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.

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.

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.

scholarly journals Algebraic Characteristics of the Matrix Conversions Class and Its Hardware Implementation

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Stanislav V. Kudlai
Keyword(s):  
Algebraic System ◽  
Hardware Implementation ◽  
Matrix Transformations ◽  
Matrix Functions ◽  
Hardware Support ◽  
Algebra Isomorphism ◽  
Program Algebra ◽  
Matrix Operations ◽  
The Matrix ◽  
Recursive Matrix

This paper derives the algebraic characteristic of the matrix transformations class by the method of isomorphic mappings on the algebraic characteristic of the class of vector transformations using the primitive program algebras. The paper also describes the hardware implementation of the matrix operations accelerator based on the obtained results. The urgency of the work is caused by the fact that today there is a rapid integration of computer technology in all spheres of society and, as a consequence, the amount of data that needs to be processed per unit time is constantly increasing. Many problems involving large amounts of complex computation are solved by methods based on matrix operations. Therefore, the study of matrix calculations and their acceleration is a very important task. In this paper, as a contribution in this direction, we propose a study of the matrix transformations class using signature operations of primitive program algebra such as multi place superposition, branching, cycling, which are refinements of the most common control structures in most high-level programming languages, and also isomorphic mapping. Signature operations of primitive program algebra in combination with basic partial-recursive matrix functions and predicates allow to realize the set of all partial-recursive matrix functions and predicates. Obtained the result on the basis of matrix primitive program algebra. Isomorphism provides the reproduction of partially recursive functions and predicates for matrix transformations as a map of partially recursive vector functions and predicates. The completeness of the algebraic system of matrix transformations is ensured due to the available results on the derivation of the algebraic system completeness for vector transformations. A name model of matrix data has been created and optimized for the development of hardware implementation. The hardware implementation provides support for signature operations of primitive software algebra and for isomorphic mapping. Hardware support for the functions of sum, multiplication and transposition of matrices, as well as the predicate of equality of two matrices is implemented. Support for signature operations of primitive software algebra is provided by the design of the control part of the matrix computer based on the RISC architecture. The hardware support of isomorphism is based on counters, they allow to intuitively implement cycling in the functions of isomorphic mappings. Fast execution of vector operations is provided by the principle of computer calculations SIMD.

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.

A Matrix Representation and Motion Space Exchange Metamorphic Operation

2011 ◽  
Vol 308-310 ◽  
pp. 2058-2061
Author(s):  
Shu Jun Li ◽  
Jian Sheng Dai
Keyword(s):  
Adjacency Matrix ◽  
Matrix Representation ◽  
Matrix Operation ◽  
Planar Mechanism ◽  
Kinematic Chains ◽  
Orientation Change ◽  
Joint Axis ◽  
The Matrix

The paper presents a matrix representation of mechanical chains based on proposed joint-axis matrix, and a matrix operation of joints orientation change metamorphic processes. A four elements joint-axis matrix with joints types and orientations is developed first, and an augmented adjacency matrix of kinematic chains is formed by adding the elements of joint-axis matrix into the corresponding positions of general adjacency matrix of kinematic chains. Then the matrix operation of metamorphic process is performed through changing the orientation of metamorphic joint of augmented planar mechanism to transform the configuration of the mechanism from planar to spatial one.

scholarly journals DNA Matrix Operation Based on the Mechanism of the DNAzyme Binding to Auxiliary Strands to Cleave the Substrate

Biomolecules ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1797
Author(s):  
Shaoxia Xu ◽  
Yuan Liu ◽  
Shihua Zhou ◽  
Qiang Zhang ◽  
Nikola K. Kasabov
Keyword(s):  
Numerical Computation ◽  
Dna Computing ◽  
Computing System ◽  
Matrix Operation ◽  
Computing Systems ◽  
Multiplication Operation ◽  
Matrix Operations ◽  
The Matrix ◽  
Speed And Accuracy ◽  
Binding Substrate

