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]

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.

scholarly journals Structural synthesis of plane kinematic chain inversions without detecting isomorphism

2021 ◽  
Vol 12 (2) ◽  
pp. 1061-1071
Author(s):  
Jinxi Chen ◽  
Jiejin Ding ◽  
Weiwei Hong ◽  
Rongjiang Cui
Keyword(s):  
Mechanism Design ◽  
Adjacency Matrix ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Synthesis Methods ◽  
Creative Design ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract. A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

scholarly journals STRUCTURAL IDENTIFICATION OF DISTINCT INVERSIONS OF PLANAR KINEMATIC CHAINS

2011 ◽  
Vol 12 (3) ◽  
Author(s):  
Dr. Shubhashis Sanyal
Keyword(s):  
Present Method ◽  
Kinematic Chain ◽  
Structural Identification ◽  
Degree Of Freedom ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Single Degree

Inversions are various structural possibilities of a kinematic chain. The number of inversions depends on the number of links of a kinematic chain. At the stage of structural synthesis, identification of distinct structural inversions of a particular type of kinematic chain is necessary. Various researchers have proposed methods for identification of distinct inversions. Present method based on Link joint connectivity is proposed to identify the distinct inversions of a planar kinematic chain. Method is tested successfully on single degree and multiple degree of freedom planar kinematic chains. ABSTRAK: Penyonsangan merupakan kebarangkalian pelbagai struktur suatu rangkaian kinematik. Jumlah songsangan bergantung kepada jumlah hubungan suatu rangkaian kinematik. Pada peringkat sintesis struktur, pengenalan songsangan struktur yang berbeza untuk suatu jenis rangkaian kinematik adalah perlu. Ramai penyelidik telah mencadangkan pelbagai kaedah pengenalan songsangan yang berbeza. Kaedah terkini berdasarkan hubungan kesambungan bersama telah dicadangkan untuk mengenalpasti songsangan yang berbeza dalam suatu satah rangkaian kinematik.

An algorithm for structural synthesis of planar simple and multiple joint kinematic chains

2013 ◽  
Vol 228 (12) ◽  
pp. 2178-2192 ◽  
Author(s):  
Jinkui Chu ◽  
Yanhuo Zou
Keyword(s):  
Mechanical Design ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Structural Synthesis ◽  
Joint Kinematic ◽  
Kinematic Chains

Structural synthesis of kinematic chains is one of the most creative and important stages in mechanical design. It provides a number of optional structure types when new mechanisms are created. In this paper, a new algorithm for structural synthesis of planar simple and multiple joint kinematic chains has been proposed by subsequently adding single-kinematic-chain method. By this algorithm, the structure of multiple joint kinematic chains with specified degree-of-freedom, the number of links, and total multiple joint factors P can be synthesized in batch. When P = 0, the structure of simple joint kinematic chains with specified degree-of-freedom, and the number of links can also be generated. Finally, structural synthesis examples of planar simple and multiple joint kinematic chains have been studied to show effectiveness of this algorithm.

scholarly journals A New Algorithm for Unique Representation and Isomorphism Detection of Planar Kinematic Chains with Simple and Multiple Joints

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 601
Author(s):  
Mahmoud Helal ◽  
Jong Wan Hu ◽  
Hasan Eleashy
Keyword(s):  
Degree Of Freedom ◽  
Synthesis Process ◽  
Structural Synthesis ◽  
Joint Configuration ◽  
Unique Representation ◽  
Kinematic Chains

In this work, a new algorithm is proposed for a unique representation for simple and multiple joint planar kinematic chains (KCs) having any degree of freedom (DOF). This unique representation of KCs enhances the isomorphism detection during the structural synthesis process of KCs. First, a new concept of joint degree is generated for all joints of a given KC based on joint configuration. Then, a unified loop array (ULA) is obtained for each independent loop. Finally, a unified chain matrix (UCM) is established as a unique representation for a KC. Three examples are presented to illustrate the proposed algorithm procedures and to test its validity. The algorithm is applied to get a UCM for planar KCs having 7–10 links. As a result, a complete atlas database is introduced for 7–10-link non-isomorphic KCs with simple or/and multiple joints and their corresponding unified chain matrix.

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).

A Method for Detection of Distinct Mechanisms of a Planar Kinematic Chain

1988 ◽  
Vol 12 (1) ◽  
pp. 15-20 ◽  
Author(s):  
L.K. Patel ◽  
A.C. Rao
Keyword(s):  
Efficient Method ◽  
Numerical Scheme ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
A Chain

This paper presents a computationally simple and efficient method for identification of distinct mechanisms of a planar kinematic chain having a single degree of freedom. It is proposed that velocity diagrams for all the inversions of a chain be drawn and the possible isomorphism among these velocity diagrams be detected. From the velocity diagram, a motion transfer point matrix can be prepared resulting in the development of a numerical scheme to be associated with a mechanism. Identical schemes lead to detection of isomorphism between mechanisms. The main advantage of this method is that, apart form detecteing isomorphism, it indicates which of the inversions is better kinematically e.g. higher the total number of vectors, better is the mechanism.

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.

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.

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