Some Applications of Graph Theory to the Structural Analysis of Mechanisms

1967 ◽  
Vol 89 (1) ◽  
pp. 153-158 ◽  
Author(s):  
L. Dobrjanskyj ◽  
F. Freudenstein
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Incidence Matrix ◽  
Mechanical Systems ◽  
Kinematic Chains ◽  
Computerized Method ◽  
Spatial Mechanisms ◽  
Structural Identity ◽  
Computer Aided ◽  
Systematic Enumeration

Concepts in graph theory, which have been described elsewhere [2, 4, 6] have been applied to the development of (a) a computerized method for determining structural identity (isomorphism) between kinematic chains, (b) a method for the automatic sketching of the graph of a mechanism defined by its incidence matrix, and (c) the systematic enumeration of general, single-loop constrained spatial mechanisms. These developments, it is believed, demonstrate the feasibility of computer-aided techniques in the initial stages of the design of mechanical systems.

scholarly journals Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains

1973 ◽  
Vol 95 (2) ◽  
pp. 525-532 ◽  
Author(s):  
M. Huang ◽  
A. H. Soni
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Piston Cylinder ◽  
General Constraints ◽  
Analysis And Synthesis ◽  
Linear And Nonlinear

Using graph theory and Polya’s theory of counting, the present paper performs structural synthesis and analysis of planar and three-dimensional kinematic chains. The Section 2 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of planar kinematic chains with kinematic elements such as revolute pairs, cam pairs, springs, belt-pulley, piston-cylinder, and gears. The theory developed is applied to enumerate eight-link kinematic chains with these kinematic elements. The Section 3 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of multi-loop spatial kinematic chains with higher and lower kinematic pairs. The theory developed is applied to enumerate all possible two-loop kinematic chains with or without general constraints.

Structural Analysis and Mobility Test of Fourteen Links Kinematic Chain Using Graph Theory

2014 ◽  
Vol 592-594 ◽  
pp. 1165-1169
Author(s):  
Preeti Gulia ◽  
V.P. Singh
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Incidence Matrix ◽  
Reliable Method ◽  
Kinematic Chain ◽  
Polynomial Equation ◽  
Degree Of Freedom ◽  
Mobility Test ◽  
Structural Problems ◽  
Algebraic Test

The present work is focused on the graph theory which is used for structural analysis of kinematic chain and identification of degree of freedom. A method based on graph theory is proposed in this paper to solve structural problems by using a suitable example of fourteen links kinematic chain. Purpose of this paper is to give an easy and reliable method for structural analysis of fourteen links kinematic chain. Here, a simple incidence matrix is used to represent the kinematic chain. The proposed method is applied for determining the characteristic polynomial equation of fourteen links kinematic chain. An algebraic test based on graph theory is also used for identifying degree of freedom of kinematic chain whether it is total, partial or fractionated degree of freedom.

An Algorithm for Automatic Sketching of Planar Kinematic Chains

1985 ◽  
Vol 107 (1) ◽  
pp. 106-111 ◽  
Author(s):  
D. G. Olson ◽  
T. R. Thompson ◽  
D. R. Riley ◽  
A. G. Erdman
Keyword(s):  
Graph Theory ◽  
Line Graph ◽  
Kinematic Chain ◽  
Graph Representation ◽  
Synthesis Process ◽  
Line Graphs ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Synthesis Of Mechanisms ◽  
Computer Aided

One of the problems encountered in attempting to computerize type synthesis of mechanisms is that of automatically generating a computer graphics display of candidate kinematic chains or mechanisms. This paper presents the development of a computer algorithm for automatic sketching of kinematic chains as part of the computer-aided type synthesis process. Utilizing concepts from graph theory, it can be shown that a sketch of a kinematic chain can be obtained from its graph representation by simply transforming the graph into its line graph, and then sketching the line graph. The fundamentals of graph theory as they relate to the study of mechanisms are reviewed. Some new observations are made relating to graphs and their corresponding line graphs, and a novel procedure for transforming the graph into its line graph is presented. This is the basis of a sketching algorithm which is illustrated by computer-generated examples.

