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.

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.

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.

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.

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.

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 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.

Synthesis of planar kinematic chains with prismatic pairs based on a similarity recognition algorithm

2021 ◽  
pp. 1-13
Author(s):  
Rongjiang Cui ◽  
Zhizheng Ye ◽  
Shifu Xu ◽  
Chuan-yu Wu ◽  
Liang Sun
Keyword(s):  
Recognition Algorithm ◽  
Synthesis Process ◽  
Synthesis Methods ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract The structural synthesis of planar kinematic chains (KCs) with prismatic pairs (P-pairs) is the basis of innovating mechanisms containing P-pairs. In literature, only a little research has been carried out to synthesize planar KCs with P-pairs. Moreover, these synthesis methods for KCs with P-pairs involve all possible combinations of edges, resulting in a large number of isomorphic KCs and a low synthesis efficiency. In this study, our previous similarity recognition algorithm is improved and applied to synthesize planar KCs with P-pairs. Only a small number of isomorphic KCs are generated in the synthesis process, and the synthesis efficiency is greatly enhanced. Our method is applied to synthesize 9-link 2-DOF, 10-link 1-DOF, and 11-link 2-DOF KCs with one and two P-pairs. Our synthesis results are consistent with those of the existing literature. The present work is helpful to design mechanisms with P-pairs and can be extended to mechanisms with other types of kinematic pairs.

Novel Algorithmic Approach to Deciphering Rovash Inscriptions

2015 ◽  
pp. 7222-7233 ◽  
Author(s):  
Loránd Lehel Tóth ◽  
Raymond Pardede ◽  
Gábor Hosszú
Keyword(s):  
Experimental Results ◽  
The Novel ◽  
Statistical Probability ◽  
Algorithmic Approach ◽  
Topological Parameters ◽  
Novel Method ◽  
Novel Algorithm

The article presents a method to decipher Rovash inscriptions made by the Szekelys in the 15th-18th centuries. The difficulty of the deciphering work is that a large portion of the Rovash inscriptions contains incomplete words, calligraphic glyphs or grapheme errors. Based on the topological parameters of the undeciphered symbols registered in the database, the presented novel algorithm estimates the meaning of the inscriptions by the matching accuracies of the recognized graphemes and gives a statistical probability for deciphering. The developed algorithm was implemented in software, which also contains a built-in dictionary. Based on the dictionary, the novel method takes into account the context in identifying the meaning of the inscription. The proposed algorithm offers one or more words in a different random values as a result, from which users can select the relevant one. The article also presents experimental results, which demonstrate the efficiency of method.

A Novel Neutrosophic Image Segmentation Based on Improved Fuzzy C-Means Algorithm (NIS-IFCM)

2019 ◽  
Vol 34 (05) ◽  
pp. 2055011
Author(s):  
Jing Zhao ◽  
Xiaoli Wang ◽  
Ming Li
Keyword(s):  
Computer Vision ◽  
Particle Swarm Optimization ◽  
Image Segmentation ◽  
Classical Problem ◽  
Local Optimum ◽  
The Novel ◽  
Swarm Optimization ◽  
Novel Method ◽  
Fuzzy C Means Algorithm ◽  
Novel Algorithm

Image segmentation is a classical problem in the field of computer vision. Fuzzy [Formula: see text]-means algorithm (FCM) is often used in image segmentation. However, when there is noise in the image, it easily falls into the local optimum, which results in poor image boundary segmentation effect. A novel method is proposed to solve this problem. In the proposed method, first, the image is transformed into a neutrosophic image. In order to improve the ability of global search, a combined FCM based on particle swarm optimization (PSO) is proposed. Finally, the proposed algorithm is applied to the neutrosophic image segmentation. The results of experiments show that the novel algorithm can eliminate image noise more effectively than the FCM algorithm, and make the boundary of the segmentation area clearer.

Sign in / Sign up

Export Citation Format

Share Document