Configuration Analysis of Metamorphic Mechanisms Based on Extended Adjacency Matrix Operations

2011 ◽  
Vol 24 (05) ◽  
pp. 767 ◽  
Author(s):  
Duanling LI
Keyword(s):  
Adjacency Matrix ◽  
Matrix Operations ◽  
Metamorphic Mechanisms

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.

Topology and Constraint Analysis of Reconfiguration in Metamorphic Mechanisms

2010 ◽  
Author(s):  
Ketao Zhang ◽  
Jian S. Dai ◽  
Yuefa Fang ◽  
Zi-Qiang Zhu
Keyword(s):  
Phase Change ◽  
Adjacency Matrix ◽  
Matrix Phase ◽  
Topological Phase ◽  
Revolute Joints ◽  
Constraint Analysis ◽  
Metamorphic Mechanisms

This paper investigates the reconfiguration of the metamorphic mechanisms and proposes mechanism topology matrix, phase matrix and augmented adjacency matrix to identify variation of geometric and topological configurations. This is then used to investigate the two generic ways in the study of induced constraint change of the metamorphic mechanisms. The topological phase change of the metamorphic mechanisms correlative to the variable-axis revolute joints and link annex is hence investigated and constraint analysis is then presented in the working phases of the new metamorphic mechanisms.

Block Adjacency Matrix Method for Analyzing the Configuration Transformations of Metamorphic Parallel Mechanisms

2014 ◽  
Author(s):  
Duanling Li ◽  
Chunxia Li ◽  
Zhonghai Zhang ◽  
Xianwen Kong
Keyword(s):  
Adjacency Matrix ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
New Method ◽  
Parallel Mechanisms ◽  
Adjacency Matrices ◽  
Moving Platform ◽  
Internal Configuration ◽  
Spherical Motion ◽  
Metamorphic Mechanisms

Metamorphic transformation is a fundamental and key issue in the design and analysis of metamorphic mechanisms. It is tedious to represent and calculate the metamorphic transformations of metamorphic parallel mechanisms using the existing adjacency matrix method. To simplify the configuration transformation analysis, we propose a new method based on block adjacency matrix to analyze the configuration transformations of metamorphic parallel mechanisms. A block adjacency matrix is composed of three types of elements, including limb matrices that are adjacency matrices each representing a limb of a metamorphic parallel mechanism, row matrices each representing how a limb is connected to the moving platform, and column matrices each representing how a limb is connected to the base. Manipulations of the block adjacency matrix for analyzing the metamorphic transformations are presented systematically. If only the internal configuration of a limb changes, the configuration transformations can be obtained by simply calculating the corresponding limb matrix. A 3-URRRR metamorphic parallel mechanism, which has five configurations including a 1-DOF translation configuration and a 3-DOF spherical motion configuration, is taken as an example to illustrate the effectiveness of the proposed approach to the metamorphic transformation analysis of metamorphic parallel mechanism.

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.

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.

Assur-Group Inferred Structural Synthesis for Planar Mechanisms

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Shujun Li ◽  
Hongguang Wang ◽  
Jian S. Dai
Keyword(s):  
Adjacency Matrix ◽  
Synthesis Method ◽  
Matrix Group ◽  
Structural Synthesis ◽  
Planar Mechanisms ◽  
Comprehensive List ◽  
Assur Group ◽  
The Given ◽  
First Time ◽  
Metamorphic Mechanisms

In order to obtain a comprehensive list of possible mechanisms with various choices of both R and P pairs and mechanism inversion of planar mechanisms, a new structural synthesis method is developed by integrating Assur groups (AGs) as elements in the newly developed group-based adjacency matrix. This extended adjacency matrix is proposed with the diagonal elements representing three fundamental elements as the frame link, driving link, AG and augmented AG (AAG) if metamorphic mechanisms are to be synthesized. The off-diagonal elements provide information on group combination and connection forms of the above three fundamental elements and that on the associated kinematic pairs. Based on the extended adjacency matrix, all assembly modes for the given AGs can be established and isomorphism mechanisms can be identified at the same time. Considering all types of the AGs in the extended adjacency matrix, group permutation and combination are used and connection forms are generated including variation of the driving link and mechanism inversion. The structural synthesis is then extending to generating a comprehensive list of types of mechanisms and illustrated by the synthesis for class II 6-bar planar mechanisms with both R and P pairs, generating a list of 588 types of mechanisms that are derived for the first time. The paper further applies the approach to metamorphic mechanisms, and obtained five connection forms of the 7-bar 2DOF metamorphic mechanisms.

Analysis Method of Screw Algebra for Motion Characteristics of a 4-URU Parallel Metamorphic Mechanism

2013 ◽  
Vol 753-755 ◽  
pp. 2062-2065
Author(s):  
Zhong Hai Zhang ◽  
Duan Ling Li ◽  
Chun Xia Li
Keyword(s):  
Adjacency Matrix ◽  
Degrees Of Freedom ◽  
Linear Equations ◽  
Homogeneous System ◽  
Basic Solution ◽  
Moving Platforms ◽  
Metamorphic Mechanism ◽  
Screw Motions ◽  
Motion Characteristics ◽  
Metamorphic Mechanisms

A new 4-URU parallel metamorphic mechanism is proposed. A new method using screw adjacency matrix to describe the structural transformation of metamorphic mechanisms is put forward. This method overcomes the limitations of existing topological description method which cannot analyze the metamorphic mechanisms spatial structures and motion characteristics. Then the screw algebra method for analyzing the metamorphic mechanisms motion characteristics is introduced in detail. Firstly, screw motions homogeneous system of linear equations is determined by the screw adjacency matrix. Then the equations basic solution system determines the anti-screw system. Finally calculate the moving platforms motion screw system. Thus the metamorphic mechanisms motion characteristics, such as spatial structure in different configurations, the number of components and joints, degrees of freedom are obtained.

Representation of Topological Changes in Metamorphic Mechanisms With Matrices of the Same Dimension

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
Z. H. Lan ◽  
R. Du
Keyword(s):  
Adjacency Matrix ◽  
Short Paper ◽  
Metamorphic Mechanisms ◽  
Topological Changes

This short paper introduces a new adjacency matrix to represent the topological changes of metamorphic mechanisms. An element “−1” is introduced to indicate the frozen kinematic pairs, which gives an easy way to represent the transformation and the dimension of the adjacency matrix is kept unchanged after the transformation. In this way, the information of the original mechanism is preserved and all possible changes of the mechanism can be derived according to the adjacency matrix. A demonstration example is included.

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