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 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.

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.

Mobility analysis and structural synthesis of a class of spatial mechanisms with coupling chains

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2467-2485 ◽  
Author(s):  
Wen-ao Cao ◽  
Huafeng Ding ◽  
Ziming Chen ◽  
Shipei Zhao
Keyword(s):  
Structural Analysis ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Structural Synthesis ◽  
Systematic Method ◽  
General Methodology ◽  
Spatial Mechanisms ◽  
Analysis And Synthesis

SUMMARYThis paper presents a systematic method for dealing with mobility analysis and structural synthesis of a class of important spatial mechanisms with coupling chains, which involve more complex coupling relations than spatial parallel mechanisms. First, an approach to the establishment of the motion screw equation of the class of mechanisms is derived. Then, a general methodology for mobility analysis along with detection of rigid substructures is proposed based on the motion screw equation. Third, the principle of structural synthesis of the class of mechanisms is established on the basis of the method of mobility analysis. Finally, some novel spatial mechanisms with coupling chains are synthesized, illustrating the effectiveness of the method. The study of the paper will benefit structural analysis and synthesis of more complex spatial mechanisms with coupling chains.

scholarly journals Structural Synthesis of a Family of Planar 8-Link Kinematic Chains for Linkages with Multiple Joints and the Most Complex Ternary Link

2020 ◽  
pp. 21-31
Author(s):  
V.I. Pozhbelko ◽  
E.N. Kuts
Keyword(s):  
Mathematical Model ◽  
Creative Design ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Modern Engineering ◽  
Integer Solutions ◽  
Synthesis Procedure ◽  
P Matrix ◽  
Structural Solutions

Structural synthesis of closed kinematic chains to create various mechanisms is the first and most difficult stage of creative design of complex machines due to the large variance of possible structural solutions. In this paper, the authors examine the problem of structural synthesis of a family of eight-link kinematic chains with multiple joints of various types and the most complex three-joint link in order to create multi-loop multiple-joint mechanisms with one degree of freedom. To solve this problem, a synthesis technique is proposed based on the search for all integer solutions of a generalized structural mathematical model of plane linkage mechanisms and the identification of all structurally nonisomorphic kinematic chains using a two-column P-matrix. As the result of the structural synthesis, a family of eight-link multiple joint kinematic chains is obtained, which contains seven new kinematic structures. Examples of creating 1-DOF mechanisms with multiple joints based on the obtained new structures are presented. They confirm the effectiveness of using the structural synthesis procedure and analysis of complex mechanisms with multiple joints in various areas of modern engineering (precise guiding mechanisms, automatic lines, technological machines, robots, manipulators, etc.).

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.

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.

“Exact” Three-Dimensional Linear and Nonlinear Seismic Analysis of Structures with Two-Dimensional Models

2003 ◽  
Vol 19 (4) ◽  
pp. 897-912 ◽  
Author(s):  
Michael Mehrain ◽  
Farzad Naeim
Keyword(s):  
Structural Analysis ◽  
Nonlinear Analysis ◽  
Seismic Analysis ◽  
Three Dimensional ◽  
Modeling Technique ◽  
Two Dimensional ◽  
Single Model ◽  
Relative Ease ◽  
Conventional Analysis ◽  
Linear And Nonlinear

This paper presents a modeling technique by which a complete three-dimensional (3-D) structural analysis of a structure can be performed using two-dimensional (2-D) models, and hence 2-D software. The approach includes the effect of torsion, walls perpendicular and inclined to the direction of motion as well as walls with L, T, and H shapes in plan. Diaphragm displacements are easily modeled. The method can be used with linear and nonlinear analysis. Nonlinearity in the diaphragms can also be modeled with relative ease. Furthermore, unlike the conventional analysis that requires two 2-D models, one in each direction of motion, to model the 3-D structure, this approach requires only a single model.

A More Direct Method for Structural Synthesis of Simple-Jointed Planar Kinematic Chains

1994 ◽  
Author(s):  
Varada Raju Dharanipragada ◽  
Nagaraja Kumar Yenugadhati ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Computer Program ◽  
Reliable Method ◽  
Direct Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Structural Synthesis ◽  
Indirect Methods ◽  
Kinematic Chains ◽  
A Chain

Abstract Structural synthesis of kinematic chains leans heavily on indirect methods, most of them based on Graph Theory, mainly because reliable isomorphism tests are not available. Recently however, the first and third authors have established the Secondary Hamming String of a kinematic chain as an excellent indicator of its isomorphism. In the present paper this Hamming String method was applied with slight modifications for synthesizing on a PC-386, distinct kinematic chains with given number of links and family description. The computer program, written in Pascal, generated both the six-bar and all 16 eight-bar chains as well as one sample family (2008) of ten-bar chains, verifying previously established results. Hence this paper presents a direct, quick and reliable method to synthesize planar simple-jointed chains, open or closed, with single- or multi-degree of freedom, containing any number of links. A spin-off of this paper is a simple, concise and unambiguous notation for representing a chain.

Structural Analysis of Two General Constraint Kinematic Chains and Their Practical Application

1971 ◽  
Vol 93 (1) ◽  
pp. 231-238 ◽  
Author(s):  
A. H. Soni
Keyword(s):  
Structural Analysis ◽  
Practical Application ◽  
General Constraint ◽  
Kinematic Chains ◽  
General Constraints

The structural analysis of space linkages with two general constraints has been conducted by using Franke’s condensed notation. Linkages with mobility one and mobility two with up to three loops are considered. Censuses of chains with eight, nine, eleven and twelve links and a case study describing a practical application of these chains are presented.

Sign in / Sign up

Export Citation Format

Share Document