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Research Papers

A Network of Type III Bricard Linkages

[+] Author and Article Information
Shengnan Lu

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: lvshengnan5@gmail.com

Dimiter Zlatanov

PMAR Robotics,
University of Genoa,
Genoa 16145, Italy
e-mail: zlatanov@dimec.unige.it

Xilun Ding

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: xlding@buaa.edu.cn

Matteo Zoppi

PMAR Robotics,
University of Genoa,
Genoa 16145, Italy
e-mail: Zoppi@dimec.unige.it

Simon D. Guest

Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK
e-mail: sdg@eng.cam.ac.uk

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received April 21, 2018; final manuscript received September 26, 2018; published online December 10, 2018. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 11(1), 011013 (Dec 10, 2018) (9 pages) Paper No: JMR-18-1112; doi: 10.1115/1.4041641 History: Received April 21, 2018; Revised September 26, 2018

Among Bricard's overconstrained 6R linkages, the third type has two collapsed configurations, where all joint axes are coplanar. This paper presents a one-degree-of-freedom network of such linkages. Using the two coplanar states of the constituent Bricard units, the network is able to cover a large surface with a specific outline when deployed and can be folded compactly into a stack of much smaller planar shapes. Five geometric parameters describing each type III Bricard mechanism are introduced. Their influence on the outline of one collapsed configuration is discussed and inverse calculation to obtain the parameter values yielding a desired planar shape is performed. The network is built by linking the units, either using scissor linkage elements, if the thickness of the panels can be ignored, or with hinged parallelograms, for a thicker material. Two case studies, in which the Bricard network deploys as a rectangle and a regular hexagon, respectively, are presented, validating the analysis and design methods.

Copyright © 2019 by ASME
Topics: Linkages , Shapes
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References

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Figures

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Fig. 1

Construction of a Bricard linkage

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Fig. 2

Schematic of the type III Bricard linkage

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Fig. 3

Two collapsed configurations of the type III Bricard

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Fig. 4

Dimensions of the quadrangle

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Fig. 5

Construction of a crinkle mechanism

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Fig. 6

Movement process of a crinkle linkage

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Fig. 7

Limit positions of A and A′

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Fig. 8

Influence of R on the collapsed configurations

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Fig. 9

Influence of θ and r on the collapsed configurations: (a) influence of θ and (b) influence of r

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Fig. 10

Influence of lA and lA′ on the collapsed configurations

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Fig. 11

Simulation of inverse calculation

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Fig. 12

Two Bricard linkages linked by scissor linkage

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Fig. 13

The compact and deployed configuration of the network linked with scissor linkage

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Fig. 14

Working principle of the parallelogram mechanism

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Fig. 15

Assembly comprised of Bricard linkages and a parallelogram mechanism

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Fig. 16

Formed rectangle corresponding to variable θ

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Fig. 18

Bricard linkages in case study II

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