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.

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.

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.

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 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.

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.

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 Simplified Approach for Force and Power-Flow Analysis of Compound Epicyclic Spur-Gear Trains

1992 ◽  
Author(s):  
L. Saggere ◽  
D. G. Olson
Keyword(s):  
Graph Theory ◽  
Kinematic Analysis ◽  
Power Flow ◽  
Flow Analysis ◽  
Spur Gear ◽  
Gear Train ◽  
Force Analysis ◽  
Power Flow Analysis ◽  
Torque Analysis ◽  
Gear Trains

Abstract After conceptual design and dimensional synthesis of a compound epicyclic gear train (EGT), its performance evaluation involves kinematic analysis, force analysis, torque analysis, and power-flow analysis. In recent years, graph theory has proven to be a powerful symbolic representation for design of mechanisms. Application of graph theory for the topological representation and kinematic analysis of EGTs is quite well established. However, graph theory based methods for power-flow and force analysis lack certain features, making them unsuitable or difficult to implement in a general purpose program for automatic design of EGTs. The traditional approach has been to perform force and torque analysis first, and then use the results to perform power-flow analysis. This paper presents a novel, systematic approach in which power-flow analysis is performed first, and then the results are used to determine the inter-link forces in epicyclic spur-gear trains. This method is based only on the graph of the gear-train and the angular velocities of the elements, and hence, is more suitable for automatic computation, simpler to implement in a program, and also avoids requiring the formulation of tedious torque equilibrium equations. A numerical example is presented to illustrate the simplicity and generality of the method.

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.

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 3D-Modeling and Motion Simulation of Composite Wheel Gears Transmission Based on UG

2018 ◽  
Vol 175 ◽  
pp. 03006
Author(s):  
Mingxia Zhao
Keyword(s):  
3D Modeling ◽  
Rotational Speed ◽  
Spur Gear ◽  
Transmission Mechanism ◽  
Gear Train ◽  
Gear Pair ◽  
Calculation Formula ◽  
Motion Simulation ◽  
Gear Trains ◽  
Simulation Parameters

Taking the compound gear trains as an example, the principle of the transmission mechanism was analyzed, and the rotational speed of the key gears in the compound gear trains was calculated by using the calculation formula of transmission ratio to obtain the simulation parameters of UG movement. The gear tool box in UG was applied to complete the modeling and meshing assembly of the bevel gear and spur gear, the rotation pair and gear pair was to motion simulation, the gear transmission state could have visually observed by motion simulation, and then the chart was analyzed to verify the design rationality of the gear train.

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