An Efficient Algorithm for Finding Optimum Code Under the Condition of Incident Degree

1992 ◽  
Author(s):  
T. J. Jongsma ◽  
W. Zhang
Keyword(s):  
Computer Program ◽  
Efficient Algorithm ◽  
Kinematic Chain ◽  
Isomorphism Problem ◽  
Kinematic Chains ◽  
Adjacency Matrices ◽  
Set Up

Abstract This paper deals with the identification of kinematic chains. A kinematic chain can be represented by a weighed graph. The identification of kinematic chains is thereby transformed into the isomorphism problem of graph. When a computer program has to detect isomorphism between two graphs, the first step is to set up the corresponding connectivity matrices for each graph, which are adjacency matrices when considering adjacent vertices and the weighed edges between them. Because these adjacency matrices are dependent of the initial labelling, one can not conclude that the graphs differ when these matrices differ. The isomorphism problem needs an algorithm which is independent of the initial labelling. This paper provides such an algorithm.

Laplace and Extended Adjacency Matrices for Isomorphism Detection of Kinematic Chains Using the Characteristic Polynomial Approach

2005 ◽  
Author(s):  
Rajesh Pavan Sunkari ◽  
Linda C. Schmidt
Keyword(s):  
Characteristic Polynomial ◽  
Spectral Properties ◽  
Kinematic Chain ◽  
Detection Algorithm ◽  
Isomorphism Problem ◽  
Characteristic Polynomials ◽  
Kinematic Chains ◽  
Laplace Matrix ◽  
Adjacency Matrices ◽  
Single Matrix

The kinematic chain isomorphism problem is one of the most challenging problems facing mechanism researchers. Methods using the spectral properties, characteristic polynomial and eigenvectors, of the graph related matrices were developed in literature for isomorphism detection. Detection of isomorphism using only the spectral properties corresponds to a polynomial time isomorphism detection algorithm. However, most of the methods used are either computationally inefficient or unreliable (i.e., failing to identify non-isomorphic chains). This work establishes the reliability of using the characteristic polynomial of the Laplace matrix for isomorphism detection of a kinematic chain. The Laplace matrix of a graph is used extensively in the field of algebraic graph theory for characterizing a graph using its spectral properties. The reliability in isomorphism detection of the characteristic polynomial of the Laplace matrix was comparable with that of the adjacency matrix. However, using the characteristic polynomials of both the matrices is superior to using either method alone. In search for a single matrix whose characteristic polynomial unfailingly detects isomorphism, novel matrices called the extended adjacency matrices are developed. The reliability of the characteristic polynomials of these matrices is established. One of the proposed extended adjacency matrices is shown to be the best graph matrix for isomorphism detection using the characteristic polynomial approach.

A New Multivalued Neural Network for Isomorphism Identification of Kinematic Chains

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Gloria Galán-Marín ◽  
Domingo López-Rodríguez ◽  
Enrique Mérida-Casermeiro
Keyword(s):  
Neural Network ◽  
Intelligent Systems ◽  
Initial Conditions ◽  
Graph Isomorphism ◽  
Kinematic Chain ◽  
Parameter Tuning ◽  
Isomorphism Problem ◽  
Kinematic Chains ◽  
Graph Isomorphism Problem ◽  
Better Than

A lot of methods have been proposed for the kinematic chain isomorphism problem. However, the tool is still needed in building intelligent systems for product design and manufacturing. In this paper, we design a novel multivalued neural network that enables a simplified formulation of the graph isomorphism problem. In order to improve the performance of the model, an additional constraint on the degree of paired vertices is imposed. The resulting discrete neural algorithm converges rapidly under any set of initial conditions and does not need parameter tuning. Simulation results show that the proposed multivalued neural network performs better than other recently presented approaches.

