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.

Simplified Kinematic Analysis of Bevel Epicyclic Gear Trains With Application to Power-Flow and Efficiency Analyses

2005 ◽  
Vol 127 (2) ◽  
pp. 278-286 ◽  
Author(s):  
Carl A. Nelson ◽  
Raymond J. Cipra
Keyword(s):  
Graph Theory ◽  
Kinematic Analysis ◽  
Power Flow ◽  
Computer Software ◽  
Input And Output ◽  
Automatic Transmissions ◽  
Epicyclic Gear ◽  
Analysis Technique ◽  
Angular Velocities ◽  
Gear Trains

A kinematic analysis technique is introduced to find the angular velocities of all links in bevel epicyclic gear trains. The method relies on previous work in graph theory. It improves on existing techniques used for analysis of planar geared mechanisms in its ability to accurately solve the kinematics of spatial geared mechanisms, particularly bevel gear trains, in a simpler manner. Usefulness of the method is demonstrated through its application to power-flow and efficiency analyses as well as its implementation in computer software. This discussion is limited to gear trains whose input and output axes are collinear, such as automotive automatic transmissions.

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 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.

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 New Method of Design of Epicyclic Gear Trains

2013 ◽  
Vol 457-458 ◽  
pp. 707-712
Author(s):  
Pei Wen An ◽  
Zhong Liang Lv
Keyword(s):  
New Method ◽  
Combination Method ◽  
Engineering Practice ◽  
Type Number ◽  
Practical Application ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Number Synthesis ◽  
Method Of Design

Epicyclic gear trains have been broadly applied in engineering practice. In this paper, kinematic chains (K.C.) with single-joint (S.J.) were applied to innovative synthesis of the epicyclic gear trains. The method of the innovative synthesis of the epicyclic gear trains was presented. Not only the epicyclic gear trains in common uses were obtained, but some new types of epicyclic gear trains that are got difficultly by means of conventional combination method were gained. Thereby, a new way has been offered for the innovative synthesis of the epicyclic gear trains, at the same time, a way has also been offered for practical application of some multi-link kinematic chains gained by using the theory of type-number synthesis of the K.C. with S.J.. Examples show that the method presented in this paper is right and feasible, and the method is efficient and practical for the innovative synthesis of the epicyclic gear trains.

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.

Intelligent Design of Mechanism Kinematic Chains by Advanced Optimal Methods

2011 ◽  
Vol 201-203 ◽  
pp. 2182-2185
Author(s):  
Miao Zhang ◽  
Ning Bo Liao ◽  
Chen Zhou ◽  
Xi Tao
Keyword(s):  
Graph Theory ◽  
Intelligent Design ◽  
Kinematic Structure ◽  
Kinematic Chains ◽  
Complicated Problem ◽  
Optimal Methods ◽  
Advantages And Disadvantages ◽  
Mechanism Kinematic ◽  
Isomorphism Identification ◽  
Structure Enumeration

When using graph theory to conduct intelligent design for kinematic structure enumeration, the isomorphism identification of graphs is an important and complicated problem. In this paper, the methodology of transferring isomorphism identification into optimization issue was introduced. Then the recent development of applying advanced optimal methods for isomorphism identification was reviewed, the advantages and disadvantages of there methods were discussed.

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