Matrix Representation of Topological Changes in Metamorphic Mechanisms

2004 ◽  
Vol 127 (4) ◽  
pp. 837-840 ◽  
Author(s):  
Jian S. Dai ◽  
John Rees Jones
Keyword(s):  
Matrix Representation ◽  
Mechanistic Models ◽  
Matrix Operation ◽  
Elementary Matrix ◽  
Matrix Operations ◽  
Metamorphic Mechanism ◽  
Complete Transformation ◽  
Industrial Packaging ◽  
Metamorphic Mechanisms ◽  
Topological Changes

Metamorphic mechanisms form a class of mechanisms that has the facilities to change configuration from one kind to another with a resultant change in the number of effective links and mobility of movement. This paper develops formal matrix operations to describe the distinct topology of configurations found in a metamorphic mechanism and to complete transformation between them. A new way is hence introduced for modeling topological changes of metamorphic mechanisms in general. It introduces a new elimination E-elementary matrix together with a U-elementary matrix to form an EU-elementary matrix operation to produce the configuration transformation. The use of these matrix operations is demonstrated in both spherical and spatial metamorphic mechanisms, the mechanistic models taken from the industrial packaging operations of carton folding manipulation that stimulated this study.

Configuration Based Improved Synthesis of Metamorphic Mechanisms

2009 ◽  
Author(s):  
Duanling Li ◽  
Zhonghai Zhang ◽  
Jian S. Dai ◽  
J. Michael McCarthy
Keyword(s):  
Adjacency Matrix ◽  
Matrix Transformations ◽  
Mechanism Synthesis ◽  
Matrix Operation ◽  
Elementary Matrix ◽  
Matrix Operations ◽  
The Matrix ◽  
Potential Applications ◽  
Synthesis Procedure ◽  
Metamorphic Mechanisms

Metamorphic mechanisms are a class of mechanisms that change their mobility during motions. The deployable and retractable characteristics of these unique mechanisms generate much interest in further investigating their behaviors and potential applications. This paper investigates the resultant configuration variation based on adjacency matrix operation and an improved approach to mechanism synthesis is proposed by adopting elementary matrix operations on the configuration states so as to avoid some omissions caused by existing methods. The synthesis procedure begins with a final configuration of the mechanism, then enumerates possible combinations of different links and associates added links with the binary inverse operations in the matrix transformations of the configuration states, and finally obtains a synthesis result. An algorithm is presented and the topological symmetry of links is used to reduce the number of mechanisms in the synthesis. Some mechanisms of this kind are illustrated as examples.

scholarly journals A holographic matrix representation of the metamorphic parallel mechanisms

2019 ◽  
Vol 10 (2) ◽  
pp. 437-447
Author(s):  
Wei Sun ◽  
Jianyi Kong ◽  
Liangbo Sun
Keyword(s):  
Adjacency Matrix ◽  
Topological Structure ◽  
Incidence Matrix ◽  
Matrix Representation ◽  
Evolutionary Relationships ◽  
Parallel Mechanisms ◽  
Metamorphic Mechanism ◽  
The Matrix ◽  
Metamorphic Mechanisms

Abstract. Metamorphic mechanisms belong to the class of mechanisms that are able to change their configurations sequentially to meet different requirements. In this paper, a holographic matrix representation for describing the topological structure of metamorphic mechanisms was proposed. The matrix includes the adjacency matrix, incidence matrix, links attribute and kinematic pairs attribute. Then, the expanded holographic matrix is introduced, which includes driving link, frame link and the identifier of the configurations. Furthermore, a matrix representation of an original metamorphic mechanism is proposed, which has the ability to evolve into various sub-configurations. And evolutionary relationships between mechanisms in sub-configurations and the original metamorphic mechanism are determined distinctly. Examples are provided to demonstrate the validation of the method.

scholarly journals A representation of the configurations and evolution of metamorphic mechanisms

2016 ◽  
Vol 7 (1) ◽  
pp. 39-47 ◽  
Author(s):  
W. Zhang ◽  
X. Ding ◽  
J. Liu
Keyword(s):  
Matrix Representation ◽  
General Information ◽  
Evolutionary Relationships ◽  
Metamorphic Mechanism ◽  
Adjacency Matrices ◽  
Symbolic Matrix ◽  
Single Configuration ◽  
Metamorphic Mechanisms

Abstract. Metamorphic mechanisms are members of the class of mechanisms that are able to change their configurations sequentially to meet different requirements. The paper introduces a comprehensive symbolic matrix representation for characterizing the topology of one of these mechanisms in a single configuration using general information concerning links and joints. Furthermore, a matrix representation of an original metamorphic mechanism that has the ability to evolve is proposed by uniting the matrices representing all of the mechanism's possible configurations. The representation of metamorphic kinematic joints is developed in accordance with the variation laws of these mechanisms. By introducing the joint variation matrices derived from generalized operations on the related symbolic adjacency matrices, evolutionary relationships between mechanisms in adjacent configurations and the original metmaorphic mechanism are made distinctly. Examples are provided to demonstrate the validation of the method.

scholarly journals A note on the eigenvalue free intervals of some classes of signed threshold graphs

2019 ◽  
Vol 7 (1) ◽  
pp. 218-225
Author(s):  
Milica Anđelić ◽  
Tamara Koledin ◽  
Zoran Stanić
Keyword(s):  
Tridiagonal Matrix ◽  
Constant Sign ◽  
Equitable Partition ◽  
Elementary Matrix ◽  
Matrix Operations ◽  
Threshold Graphs ◽  
The Matrix ◽  
Threshold Graph

Abstract We consider a particular class of signed threshold graphs and their eigenvalues. If Ġ is such a threshold graph and Q(Ġ ) is a quotient matrix that arises from the equitable partition of Ġ , then we use a sequence of elementary matrix operations to prove that the matrix Q(Ġ ) – xI (x ∈ ℝ) is row equivalent to a tridiagonal matrix whose determinant is, under certain conditions, of the constant sign. In this way we determine certain intervals in which Ġ has no eigenvalues.

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