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Research Papers

Origami-Inspired Integrated Planar-Spherical Overconstrained Mechanisms

[+] Author and Article Information
Guowu Wei

Research Associate
Centre for Robotics Research,
School of Natural and Mathematical Sciences,
King's College London, University of London,
London WC2R 2LS, UK
e-mail: guowu.wei@kcl.ac.uk

Jian S. Dai

Professor
Fellow of ASME
International Centre for Mechanisms
and Robotics,
MoE Key Laboratory for Mechanism Theory
and Equipment Design,
Tianjin University, Tianjin 300072China;
Centre for Robotics Research,
School of Natural and Mathematical Sciences,
King's College London,
University of London,
London WC2R 2LS, UK
e-mail: jian.dai@kcl.ac.uk

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 2, 2013; final manuscript received October 6, 2013; published online March 19, 2014. Assoc. Editor: Mary Frecker.

J. Mech. Des 136(5), 051003 (Mar 19, 2014) (13 pages) Paper No: MD-13-1059; doi: 10.1115/1.4025821 History: Received February 02, 2013; Revised October 06, 2013

This paper presents two integrated planar-spherical overconstrained mechanisms that are inspired and evolved from origami cartons with a crash-lock base. Investigating the crash-lock base of the origami cartons, the first overconstrained mechanism is evolved by integrating a planar four-bar linkage with two spherical linkages in the diagonal corners. The mechanism has mobility one and the overconstraint was exerted by the two spherical linkages. This mechanism is then evolved into another integrated planar-spherical overconstrained mechanism with two double-spherical linkages at the diagonal corners. The evolved mechanism has mobility one. It is interesting to find that the double-spherical linkage at the corner of this new mechanism is an overconstrained 6R linkage. The geometry evolution is presented and the constraint matrices of the mechanisms are formulated using screw-loop equations verifying mobility of the mechanisms. The paper further reveals the assembly conditions and geometric constraint of the two overconstrained mechanisms. Further, with mechanism decomposition, geometry and kinematics of the mechanisms are investigated with closed-form equations, leading to comparison of these two mechanisms with numerical simulation. The paper further proposes that the evolved overconstrained mechanism can in reverse lead to new origami folds and crease patterns. The paper hence not only lays the groundwork for kinematic investigation of origami-inspired mechanisms but also sheds light on the investigation of integrated overconstrained mechanisms.

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Figures

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Fig. 1

Daily-life origami folds and their corresponding crease patterns

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Fig. 2

An origami-type carton with crash-lock base

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Fig. 3

An origami-inspired overconstrained mechanism

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Fig. 4

An integrated planar 4R-2 spherical loop mechanism

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Fig. 5

An evolved planar 4R-2 double-spherical loop mechanism

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Fig. 6

Structure and geometry of corner-loop AFGE

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Fig. 7

Structure and geometry of corner-loop CIJH

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Fig. 8

Structure and geometry of corner-loop AFPGQE

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Fig. 9

Structure and geometry of corner-loop CITJSH

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Fig. 10

Constraint graph of the planar 4R-2 spherical loop mechanism

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Fig. 11

Constraint graph of the planar 4R-2 double-spherical loop mechanism

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Fig. 12

Trajectories of points G and J and variety of their distance

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Fig. 13

Orientation vector of joint G of the planar 4R-2 spherical loop mechanism

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Fig. 14

Orientation vector of joint G of the planar 4R-2 double-spherical loop mechanism

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Fig. 15

Orientation vector of the joint J of the planar 4R-2 spherical loop mechanism

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Fig. 16

Orientation vector of joint J of the planar 4R-2 double-spherical loop mechanism

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Fig. 17

New origami folds based on the planar 4R-2 double-spherical loop mechanism

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Fig. 18

Crease patterns of the new origami folds

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