scholarly journals Design Propagation in Mechanical Systems: Kinematic Analysis

1997 ◽  
Vol 119 (3) ◽  
pp. 338-345 ◽  
Author(s):  
H. Zou ◽  
K. A. Abdel-Malek ◽  
J. Y. Wang
Keyword(s):  
Graph Theory ◽  
Design Variable ◽  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Mechanical Systems ◽  
Joint Position ◽  
Closed Loops ◽  
Cartesian Space ◽  
Spatial Mechanisms ◽  
Joint Coordinates

A broadly applicable formulation for investigating design propagations in mechanisms is developed and illustrated. Analytical criteria in terms of the variations of joint position vectors and orientation matrices for planar and spatial mechanisms are presented. Mechanisms are represented using graph theory and closed loops are converted to a tree-like structure by cutting joints and introducing new constraints. The Jacobian matrix in Cartesian space is then transformed to Joint coordinates space. Two cases are considered: a pair of bodies remain connected by one joint after cutting additional joints and a pair of bodies are disconnected after cutting joints. Using this method, a designer has the ability to study the propagated effect of changing a design variable on the design. The presented formulation is validated through a numerical example of a McPherson strut suspension system. The system is analyzed and an assembled configuration is computed after a change in design.

Detection of Isomorphism Between Planar Kinematic Chains

1987 ◽  
Author(s):  
L. K. Patel ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Efficient Method ◽  
Computational Effort ◽  
New Method ◽  
Structural Topology ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Single Degree ◽  
Analysis And Synthesis

Abstract Structural analysis and synthesis of linkages is a very important aspect. Detection of isomorphism (equivalent structural topology) is essential to determine structurally distinct chains. Some methods to detect distinct chains and mechanisms have already been developed. These methods besides being falliable, require enormous computational effort and as such necessitate development of an easy and efficient method. This paper presents a new method based on graph theory, for detection of isomorphism among kinematic chains. A probability scheme is attached with the chains and relative loop positions are determined for the chains having identical probability schemes. Isomorphism is detected between planar kinematic chains having single degree of freedom.

NUMERICAL ANALYSIS OF DISPLACEMENTS IN SPATIAL MECHANISMS WITH SPHERICAL JOINTS UTILIZING AN EXTENDED D-H NOTATION

2010 ◽  
Vol 34 (3-4) ◽  
pp. 417-431 ◽  
Author(s):  
Jung-Fa Hsieh
Keyword(s):  
Numerical Analysis ◽  
Translational Motion ◽  
Mechanical Systems ◽  
Kinematic Chains ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Spherical Surfaces ◽  
Analysis And Synthesis ◽  
Independent Parameters ◽  
Rotational Freedom

Spherical joints consist of a pair of concave and convex spherical surfaces engaged in such a way as to prevent translational motion of the ball and socket whilst simultaneously allowing three degrees of rotational freedom. The kinematics of spatial mechanisms comprising links and joints are commonly analyzed using the Denavit-Hartenberg (D-H) notation. However, whilst this method allows the kinematics of mechanisms containing prismatic, revolute, helical and cylindrical joints to be explicitly defined, it cannot be directly applied to mechanical systems containing spherical pairs. Accordingly, this paper proposes an extended D-H notation which allows the independent parameters of any spatial mechanism, including one with spherical pairs, to be derived for analysis and synthesis purposes. The validity of the proposed notation is demonstrated via its application to the analysis of mechanisms containing revolute (R), spherical (S), cylindrical (C) and prismatic (P) joints. The results confirm the viability of the extended D-H notation as a means of analyzing the displacements of mechanical systems containing kinematic chains such as RSCR, RSCP, CSSR and CSSP.

