Computational Identification of Link Adjacency and Joint Incidence in Kinematic Chains and Mechanisms

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Chien-Jong Shih
Keyword(s):  
Mechanism Design ◽  
Design Automation ◽  
Systematic Approach ◽  
Computational Approach ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Careful Observation ◽  
Synthesis Of Mechanisms ◽  
Computational Identification ◽  
Observation Method

The identification of link adjacency and joint incidence of kinematic chains and mechanisms is important and essential prior to the task of conceptual mechanism design. A careful observation method can be done in general; however, a computational approach is particularly needed for the design automation and algorithmic enumeration. This paper proposes a systematic approach for this goal in which a pseudogenetic concept is employed. The graph identification is then generalized from which the identifications of kinematic chains and mechanisms are automatically mapped. The illustrative examples show that the computation is simple and easily programmable. This development is helpful for the automated structural synthesis of mechanisms.

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.

A distinct matrix representation of the planar kinematic chains and isomorphism recognition

2019 ◽  
Vol 13 (4) ◽  
pp. 5717-5734
Author(s):  
M. S. Alam ◽  
M. Suhaib
Keyword(s):  
Mechanism Design ◽  
Design Problem ◽  
Matrix Representation ◽  
Degree Of Freedom ◽  
New Method ◽  
Structural Synthesis ◽  
Primary Condition ◽  
Secondary Conditions ◽  
Kinematic Chains ◽  
Three Degree Of Freedom

Structural synthesis of kinematic chains has been an indispensable area of the mechanism-design problem. The duplication may occur while developing kinematic chains. Therefore, an isomorphic test is required to eliminate duplication. For this purpose, the numbers of methods are proposed during recent years. However, most of the methods are complex and difficult to understand, and fulfil the only primary condition, but not the secondary conditions for isomorphism detection. In the present work, a new method is introduced to detect isomorphism in planar kinematic chains (KCs) fulfilling both primary and secondary conditions. First, KC’s are topologically transformed into skeleton diagrams, and then skeleton matrices [S] and identification strings [IS] are formulated consequently. In order to detect isomorphism, the IS is considered as an invariant string of a KC which in turn, enables the detection of isomorphism between the KCs. The proposed method accurately recognizes isomorphism up to 12 links KCs with no counter examples found in the literature. Three examples with one degree of freedom having 10 links 12 joints, 10 links 13 joints and 12 links three degree of freedom systems are introduced to reveal the reliability and strength of the proposed method.

Reconciling enumeration contradictions: Complete list of Baranov chains with up to 15 links with mathematical proof

2020 ◽  
pp. 1-13
Author(s):  
Fernando V. Morlin ◽  
Andrea Piga carboni ◽  
Daniel Martins
Keyword(s):  
Systematic Approach ◽  
Mathematical Proof ◽  
Identification Problem ◽  
Matroid Theory ◽  
Structural Synthesis ◽  
Crucial Step ◽  
Kinematic Chains ◽  
Novel Method ◽  
Isomorphic Graphs ◽  
Novel Algorithm

Abstract The identification of Baranov chains is associated with the rigid subchain identification problem, which is a crucial step in several methods of structural synthesis of kinematic chains. In this paper, a systematic approach for the detection of rigid subchains, based on matroid theory, is presented and proved. Based on this approach, a novel method for the enumeration of Baranov chains is proposed. A novel algorithm is applied to a database of non-isomorphic graphs of non-fractionated zero-mobility kinematic chains. By means of the proposed algorithm, the previous results for Baranov chains presented in literature with up to 11 links are compared and validated. Furthermore, discrepancies in the number of Baranov chains with up to 13 links, presented in literature, are pointed out, discussed and the proven results are presented. Finally, the complete family of Baranov chains with up to 15 links is obtained. Examples of application of the proposed method are provided.

An Application of Generalized Kinematic Chains to the Structural Synthesis of Nonfractionated Epicyclic Gear Trains

1992 ◽  
Author(s):  
Cheng-Ho Hsu
Keyword(s):  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Kinematic Chain ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Three Degrees Of Freedom

Abstract This paper presents a systematic approach, which is based on the concept of generalization for the structural synthesis of geared kinematic chains for epicyclic gear trains with any number of degrees of freedom. First, the fundamental rules of generalized kinematic chains for nonfractionated epicyclic gear trains are investigated. Next, according to the numbers of gear pairs and degrees of freedom, acceptable kinematic chains for nonfractionated epicyclic gear trains are identified from an atlas of basic kinematic chains. Then, each acceptable kinematic chain is specialized to be epicyclic gear trains. Finally, geared kinematic chains for nonfractionated epicyclic gear trains with up to three degrees of freedom and four gear pairs have been susscessfully constructed.

STRUCTURAL SYNTHESIS OF MECHANISMS KINEMATICS–TYPE DELTA

2020 ◽  
Vol 339 (1) ◽  
pp. 26-33
Author(s):  
N.A. SAPRYKINA ◽  
◽  
A.V. PROSKOKOV ◽  
A.A. SAPRYKIN ◽  
◽  
...  
Keyword(s):  
Structural Synthesis ◽  
Synthesis Of Mechanisms

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.

The Degree Code—A New Mechanism Identifier

1993 ◽  
Vol 115 (3) ◽  
pp. 627-630 ◽  
Author(s):  
C. S. Tang ◽  
Tyng Liu
Keyword(s):  
Storage System ◽  
Graph Isomorphism ◽  
Critical Issue ◽  
Mathematical Representation ◽  
Structural Synthesis ◽  
Synthesis Of Mechanisms ◽  
Code Algorithm ◽  
Isomorphic Graphs ◽  
And Storage ◽  
Isomorphism Identification

An important step in the structural synthesis of mechanisms requires the identification of isomorphism between the graphs which represents the mechanism topology. Previously used methods for identifying graph isomorphism either yield incorrect results for some cases or their algorithms are computationally inefficient for this application. This paper describes a new isomorphism identification method which is well suited for the automated structural synthesis of mechanisms. This method uses a new and compact mathematical representation for a graph, called the Degree Code, to identify graph isomorphism. Isomorphic graphs have identical Degree Codes; nonisomorphic graphs have distinct Degree Codes. Therefore, by examining the Degree Codes of the graphs, graph isomorphism is easily and correctly identified. This Degree Code algorithm is simpler and more efficient than other methods for identifying isomorphism correctly. In addition, the Degree Code can serve as an effective nomenclature and storage system for graphs or mechanisms. Although this identification scheme was developed specifically for the structural synthesis of mechanisms, it can be applied to any area where graph isomorphism is a critical issue.

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.

Pattern Matching Synthesis As an Automated Approach to Mechanism Design

1989 ◽  
Author(s):  
D. A. Hoeltzel ◽  
W.-H. Chieng
Keyword(s):  
Neural Network ◽  
Mechanism Design ◽  
Pattern Matching ◽  
Network Models ◽  
Hopfield Neural Network ◽  
Neural Network Models ◽  
Knowledge Based ◽  
Synthesis Of Mechanisms ◽  
New Knowledge ◽  
Programming Techniques

Abstract A new knowledge-based approach for the synthesis of mechanisms, referred to as Pattern Matching Synthesis, has been developed based on committee machine and Hopfield neural network models of pattern matching applied to coupler curves. Computational tests performed on a dimensionally parameterized four bar mechanism have yielded 15 distinct coupler curve groups (patterns) from a total of 356 generated coupler curves. This innovative approach represents a first step toward the automation of mapping structure-to-function in mechanism design based on the application of artificial intelligence programming techniques.

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