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research-article

Rigid Foldability of Generalized Triangle Twist Origami Pattern and Its Derived 6R Linkages

[+] Author and Article Information
Huijuan Feng

School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China; Université Clermont Auvergne, CNRS, SIGMA Clermont, Institut Pascal, F-63000 Clermont-Ferrand, France; School of Mechanical Engineering, Tianjin University, No.135 Yaguan Road, Jinnan District, Tianjin 300350, P. R. China
huijuan@tju.edu.cn

Rui Peng

School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China; School of Mechanical Engineering, Tianjin University, No.135 Yaguan Road, Jinnan District, Tianjin 300350, P. R. China
pengrui@tju.edu.cn

Jiayao Ma

School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China; Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, PR China; School of Mechanical Engineering, Tianjin University, No.135 Yaguan Road, Jinnan District, Tianjin 300350, P. R. China
jiayao.ma@tju.edu.cn

Yan Chen

ASME Member, School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China; Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, PR China; School of Mechanical Engineering, Tianjin University, No.135 Yaguan Road, Jinnan District, Tianjin 300350, P. R. China
yan_chen@tju.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4040439 History: Received December 23, 2017; Revised May 16, 2018

Abstract

Rigid origami is a restrictive form of origami that permits continuous motion between folded and unfolded states along the pre-determined creases without stretching or bending of the facets. It has great potential in engineering applications, such as foldable structures that consist of rigid materials. The rigid foldability is an important characteristic of an origami pattern, which is determined by both the geometrical parameters and the mountain-valley crease (M-V) assignments. In this paper, we present a systematic method to analyze the rigid foldability and motion of the generalized triangle twist pattern using the kinematic equivalence between rigid origami and spherical linkages. All schemes of M-V assignment were derived based on the flat foldable conditions, among which rigidly foldable ones were identified. Moreover, a new type of overconstrained 6R linkage and a variation of doubly collapsible octahedral Bricard were developed by applying kirigami technique to the rigidly foldable pattern without changing its degree of freedom. The proposed method opens up a new way to generate spatial overconstrained linkage from the network of spherical linkages. It can be readily extended to other types of origami patterns.

Copyright (c) 2018 by ASME
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