The Novel Characteristic Representations of Kinematic Chains and Their Applications

2005 ◽  
Author(s):  
Z. Huang ◽  
H. F. Ding ◽  
Y. Cao
Keyword(s):  
Adjacency Matrix ◽  
Degree Sequence ◽  
Object Oriented ◽  
Kinematic Chain ◽  
Object Oriented Programming ◽  
The Novel ◽  
Topological Graphs ◽  
Kinematic Chains ◽  
Set Up ◽  
Oriented Programming Language

In this paper, based on perimeter topological graphs of kinematic chains, many novel topological concepts including the synthetic degree-sequence, the characteristic adjacency matrix and the characteristic representation code of kinematic chain are proposed. Both the characteristic adjacency matrix and the characteristic representation code are unique for any kinematic chain and easy to be set up. Therefore a quite effective isomorphism identification method is presented depending on the characteristic adjacency matrix. It high effectiveness is proved by many examples. With object-oriented programming language, a program which can sketch topological graphs of kinematic chains has been developed based on the characteristic representation code. Finally, an application software system establishing the atlas database of topological graphs is introduced. And some functions about the atlas database are also presented in this paper.

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.

Generation and Sketching of Generalized Kinematic Chains

2008 ◽  
Author(s):  
Chiu-Fan Hsieh ◽  
Yii-Wen Hwang ◽  
Hong-Sen Yan
Keyword(s):  
Computer Program ◽  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Kinematic Chains ◽  
A Chain

An algorithm of generalized kinematic chains and its computer program are developed in this paper. By this program, users can give the number of links and joints and then the link assortments and contracted link assortments can be calculated. The synthesis of multiple link adjacency matrix (MLAM) and the cut-link diagnosis are proposed to produce effectively the generalized kinematic chains. The algorithm can automatically determine the feature of a chain, which is connected, closed, non-isomorphism, without any cut-link (or cut-joint), and with simple joint only. Then, it can be called a generalized kinematic chain. Finally, various given number of links and joints, the nice looking atlas of generalized kinematic chains can also be generated. The developed computer program could help designers to be able to study and compare different devices in a very basic way.

Loop Based Detection of Isomorphism Among Chains, Inversions and Type of Freedom in Multi Degree of Freedom Chain

1999 ◽  
Vol 122 (1) ◽  
pp. 31-42 ◽  
Author(s):  
A. C. Rao ◽  
V. V. N. R. Prasad Raju Pathapati
Keyword(s):  
Unsolved Problem ◽  
Kinematic Chain ◽  
Computational Effort ◽  
Degree Of Freedom ◽  
Complete List ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Adjacency Matrices ◽  
The Creation ◽  
A Chain

Structural synthesis of kinematic chains usually involves the creation of a complete list of kinematic chains, followed by a isomorphism test to discard duplicate chains. A significant unsolved problem in structural synthesis is the guaranteed precise elimination of all isomorphs. Many methods are available to the kinematician to detect isomorphism among chains and inversions but each has its own shortcomings. Most of the study to detect isomorphism is based on link-adjacency matrices or their modification but the study based on loops is very scanty although it is very important part of a kinematic chain.  Using the loop concept a method is reported in this paper to reveal simultaneously chain is isomorphic, link is isomorphic, and type of freedom with no extra computational effort. A new invariant for a chain, called the chain loop string is developed for a planar kinematic chain with simple joints to detect isomorphism among chains. Another invariant called the link adjacency string is developed, which is a by-product of the same method to detect inversions of a given chain. The proposed method is also applicable to know the type of freedom of a chain in case of multi degree of freedom chains. [S1050-0472(00)70801-4]

The Topological Representation and Detection of Isomorphism Among Geared Linkage Kinematic Chains

1998 ◽  
Author(s):  
Tuan-Jie Li ◽  
Wei-Qing Cao ◽  
Jin-Kui Chu
Keyword(s):  
Computer Program ◽  
Kinematic Chain ◽  
Topological Representation ◽  
Kinematic Chains ◽  
Topological Relationship ◽  
Systematic Procedure ◽  
Topological Characteristics ◽  
Structural Invariants

