic Analysis of Planetary Spur-Gear Trains

1992 ◽  
Vol 114 (1) ◽  
pp. 196-200 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Kin-Tak Lam
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Spur Gear ◽  
Gear Train ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Rotational Displacement ◽  
Interactive Computer Program ◽  
Gear Trains

The purpose of this paper is to propose a new graph representation to represent the kinematic structure of a planetary spur-gear train efficiently. Based on the graph representation, the kinematic analysis of planetary spur-gear trains is largely simplified. An interactive computer program is developed for the kinematic analysis of planetary spur-gear trains with any number of degrees of freedom. By only inputting the graph representation of a planetary spur-gear train and the data for the mating gear pairs, all possible fundamental circuits are determined and the rotational displacement equations are derived and solved automatically.

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.

A New Graph Representation for the Automatic Kinematic Analysis of Planetary Spur-Gear Trains

1989 ◽  
Author(s):  
C.-H. Hsu ◽  
K. T. Lam
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Spur Gear ◽  
Gear Train ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Rotational Displacement ◽  
Interactive Computer Program ◽  
Gear Trains

Abstract The purpose of this paper is to propose a new graph representation to represent the kinematic structure of a planetary spur-gear train efficiently. Based on the graph representation, the kinematic analysis of planetary spur-gear trains is largely simplified. An interactive computer program is developed for the kinematic analysis of planetary spur-gear trains with any numbers of degrees of freedom. By only inputting the graph representation of a planetary spur-gear trains and the data of the mating gear pairs, all possible fundamental circuits are determined and the rotational displacement equations are derived and solved automatically.

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.

Conceptual Design of Gear Differentials for Automotive Vehicles

1994 ◽  
Vol 116 (2) ◽  
pp. 565-570 ◽  
Author(s):  
Hong-Sen Yan ◽  
Long-Chang Hsieh
Keyword(s):  
Conceptual Design ◽  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Gear Train ◽  
Design Constraints ◽  
Two Degrees Of Freedom ◽  
Design Concepts ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Gear Differential

An automotive gear differential is a joint-fractionated planetary gear train with two degrees-of-freedom. We summarize the characteristics of planetary gear trains and the design constraints of noncoupled automotive gear differentials to synthesize their corresponding kinematic graphs. Based on these graphs and the proposed respecializing process, we generate the atlas of design concepts for automotive gear differentials with any types of gear pairs. As a result, there are 4, 25, and 156 design concepts for five-, six-, and seven-bar automotive gear differentials, respectively.

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 GEAR-SHIFTING MECHANISM WITH A ROTARY CONFIGURATION FOR APPLICATIONS IN A 16-SPEED BICYCLE TRANSMISSION HUB

2016 ◽  
Vol 40 (4) ◽  
pp. 597-606
Author(s):  
Yi-Chang Wu ◽  
Li-An Chen
Keyword(s):  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Systematic Design ◽  
Embodiment Design ◽  
Planetary Gear Trains ◽  
Epicyclic Gear ◽  
Gear Mechanism ◽  
Gear Trains ◽  
To Come ◽  
Gear Differential

A multi-speed bicycle transmission hub includes a geared speed-changing mechanism for providing different speed ratios and a gear-shifting mechanism for controlling the gear stage. This paper focuses on the embodiment design of a mechanical gear-shifting mechanism with a rotary configuration used in a 16-speed transmission hub for bicycles. A 16-link, five-degrees of freedom (DOF) split-power epicyclic gear mechanism, which consists of a gear differential and four sets of parallel-connected basic planetary gear trains, is introduced. Based on the clutching sequence table, a systematic design process is developed to come up with the embodiment design of the gear-shifting mechanism. A feasible and compact 16-speed rear transmission hub for bicycles is presented.

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.

Transmission Analysis—Automatic Derivation of Relationships

1993 ◽  
Vol 115 (4) ◽  
pp. 1031-1037 ◽  
Author(s):  
A. Hedman
Keyword(s):  
Computer Program ◽  
Planetary Gear ◽  
Mechanical Transmission ◽  
Transmission Systems ◽  
Human Errors ◽  
Planetary Gear Trains ◽  
Computer Aided Analysis ◽  
Analysis And Synthesis ◽  
Gear Trains ◽  
Overall Efficiency

A method for derivation of relationships for general mechanical transmission systems is given. It is adapted for computer-aided analysis and synthesis of the kinematics, loads, and power flows. Losses are included. All relationships are handled by a computer program. No manual dealing with equations is necessary. The user only describes the transmission systems: (1) The transmission units, e.g., gear transmissions, planetary gear trains, clutches and input shafts. (2) How the shafts of those units are connected. Then, the computer program formulates the relationships, and a computer algebra program performs algebraic eliminations. Symbolic, non-numerical, relationships between speeds and torques of two arbitrary shafts can be derived, e.g., the overall efficiency. Special algorithms handle the power flows in split-power transmissions. The method saves time and eliminates the risk for human errors.

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