A Quadratic Form-Based Approach to Identification of Kinematic Chains in Structural Analysis and Synthesis of Mechanisms

2001 ◽  
Author(s):  
Peiren He ◽  
Wenjun Zhang ◽  
Qing Li
Keyword(s):  
Structural Analysis ◽  
Quadratic Form ◽  
Test Cases ◽  
Eigenvalues And Eigenvectors ◽  
New Approach ◽  
Kinematic Chains ◽  
Synthesis Of Mechanisms ◽  
Adjacency Matrices ◽  
Analysis And Synthesis

Abstract Identification of kinematic chains is needed when studying in structural analysis and synthesis of mechanisms. Research on detection of isomorphism in graphs/kinematic chains has a long history. Many algorithms or methods have been proposed. However, these methods have only achieved success in restricted conditions. This paper proposes a new approach using the concept of quadratic form. Graphs/kinematic chains are first represented by their adjacency matrices, the eigenvalues and their eigenvectors corresponding to these adjacency matrices are then calculated. Two graphs are represented by two quadratic expressions. The comparison of two graphs reduces to the comparison of two quadratic expressions. Quadratic expressions are characterized by the eigenvalues and eigenvectors. An algorithm is developed to compare, correspondingly, eigenvalues and eigenvectors of two graphs, known test cases are used to verify the effectiveness of the approach.

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.

A New Method for Detection of Graph Isomorphism Based on the Quadratic Form

2003 ◽  
Vol 125 (3) ◽  
pp. 640-642 ◽  
Author(s):  
P. R. He and ◽  
W. J. Zhang ◽  
Q. Li and ◽  
F. X. Wu
Keyword(s):  
Quadratic Form ◽  
Graph Isomorphism ◽  
New Method ◽  
Eigenvalues And Eigenvectors ◽  
Kinematic Chains ◽  
Quadric Surfaces

This paper proposes a new method for detection of graph isomorphism using the concept of quadratic form. Graphs/kinematic chains are represented first by quadratic form, and the comparison of two graphs is thus reduced to the comparison of two quadratic form expressions. If both the lengths and the directions of the semiaxes of quadric surfaces, which are characterized by the eigenvalues and eigenvectors, are the same, the associated graphs/kinematic chains are isomorphic. An algorithm is developed based on this idea, and tested for the counter-examples known to other methods.

A Comparative Study on Some Modular Approaches for Analysis and Synthesis of Planar Linkages: Part II — Modular Dynamic Analysis, Modular Structural Synthesis and Modular Kinematic Synthesis

1998 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao ◽  
Ming Zhang
Keyword(s):  
Structural Analysis ◽  
Comparative Study ◽  
Dynamic Analysis ◽  
Structural Synthesis ◽  
Dynamical Equations ◽  
Kinematic Synthesis ◽  
Automated Generation ◽  
Kinematic Chains ◽  
Analysis And Synthesis ◽  
Planar Linkages

Abstract This paper presents a systematical comparative study of various modular methods based on the different module types: basic kinematic chains (BKCs), single opened chains (SOCs), loops (or a tree and co-tree), links-joints, etc. for analysis and synthesis of structure, kinematics and dynamics of planar linkages. The basic idea is that any linkage can be divided into (or built up by) some modular components in sequence, and based on the component constraints and network entirty constraints of the linkage, the unified modular approaches have been used for analysis and synthesis. In systematical comparative study, the main issues of a modular method have been discussed, such as: the topological characteristics revealed via different module types; the dimension of a set of kinematic equations; the automated generation and solution of kinematic equations; the dimension and automated generation of dynamical equations, and computation complexity for generating and solving dynamical equation; the automated generation of structural analysis and type synthesis; the generation of kinematic synthesis equations etc.. This paper gives a summary of the use of modular techniques for analyzing and synthesizing planar linkages in the recently thirty years. This comparative study includes two parts: Part I-modular structural analysis and modular kinematic analysis; Part II-modular dynamic analysis, modular structural synthesis and modular kinematic synthesis. This paper is the second part.

