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

[+] Author Affiliations
Duanling Li, Chunxia Li, Zhonghai Zhang

Beijing University of Posts and Telecommunications, Beijing, China

Xianwen Kong

Heriot-Watt University, Edinburgh, UK

Paper No. DETC2014-34850, pp. V05AT08A062; 9 pages
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5A: 38th Mechanisms and Robotics Conference
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4636-0
  • Copyright © 2014 by ASME


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.

Copyright © 2014 by ASME



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