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.

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.

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.

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.

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.

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]

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 Similar Vertices and Isomorphism Detection for Planar Kinematic Chains Based on Ameliorated Multi-Order Adjacent Vertex Assignment Sequence

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Liang Sun ◽  
Zhizheng Ye ◽  
Fuwei Lu ◽  
Rongjiang Cui ◽  
Chuanyu Wu
Keyword(s):  
Degree Of Freedom ◽  
Adjacent Vertex ◽  
Topological Graph ◽  
Innovative Design ◽  
Kinematic Chains ◽  
Effectiveness And Efficiency ◽  
Definition Of ◽  
Specific Definition

AbstractIsomorphism detection is fundamental to the synthesis and innovative design of kinematic chains (KCs). The detection can be performed accurately by using the similarity of KCs. However, there are very few works on isomorphism detection based on the properties of similar vertices. In this paper, an ameliorated multi-order adjacent vertex assignment sequence (AMAVS) method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs. First, the specific definition of AMAVS is described. Through the calculation of the AMAVS, the adjacent vertex value sequence reflecting the uniqueness of the topology features is established. Based on the value sequence, all possible similar vertices, corresponding relations, and isomorphism discrimination can be realized. By checking the topological graph of KCs with a different number of links, the effectiveness and efficiency of the proposed method are verified. Finally, the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-DOF(degree of freedom) planar KCs.

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 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.

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