Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2010 August 15-18, 2010, Montreal, Quebec, Canada DETC2010-29199 DRAFT: CONFIGURATION SYNTHESIS OF METAMORPHIC MECHANISMS BASED ON CHARACTERISTIC INCIDENCE MATRIX Duanling Li Automation School Beijing University of Posts and Telecommunications, Beijing, P.R. China Email: liduanling@163.com Zhonghai Zhang Automation School Beijing University of Posts and Telecommunications, Beijing, P.R. China E-mail：zhzhonghai@sina.com Jian S Dai Department of Mechanical Engineering School of Physical Sciences and Engineering King’s College, University of London London, United Kingdom Email: Jian.Dai@kcl.ac.uk J. Michael McCarthy Robotics and Automation Laboratory University of California Irvine, California 92697 Email: jmmccart@uci.edu ABSTRACT This paper presents an approach to the configuration synthesis of metamorphic mechanisms with consideration of both link and joint changes. The technique, referred to here as computational geometry, uses a constraint graph to represent topological structure of metamorphic mechanisms instead of traditional graph representation that can not distinguish link types and multi-joints. Based on the constraint graph, a characteristic incidence matrix is proposed with the characteristic relationships between links and joints. Then, a synthetic method based on characteristic incidence matrix is put forward in this paper using operations among matrixes with different orders by binary computing. Through an example of a four-bar mechanism synthesizing into five-bar mechanisms with the proposed configuration synthetic method, it is confirmed that the approach is correct and effective for the configuration synthesis of all metamorphic mechanisms with single or multiple joints. . 1 INTRODUCTION Metamorphic Mechanisms are a kind of mechanisms that can change the number of the effective links and the degree of freedom together with the topological configuration changes during motions. It was proposed in 25th ASME biennial mechanisms and robotics conference in 1998 [1]. In recent 10 years, the configuration analysis and synthesis have been a focus of the research of metamorphic mechanisms. Though a number of studies regarding to the conceptual design of mechanisms with closed and open chains were proposed in the past years, the synthetic method of metamorphic mechanisms is in a different way because of configuration changes and changes of the number of effective links during motions. In 2002 and 2003, D L Li ([2] and [3]) presented an eliminating matrix's rank method to analyze the configuration changes based on graph representation, then a structural synthesis with adjacency matrix was proposed with an example of a 4-bar metamorphic mechanism synthesizing into 5-bar metamorphic mechanisms. In 2006, also with the similar method, a 3-bar mechanism was synthesized into 5-bar metamorphic mechanisms [4]. Dai and Rees Jones (2005) [5] used changes of the adjacency matrix of a topological graph representation to characterize metamorphic mechanisms. Although structural change is one of the characteristics of metamorphic mechanism, only changes of links during motions are analyzed by the adjacency matrices of topological graph representation. Also it is not easy for topological graph representation to express metamorphic mechanisms with multiple joints. Therefore, the existing structural synthesis can only derive metamorphic mechanisms with single joints based on operations of adjacency matrix. New synthetic method should be explored to synthesize all metamorphic mechanisms with single or multiple joints. Constraint graphs and their associated geometric constraint solvers evolved from the variational geometry techniques of Light and Gossard (1982)[6]. Bouma, et al. (1995)[7] provided an introduction to the basic principles of geometric constraint solvers based on constraint graphs, see also Homan, et al. (2004)[8]. Constraint graphs map geometric objects to vertices and geometric relationships to edges, for this reason it is a versatile tool for characterizing mechanical assemblies. The characteristic incidence matrix derived from 1 Copyright © 2010 by ASME