A Comparative Study on Some Modular Approaches for Analysis and Synthesis of Planar Linkages: Part I — Modular Structural Analysis and Modular Kinemaic Analysis

1998 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao ◽  
Ming Zhang
Keyword(s):  
Structural Analysis ◽  
Comparative Study ◽  
Type Synthesis ◽  
Dynamical Equations ◽  
Kinematic Synthesis ◽  
Automated Generation ◽  
Kinematic Chains ◽  
Analysis And Synthesis ◽  
Modular Method ◽  
Planar Linkages

Abstract This paper presents a systematical comparative study of various modular methods based on the different module types: basic kinematic chains (BKCs), single opened chains (SOCs), loops (or a tree and co-tree), links-joints, etc. for analysis and synthesis of structure, kinematics and dynamics of planar linkages. The basic idea is that any linkage can be divided into (or built up by) some modular components in sequence, and based on the component constraints and network entirty constraints of the linkage, the unified modular approaches have been used for analysis and synthesis. In the systematical comparative study, the main issues of a modular method have been discussed, such as: the topological characteristics revealed via different module types; the dimension of a set of kinematic equations; the automated generation and solution of kinematic equations; the dimension and automated generation of dynamical equations, and computation complexity for generating and solving dynamical equation; the automated generation of structural analysis and type synthesis; the generation of kinematic synthesis equations etc.. This paper gives a summary of the use of modular techniques for analyzing and synthesizing planar linkages in the recently thirty years. This comparative study includes two parts: part I — modular structural analysis and modular kinematic analysis; part II — modular dynamics analysis, modular structural synthesis and modular kinematic synthesis. This paper is the first part.

scholarly journals Replacement in a Plane Geared Linkage of High Kinematic Pairs with Lower Pairs

2021 ◽  
Vol 24 (3) ◽  
pp. 97-103
Author(s):  
E.G. Krylov ◽  
R.F. Valiev
Keyword(s):  
Kinematic Analysis ◽  
Practical Interest ◽  
Kinematic Chains ◽  
Replacement Method ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Long Time ◽  
Shape Irregularity ◽  
Kinematic Equivalence ◽  
Higher Kinematic Pairs

The analysis of constraints in plane mechanisms is an urgent problem in the theory of machines and mechanisms. Although kinematic pairs’ classification has been known for a long time, the issue of the conjugation of links, being at the heart of the analysis and synthesis of mechanisms and machines, is of considerable theoretical and practical interest and continues to attract scientists. One of the tasks that are solved in the process of analysis and synthesis of the structures of mechanisms is the re-placement of higher kinematic pairs by lower ones. As a rule, such a replacement is made to identify kinematic chains of zero mobility, Assur's structural groups, in a mechanism. The replacement may also aim at obtaining the necessary kinematic relations. That is because specific computational difficulties hamper the kinematic analysis of chains with higher kinematic pairs due to the relative sliding and shape irregularity of mating surfaces. Yet, the use of replacements to obtain kinematic and transmission functions is difficult due to nonisomorphism of the equivalent mechanism. Simultaneously, for mixed-type mechanisms, which include geared linkages, the equivalent replacement will allow unifying the kinematic analysis methods. The paper suggests the technology of replacing higher kinematic pairs with links with lower pairs as applied to a plane geared linkage. The technology is based on the properties of the involute of a circumference. The paper proved the structural and kinematic equivalence of such a replacement. The isomorphism of the equivalent linkage will enhance the kinematic analysis, make it possible using kinematic functions, and applying methods based on the instantaneous relative rotations of links, in particular, the Aronhold-Kennedy theorem. Another application of the replacement method presented in the paper will be the expansion of opportunities for identifying idle constraints in the mechanism.

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.

Linkage Characteristic Polynomials: Definitions, Coefficients by Inspection

1981 ◽  
Vol 103 (3) ◽  
pp. 578-584 ◽  
Author(s):  
H. S. Yan ◽  
A. S. Hall
Keyword(s):  
Structural Analysis ◽  
Characteristic Polynomial ◽  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Companion Paper ◽  
Characteristic Polynomials ◽  
Kinematic Chains ◽  
Analysis And Synthesis

A linkage characteristic polynomial is defined as the characteristic polynomial of the adjacency matrix of the kinematic graph of the kinematic chain. Some terminology and definitions, needed for discussions to follow in a companion paper, are stated. A rule from which all coefficients of the characteristic polynomial of a kinematic chain can be identified by inspection, based on the interpretation of a graph determinant, is derived and presented. This inspection rule interprets the topological meanings behind each characteristic coefficient, and might have some interesting possible uses in studies of the structural analysis and synthesis of kinematic chains.

