An Overview of Mechanisms and Patterns with Origami

Origami (paperfolding) has greatly progressed since its first usage for design of cult objects in Japan, and entertainment in Europe and the USA. It has now entered into artistic areas using many other materials than paper, and has been used as an inspiration for scientific and engineering realizations. This article is intended to illustrate several aspects of origami that are relevant to engineering structures, namely: geometry, pattern generation, strength of material, and mechanisms. It does not provide an exhaustive list of applications nor an in-depth chronology of development of origami patterns, but exemplifies the relationships of origami to other disciplines, with selected examples.

[1]  S D Guest,et al.  Deployable membranes designed from folding tree leaves , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[2]  G. Hunt,et al.  Twist buckling and the foldable cylinder: an exercise in origami , 2005 .

[3]  J. Guven,et al.  How paper folds: bending with local constraints , 2007, 0712.0978.

[4]  An interface element to model the mechanical response of crease lines for carton-based packaging , 2009 .

[5]  R. Lang.  Origami Design Secrets: Mathematical Methods for an Ancient Art , 2003 .

[6]  Philip R. Van Loocke.  Combination of basic origami with fractal iteration , 2010, Comput. Graph..

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

[8]  F. Escrig.  General survey of deployability in architecture , 1996 .

[9]  Thomas C. Hull.  A Note on “Impossible” Paper Folding , 1996 .

[10]  I. Ario,et al.  Non-linear dynamic behaviour of multi-folding microstructure systems based on origami skill , 2010 .

[11]  Julian F. V. Vincent,et al.  The geometry of unfolding tree leaves , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

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

[13]  Naohiko Watanabe,et al.  The Method for Judging Rigid Foldability , 2009 .

[14]  Shanmugam Saravanan,et al.  Valley-fold and mountain-fold in the micro-origami technique , 2003, Microelectron. J..

[15]  Erik D. Demaine,et al.  Curved Crease Origami , 2008 .

[16]  Tomoko Fuse,et al.  Unit Origami: Multidimensional Transformations , 1990 .

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

[18]  Erik D. Demaine,et al.  Geometric folding algorithms - linkages, origami, polyhedra , 2007 .

[19]  Tomohiro Tachi,et al.  Simulation of Rigid Origami , 2006 .

[20]  Sergio Pellegrino,et al.  Foldable bar structures , 1997 .

[21]  René Motro,et al.  FOLDABLE / UNFOLDABLE CURVED TENSEGRITY SYSTEMS BY FINITE MECHANISM ACTIVATION , 2007 .

[22]  R. Motro,et al.  A self-stress maintening folding tensegrity system by finte mechanism activation , 2005 .

[23]  S. Venkataramani.  Lower bounds for the energy in a crumpled elastic sheet - A minimal ridge , 2002 .

[24]  Gordon R. Pennock,et al.  Theory of Machines and Mechanisms , 1965 .

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

[26]  T. Buchner.  Kinematics of 3 D Folding Structures for Nanostructured , 2003 .

[27]  Ichiro Hagiwara,et al.  Optimisation of crush characteristics of the cylindrical origami structure , 2007 .

[28]  Jean-Claude Carrega.  Théorie des corps : la règle et le compas , 1981 .

[29]  Kengo Ikema,et al.  Deformation Analysis of a Joint Structure Designed for Space Suit with the Aid of an Origami Technology , 2010 .

[30]  Jean-Charles Trebbi.  L'art du pli : design et décoration , 2008 .

[31]  Georg Glaeser,et al.  Developable surfaces in contemporary architecture , 2007 .

[32]  Thomas C. Hull,et al.  Modelling the folding of paper into three dimensions using affine transformations , 2002 .

[33]  Paulo J. S. Cruz,et al.  Innovative Timber Constructions , 2009 .

[34]  Paolo Marcellini,et al.  Origami and Partial Differential Equations , 2012 .

[35]  J. P. Duncan,et al.  Folded developables , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[36]  David Dureisseix,et al.  Conception d'une Enveloppe Plissée Pliable-Dépliable , 2011 .

[37]  J. O'Rourke,et al.  Geometric Folding Algorithms: Linkages , 2007 .

[38]  Marshall W. Bern,et al.  The complexity of flat origami , 1996, SODA '96.

[39]  Keith A. Seffen,et al.  Morphing of curved corrugated shells , 2009 .

[40]  Eric Gjerde,et al.  Origami Tessellations: Awe-Inspiring Geometric Designs , 2008 .

[41]  Kunihiko Kasahara,et al.  Origami for the Connoisseur , 1987 .

[42]  J. Hutchinson,et al.  On the determinacy of repetitive structures , 2003 .

[43]  Martin Kilian,et al.  Curved folding , 2008, ACM Trans. Graph..

[44]  R. Motro,et al.  Tensegrity Systems , 2003 .

[45]  Hiroshi Maehara,et al.  Reversing a polyhedral surface by origami-deformation , 2010, Eur. J. Comb..

[46]  D. Gracias,et al.  Microassembly based on hands free origami with bidirectional curvature. , 2009, Applied physics letters.

[47]  Mel Byars,et al.  Design in Steel , 2003 .

[48]  Zhong You,et al.  Motion structures extend their reach , 2007 .