Rigidly foldable origami gadgets and tessellations

Rigidly foldable origami allows for motion where all deflection occurs at the crease lines and facilitates the application of origami in materials other than paper. In this paper, we use a recently discovered method for determining rigid foldability to identify existing flat-foldable rigidly foldable tessellations, which are also categorized. We introduce rigidly foldable origami gadgets which may be used to modify existing tessellations or to create new tessellations. Several modified and new rigidly foldable tessellations are presented.

[1]  Spencer P. Magleby,et al.  Accommodating Thickness in Origami-Based Deployable Arrays , 2013 .

[2]  Erik D. Demaine,et al.  (Non)Existence of Pleated Folds: How Paper Folds Between Creases , 2009, Graphs Comb..

[3]  Koryo Miura,et al.  Proposition of Pseudo-Cylindrical Concave Polyhedral Shells , 1969 .

[4]  Larry L. Howell,et al.  Waterbomb base: a symmetric single-vertex bistable origami mechanism , 2014 .

[5]  Zhong You,et al.  Modelling rigid origami with quaternions and dual quaternions , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[6]  Yan Chen,et al.  Folding a Patterned Cylinder by Rigid Origami , 2011 .

[7]  David A. Huffman,et al.  Curvature and Creases: A Primer on Paper , 1976, IEEE Transactions on Computers.

[8]  Galen T. Pickett,et al.  Self-folding origami membranes , 2007 .

[9]  Jian S. Dai,et al.  Classification of Origami-Enabled Foldable Linkages and Emerging Applications , 2013 .

[10]  Jian S. Dai,et al.  Origami-based robotic paper-and-board packaging for food industry , 2010 .

[11]  Devin J. Balkcom,et al.  Robotic origami folding , 2008, Int. J. Robotics Res..

[12]  Doreen Meier Origami Design Secrets Mathematical Methods For An Ancient Art , 2016 .

[13]  Milena Stavric,et al.  Quadrilateral Patterns for Rigid Folding Structures , 2014 .

[14]  Thomas C. Hull,et al.  Using origami design principles to fold reprogrammable mechanical metamaterials , 2014, Science.

[15]  Mark Schenk,et al.  Geometry of Miura-folded metamaterials , 2013, Proceedings of the National Academy of Sciences.

[16]  Arthur Lebée,et al.  Transverse shear stiffness of a chevron folded core used in sandwich construction , 2010 .

[17]  Tomohiro Tachi,et al.  Freeform Rigid-Foldable Structure using Bidirectionally Flat-Foldable Planar Quadrilateral Mesh , 2010, AAG.

[18]  Rui Peng,et al.  Origami of thick panels , 2015, Science.

[19]  B. Chen,et al.  Origami multistability: from single vertices to metasheets. , 2014, Physical review letters.

[20]  Devin J. Balkcom,et al.  Introducing robotic origami folding , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[21]  Levi H. Dudte,et al.  Geometric mechanics of periodic pleated origami. , 2012, Physical review letters.

[22]  Yoshimaru Yoshimura On the Mechanism of Buckling of a Circular Cylindrical Shell Under Axial Compression , 1955 .

[23]  K. Kuribayashi,et al.  Self-deployable origami stent grafts as a biomedical application of Ni-rich TiNi shape memory alloy foil , 2006 .

[24]  Tomohiro Tachi Generalization of rigid foldable quadrilateral mesh origami , 2009 .

[25]  Spencer P. Magleby,et al.  Origami-like creases in sheet materials for compliant mechanism design , 2013 .

[26]  Koryo Miura,et al.  Method of Packaging and Deployment of Large Membranes in Space , 1985 .

[27]  Thomas Hull Counting Mountain-Valley Assignments for Flat Folds , 2003, Ars Comb..

[28]  Larry L. Howell,et al.  Rigidly Foldable Origami Twists , 2015 .

[29]  Thomas C. Hull On the Mathematics of Flat Origamis , 1994 .