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Research Papers

Topology and Constraint Analysis of Phase Change in the Metamorphic Chain and Its Evolved Mechanism

[+] Author and Article Information
Ketao Zhang

Department of Mechanical Engineering, King’s College London, University of London, Strand, London WC2R 2LS, UK; Department of Mechanical Engineering, Beijing Jiaotong University, Beijing, 100044, P. R. Chinaketao.zhang@kcl.ac.uk

Jian S. Dai

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

Yuefa Fang

Department of Mechanical Engineering, Beijing Jiaotong University, Beijing, 100044, P. R. Chinayffang@bjtu.edu.cn

J. Mech. Des 132(12), 121001 (Nov 23, 2010) (11 pages) doi:10.1115/1.4002691 History: Received September 18, 2009; Revised September 20, 2010; Published November 23, 2010; Online November 23, 2010

This paper presents a metamorphic kinematic pair extracted from origami folds in the context of mechanisms, its evolved metamorphic chain, and the novel metamorphic parallel mechanism. This paper starts from the generic issues of topological representation for metamorphic mechanism, leading to unified elementary matrix operation for presentation of topological variation. Phase matrix and augmented adjacency matrix are developed to present the topological state and geometry of metamorphic mechanism in an evolutionary process. The metamorphic kinematic pair has the ability of changing mobility to generate different motion patterns based on mobility change correlated with the link annex induced topological phase change. This paper then investigates topological variation of the metamorphic chain and the topological subphases are enumerated in accordance with structure evolution. Using the metamorphic chain as chain-legs, a multiloop metamorphic mechanism with ability of performing phase change and orientation switch is constructed. The disposition of constraints and geometric constraints induced bifurcated motion are analyzed based on screw theory. The topological variation of the metamorphic parallel mechanism is addressed and the foldability is verified by physical device.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Digraph representation of topological phase change

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Figure 2

An L-shaped flat cardboard with precut creases

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Figure 3

Source phase of the metamorphic kinematic pair: (a) partially folded L-shaped cardboard and (b) equivalent 3R spherical unit

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Figure 4

The first subphase of the metamorphic kinematic pair: (a) folded cardboard and (b) equivalent Hooke joint

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Figure 5

Second subphase of the metamorphic kinematic pair: (a) deployed cardboard and (b) equivalent compound revolute pair

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Figure 6

Physical transition of the metamorphic kinematic pair

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Figure 7

Digraph representation of the generalized metamorphic kinematic pair

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Figure 8

The metamorphic chain from closed-loop cardboard: (a) closed-loop cardboard and (b) metamorphic chain

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Figure 9

Graph representation for the subphases of the metamorphic chain

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Figure 10

Digraph representation of the phase change of the metamorphic chain

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Figure 11

Metamorphic parallel mechanism with two identical chain-legs

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Figure 12

Closed-loop subchain of chain-leg C1 in a symmetrical configuration

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Figure 13

Disposition of constraints in the configuration of motion branch with one translation

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Figure 14

Kinematic structure of the metamorphic mechanism and equivalent model with bifacial constraint forces

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Figure 15

Motion branch with two translations

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Figure 16

Sketch of four subphases with translational motion

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Figure 17

Two orientation switch positions

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Figure 18

Physical device of the metamorphic mechanism

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