On the Maximum Value of the Maximum Degree of Kinematic Chains

1987 ◽  
Vol 109 (4) ◽  
pp. 487-490 ◽  
Author(s):  
Hong-Sen Yan ◽  
Frank Harary
Keyword(s):  
Graph Theory ◽  
Maximum Degree ◽  
Design Methodology ◽  
Creative Design ◽  
Systematic Design ◽  
Kinematic Chains ◽  
Maximum Value ◽  
Mathematical Expressions

One of the major steps in the development of a systematic design methodology for the creative design of vehicle mechanisms is to obtain all possible link assortments, and then to generate the catalogs of kinematic chains. If the generalized mathematical expressions for the maximum value M of the maximum number of joints incident to a link of kinematic chains with N links and J joints can be derived, the process of solving link assortments can be more systematic. Using elementary concepts of graph theory, we derived explicit relationships for M for two regions of the J-N plane.

Structural Analysis for Space-Swing Mechanism on Gyratory Compactor

2014 ◽  
Vol 621 ◽  
pp. 253-259
Author(s):  
Jing Qian ◽  
Ling Wei Meng
Keyword(s):  
Structural Analysis ◽  
Dynamic Analysis ◽  
Initial Phase ◽  
Mechanical Systems ◽  
Systems Software ◽  
Superpave Gyratory Compactor ◽  
Flexible Models

Based on the automatic dynamic analysis of mechanical systems software, both rigid and flexible models of the space-swing mechanism for the superpave gyratory compactor are developed. The structural analysis shows that the length and the initial phase of cranks, and the assembling accuracy (coordinates) of some points are very sensitive relative to the waving of compaction angle. Greater rigidity helps stabilize the change of the compaction angles.

scholarly journals Logistics management of the rail connections using graph theory: the case of a public transportation company on the example of Koleje Dolnośląskie S.A.

2018 ◽  
Vol 10 (3) ◽  
pp. 7-22
Author(s):  
Paweł Sobczak ◽  
Ewa Stawiarska ◽  
Judit Oláh ◽  
József Popp ◽  
Tomas Kliestik
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Public Transportation ◽  
Transportation Networks ◽  
Logistics Management ◽  
Simulation Methods ◽  
Southern Poland ◽  
Transport Services ◽  
Network Simulations ◽  
Simulation Results

Abstract The main purpose of the paper was the structural analysis of the connections network used by a railway carrier Koleje Dolnośląskie S.A. operating in southern Poland. The analysis used simulation methods. The analysis and simulation were based on graph theory, which is successfully used in analysing a wide variety of networks (social, biological, computer, virtual and transportation networks). The paper presents indicators which allow judging the analysed connections network according to an appropriate level of transport services. Simulation results allowed proposing some modifications for the improvement of the analysed connections network. The paper also demonstrates that graph theory and network simulations should be used as tools by transportation companies during the stage of planning a connections network.

Parametric Continuity and Smooth Motion Interpolation

1995 ◽  
Author(s):  
Lakshmi N. Srinivasan ◽  
Q. J. Ge
Keyword(s):  
Mechanical Systems ◽  
Trajectory Generation ◽  
Geometric Design ◽  
Second Derivative ◽  
Computer Aided Geometric Design ◽  
Smooth Motion ◽  
Computer Aided ◽  
Cad Cam ◽  
C2 Continuity ◽  
Parametric Continuity

Abstract This paper deals with the design of a second derivative continuous (C2) motion that interpolates through a given set of configurations of an object. It derives conditions for blending two motion segments with C2 continuity and develops an algorithm for constructing a C2 composite Bézier type motion that has similarities to Beta-splines in the field of Computer Aided Geometric Design. A criteria for evaluating the smoothness of motion is established and is used to synthesize “globally smooth” motions. The results have applications in trajectory generation in robotics, mechanical systems animation and CAD/CAM.

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