Abstract Proceeded from the topological characteristics of Geared Linkage Mechanisms (GLM) structure, a fully new graph, combinatorial graph, which can be used to describe the topological relationship in a Geared Linkage Kinematic Chain (GLKC), is firstly proposed. Then the corresponding matrix, combinatorial matrix, and the structural invariants of GLKC are presented. Based on the structural invariants, this paper establishes a systematic procedure for detecting isomorphism among GLKCs using the powers of combinatorial matrix. A computer program based on the procedure has been applied successfully for detecting isomorphism among both the planar kinematic chains as well as GLKCs.

Structure Based Grading of Kinematic Chains

2014 ◽  
Vol 575 ◽  
pp. 501-506 ◽  
Author(s):  
Shubhashis Sanyal ◽  
G.S. Bedi
Keyword(s):  
Structural Properties ◽  
Structural Property ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Structural Differences ◽  
The Individual ◽  
Independent Loops

Kinematic chains differ due to the structural differences between them. The location of links, joints and loops differ in each kinematic chain to make it unique. Two similar kinematic chains will produce similar motion properties and hence are avoided. The performance of these kinematic chains also depends on the individual topology, i.e. the placement of its entities. In the present work an attempt has been made to compare a family of kinematic chains based on its structural properties. The method is based on identifying the chains structural property by using its JOINT LOOP connectivity table. Nomenclature J - Number of joints, F - Degree of freedom of the chain, N - Number of links, L - Number of basic loops (independent loops plus one peripheral loop).

Combined Graph Layout Algorithms for Automated Sketching of Kinematic Chains

2012 ◽  
Author(s):  
Martín A. Pucheta ◽  
Nicolás E. Ulrich ◽  
Alberto Cardona
Keyword(s):  
Computational Cost ◽  
Kinematic Chain ◽  
Initial Position ◽  
Graph Representation ◽  
Combinatorial Algorithms ◽  
Graph Layout ◽  
Kinematic Chains ◽  
Aesthetic Characteristics ◽  
Edge Crossings ◽  
Independent Loops

The graph layout problem arises frequently in the conceptual stage of mechanism design, specially in the enumeration process where a large number of topological solutions must be analyzed. Two main objectives of graph layout are the avoidance or minimization of edge crossings and the aesthetics. Edge crossings cannot be always avoided by force-directed algorithms since they reach a minimum of the energy in dependence with the initial position of the vertices, often randomly generated. Combinatorial algorithms based on the properties of the graph representation of the kinematic chain can be used to find an adequate initial position of the vertices with minimal edge crossings. To select an initial layout, the minimal independent loops of the graph can be drawn as circles followed by arcs, in all forms. The computational cost of this algorithm grows as factorial with the number of independent loops. This paper presents a combination of two algorithms: a combinatorial algorithm followed by a force-directed algorithm based on spring repulsion and electrical attraction, including a new concept of vertex-to-edge repulsion to improve aesthetics and minimize crossings. Atlases of graphs of complex kinematic chains are used to validate the results. The layouts obtained have good quality in terms of minimization of edge crossings and maximization of aesthetic characteristics.

A Novel Method for Constructing Multi-Mode Deployable Polyhedron Mechanisms Using Symmetric Spatial RRR Compositional Units

2018 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Loop ◽  
Kinematic Chains ◽  
The Third ◽  
Motion Modes ◽  
3D Printed ◽  
Novel Method ◽  
Multi Mode ◽  
Motion Mode

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are further assembled into polyhedron mechanisms by connecting single-loop kinematic chains using RRR units. The proposed mechanisms are over-constrained and can be deployed through two approaches. The prism mechanism constructed using two Bricard linkages and six RRR limbs has one degree-of-freedom (DOF). When removing three of the RRR limbs, the mechanism obtains one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms are variable-DOF mechanisms. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

Sign in / Sign up

Export Citation Format

Share Document