Scientific-methodological approach to the substantiation of the rational seasonal scenario of using combine harvesters by large-scale agricultural producers

2020 ◽  
pp. 205-217
Author(s):  
V. Skibchyk ◽  
V. Dnes ◽  
R. Kudrynetskyi ◽  
O. Krypuch
Keyword(s):  
Large Scale ◽  
System Analysis ◽  
Methodological Approach ◽  
Production Unit ◽  
Agricultural Producers ◽  
New Approach ◽  
Rational Use ◽  
Road Map ◽  
Analysis And Synthesis ◽  
Combine Harvesters

Аnnotation Purpose. To increase the efficiency of technological processes of grain harvesting by large-scale agricultural producers due to the rational use of combine harvesters available on the farm. Methods. In the course of the research the methods of system analysis and synthesis, induction and deduction, system-factor and system-event approaches, graphic method were used. Results. Characteristic events that occur during the harvesting of grain crops, both within a single production unit and the entire agricultural producer are identified. A method for predicting time intervals of use and downtime of combine harvesters of production units has been developed. The roadmap of substantiation the rational seasonal scenario of the use of grain harvesters of large-scale agricultural producers is developed, which allows estimating the efficiency of each of the scenarios of multivariate placement of grain harvesters on fields taking into account influence of natural production and agrometeorological factors on the efficiency of technological cultures. Conclusions 1. Known scientific and methodological approaches to optimization of machine used in agriculture do not take into account the risks of losses of crops due to late harvesting, as well as seasonal natural and agrometeorological conditions of each production unit of the farmer, which requires a new approach to the rational use of rational seasonal combines of large agricultural producers. 2. The developed new approach to the substantiation of the rational seasonal scenario of the use of combined harvesters of large-scale agricultural producers allows taking into account the costs of harvesting of grain and the cost of the lost crop because of the lateness of harvesting at optimum variants of attraction of additional free combine harvesters. provides more profit. 3. The practical application of the developed road map will allow large-scale agricultural producers to use combine harvesters more efficiently and reduce harvesting costs. Keywords: combine harvesters, use, production divisions, risk, seasonal scenario, large-scale agricultural producers.

REPRESENTATIONS AND IDENTIFICATIONS OF STRUCTURAL AND MOTION STATE CHARACTERISTICS OF MECHANISMS WITH VARIABLE TOPOLOGIES

2006 ◽  
Vol 30 (1) ◽  
pp. 19-40 ◽  
Author(s):  
Hong-Sen Yan ◽  
Chin-Hsing Kuo
Keyword(s):  
Topological Structure ◽  
Topological Analysis ◽  
State Machines ◽  
Matrix Representations ◽  
Motion State ◽  
New Concepts ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Finite State ◽  
State Graphs

A mechanism that encounters a certain changes in its topological structure during operation is called a mechanism with variable topologies (MVT). This paper is developed for the structural and motion state representations and identifications of MVTs. For representing the topological structures of MVTs, a set of methods including graph and matrix representations is proposed. For representing the motion state characteristics of MVTs, the idea of finite-state machines is employed via the state tables and state graphs. And, two new concepts, the topological homomorphism and motion homomorphism, are proposed for the identifications of structural and motion state characteristics of MVTs. The results of this work provide a logical foundation for the topological analysis and synthesis of mechanisms with variable topologies.

Variational characterization of real eigenvalues in linear viscoelastic oscillators

2017 ◽  
Vol 23 (10) ◽  
pp. 1377-1388 ◽  
Author(s):  
Seyyed Abbas Mohammadi ◽  
Heinrich Voss
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Eigenvalue Problem ◽  
Eigenvalues And Eigenvectors ◽  
Variational Characterization ◽  
Viscoelastic System ◽  
New Approach ◽  
Motion Equations ◽  
Multiple Degrees Of Freedom ◽  
Linear Viscoelastic

This paper proposes a new approach for computing the real eigenvalues of a multiple-degrees-of-freedom viscoelastic system in which we assume an exponentially decaying damping. The free-motion equations lead to a nonlinear eigenvalue problem. If the system matrices are symmetric, the eigenvalues allow for a variational characterization of maxmin type, and the eigenvalues and eigenvectors can be determined very efficiently by the safeguarded iteration, which converges quadratically and, for extreme eigenvalues, monotonically. Numerical methods demonstrate the performance and the reliability of the approach. The method succeeds where some current approaches, with restrictive physical assumptions, fail.

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