Matrix Representation of Topological Changes in Metamorphic Mechanisms

[+] Author and Article Information
Jian S. Dai1

Department of Mechanical Engineering, School of Physical Sciences and Engineering, King’s College London,  University of London, Strand, London WC2R 2LS, UKjian.dai@kcl.ac.uk

John Rees Jones

Beaumaris Drive, Thingwall, Heswall, Wirral CH61 7XP, UKj.reesjones@zen.co.uk


To whom correspondence should be addressed.

J. Mech. Des 127(4), 837-840 (Jul 24, 2004) (4 pages) doi:10.1115/1.1866159 History: Received January 12, 2004; Revised July 24, 2004

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.

Copyright © 2005 by American Society of Mechanical Engineers
Topics: Mechanisms
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Figure 2

Configuration state when a five-bar linkage configuration changes to a four-bar linkage configuration

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Figure 3

A spatial mechanism

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Figure 4

Equivalent spatial mechanism superimposed on a carton

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Figure 1

Five-bar spherical metamorphic mechanism

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Figure 5

Partially folded carton

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Figure 6

A spherical four-bar linkage with serial kinematic chains



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