Numerical computation is a focus of DNA computing, and matrix operations are among the most basic and frequently used operations in numerical computation. As an important computing tool, matrix operations are often used to deal with intensive computing tasks. During calculation, the speed and accuracy of matrix operations directly affect the performance of the entire computing system. Therefore, it is important to find a way to perform matrix calculations that can ensure the speed of calculations and improve the accuracy. This paper proposes a DNA matrix operation method based on the mechanism of the DNAzyme binding to auxiliary strands to cleave the substrate. In this mechanism, the DNAzyme binding substrate requires the connection of two auxiliary strands. Without any of the two auxiliary strands, the DNAzyme does not cleave the substrate. Based on this mechanism, the multiplication operation of two matrices is realized; the two types of auxiliary strands are used as elements of the two matrices, to participate in the operation, and then are combined with the DNAzyme to cut the substrate and output the result of the matrix operation. This research provides a new method of matrix operations and provides ideas for more complex computing systems.

scholarly journals The normalized distance Laplacian

2021 ◽  
Vol 9 (1) ◽  
pp. 1-18
Author(s):  
Carolyn Reinhart
Keyword(s):  
Spectral Radius ◽  
Characteristic Polynomial ◽  
Adjacency Matrix ◽  
Connected Graph ◽  
Distance Matrix ◽  
Laplacian Matrix ◽  
Diagonal Matrix ◽  
The Matrix

Abstract The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of transmissions of the vertices of the graph. The normalized distance Laplacian, 𝒟𝒧(G) = I−T(G)−1/2 𝒟(G)T(G)−1/2, is introduced. This is analogous to the normalized Laplacian matrix, 𝒧(G) = I − D(G)−1/2 A(G)D(G)−1/2, where D(G) is the diagonal matrix of degrees of the vertices of the graph and A(G) is the adjacency matrix. Bounds on the spectral radius of 𝒟 𝒧 and connections with the normalized Laplacian matrix are presented. Twin vertices are used to determine eigenvalues of the normalized distance Laplacian. The distance generalized characteristic polynomial is defined and its properties established. Finally, 𝒟𝒧-cospectrality and lack thereof are determined for all graphs on 10 and fewer vertices, providing evidence that the normalized distance Laplacian has fewer cospectral pairs than other matrices.

scholarly journals Development of a Decellularized Porcine Esophageal Matrix for Potential Applications in Cancer Modeling

Cells ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 1055
Author(s):  
Hersh Chaitin ◽  
Michael L. Lu ◽  
Michael B. Wallace ◽  
Yunqing Kang
Keyword(s):  
Cell Growth ◽  
Lymphatic Vessels ◽  
Significant Loss ◽  
Cancer Cell Growth ◽  
Cell Growth And Migration ◽  
Decellularized Extracellular Matrix ◽  
Cancer Models ◽  
The Matrix ◽  
Potential Applications ◽  
And Migration

Many decellularized extracellular matrix-derived whole organs have been widely used in studies of tissue engineering and cancer models. However, decellularizing porcine esophagus to obtain decellularized esophageal matrix (DEM) for potential biomedical applications has not been widely investigated. In this study a modified decellularization protocol was employed to prepare a porcine esophageal DEM for the study of cancer cell growth. The cellular removal and retention of matrix components in the porcine DEM were fully characterized. The microstructure of the DEM was observed using scanning electronic microscopy. Human esophageal squamous cell carcinoma (ESCC) and human primary esophageal fibroblast cells (FBCs) were seeded in the DEM to observe their growth. Results show that the decellularization process did not cause significant loss of mechanical properties and that blood ducts and lymphatic vessels in the submucosa layer were also preserved. ESCC and FBCs grew on the DEM well and the matrix did not show any toxicity to cells. When FBS and ESCC were cocultured on the matrix, they secreted more periostin, a protein that supports cell adhesion on matrix. This study shows that the modified decellularization protocol can effectively remove the cell materials and maintain the microstructure of the porcine esophageal matrix, which has the potential application of studying cell growth and migration for esophageal cancer models.

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