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

Duanling Li; Chunxia Li; Zhonghai Zhang; Xianwen Kong

doi:10.1115/DETC2014-34850

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

Duanling Li, Chunxia Li, Zhonghai Zhang, Xianwen Kong

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

Abstract

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.

Original language	English
Title of host publication	ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Publisher	American Society of Mechanical Engineers
Number of pages	9
Volume	5A
ISBN (Electronic)	9780791846360
DOIs	https://doi.org/10.1115/DETC2014-34850
Publication status	Published - 2014
Event	38th Mechanisms and Robotics Conference 2014 - Buffalo, United States Duration: 17 Aug 2014 → 20 Aug 2014

Conference

Conference	38th Mechanisms and Robotics Conference 2014
Country/Territory	United States
City	Buffalo
Period	17/08/14 → 20/08/14

Keywords

Block adjacency matrix
Metamorphic parallel mechanism
Metamorphic transformation

ASJC Scopus subject areas

Modelling and Simulation
Mechanical Engineering
Computer Science Applications
Computer Graphics and Computer-Aided Design

Access to Document

10.1115/DETC2014-34850

Cite this

Li, D., Li, C., Zhang, Z., & Kong, X. (2014). Block Adjacency Matrix Method for Analyzing the Configuration Transformations of Metamorphic Parallel Mechanisms. In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Vol. 5A). Article DETC2014-34850 American Society of Mechanical Engineers. https://doi.org/10.1115/DETC2014-34850

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title = "Block Adjacency Matrix Method for Analyzing the Configuration Transformations of Metamorphic Parallel Mechanisms",

abstract = "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.",

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Li, D, Li, C, Zhang, Z & Kong, X 2014, Block Adjacency Matrix Method for Analyzing the Configuration Transformations of Metamorphic Parallel Mechanisms. in ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. vol. 5A, DETC2014-34850, American Society of Mechanical Engineers, 38th Mechanisms and Robotics Conference 2014, Buffalo, United States, 17/08/14. https://doi.org/10.1115/DETC2014-34850

Block Adjacency Matrix Method for Analyzing the Configuration Transformations of Metamorphic Parallel Mechanisms. / Li, Duanling; Li, Chunxia; Zhang, Zhonghai et al.
ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Vol. 5A American Society of Mechanical Engineers, 2014. DETC2014-34850.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - 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.

AB - 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.

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

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Keywords

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