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abstract: Origami is an art transforming a flat sheet of paper into a sculpture. Among various types of origami, the focus is on a particular class called the `Rigid Origami' ("RO"). A Rigid Origami, unlike other forms, is not intended to be folded into fancy shapes. On the contrary, an RO has a simple and a geometrically well-defined crease pattern and does not have curved/smudged faces. The folds can be carried out by a continuous motion in which, at each step, each face of the origami is completely flat. As a result, these planar faces experience very minimal strain due to loading. This property allows it to be used to fold surfaces made of rigid materials. Tapping into the geometrical properties of RO will open a new field of research with great practical utility. Analyzing each new RO pattern will require generating numerous prototypes; this is practically impossible to do, as it consumes a lot of time and material. The advantages of Finite Element Analysis/numerical modeling become very clear in this scenario. A new design concept may be modeled to determine its real world behavior under various load environments and may, therefore, be refined prior to the creation of drawings, when changes are inexpensive. Since an RO undergoes a non-local deformation when subjected to a disturbance, the usage of conventional FEA will not produce accurate results. A non-local element model was developed which can be used in conjunction with the finite element package ABAQUS, via its user-defined element (UEL). This model was tested on two RO patterns, namely Miura-Ori and Ron Resch, by carrying out basic simulations. There are many other interesting origami patterns, exhibiting different meta-material properties, yet to be explored. This Finite Element Approach equips researchers with necessary tools to study those options in great detail. / Dissertation/Thesis / M.S. Mechanical Engineering 2014

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24576号 / 工博第5082号 / 新制||工||1973(附属図書館) / 京都大学大学院工学研究科建築学専攻 / (主査)教授 大崎 純, 教授 竹脇 出, 教授 聲高 裕治 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

La thèse conduit une analyse cinématique des mécanismes spatiaux allant de mécanismes sphériques aux mécanismes spatiaux sur-contraints basés sur la méthode matricielle D-H et l’applique pour explorer le comportement rigide de pliabilité et de mouvement des modèles d’origami. Dans ce processus, la pliabilité rigide du motif origami en torsion triangulaire est d’abord examinée sur la base de la cinématique du réseau de mécanismes 4 R sphériques et de nouveaux mécanismes 6 R sur-contraints dérivés par la technique du kirigami. Ensuite, la cinématique du mécanisme de Bricard 6 R plan-symétrique est analysée et ses variations de bifurcation sont discutées. Après cela, les résultats sont appliqués pour étudier le pliage symétrique de l’origami de la waterbomb à six plis à panneau épais, qui est modélisé sous laforme d’un réseau de mécanismes de Bricard 6 R plan-symétriques. Le comportement de mouvement de sa tessellation correspondante de feuille de zéro-épaisseur est démontré par unréseau de mécanismes 6 R sphériques. Enfin, le comportement de mouvement de la forme cylindrique fermée de l’origami de la waterbomb est analysé à travers une étude paramétrique, en le modélisant comme un réseau fermé de mécanismes 6 R sphériques. Ces études aident à approfondir la compréhension de la cinématique des mécanismes spatiaux et du mouvement rigide de l’origami, et à jeter les bases des applications techniques des mécanismes spatiaux et des motifs d’origami rigides. / This dissertation conducts kinematic analysis of spatial linkages ranging from spherical linkages to overconstrained linkages based on the D-H matrix method, and applies it to explore the rigid foldability and motion behaviour of origami patterns. In this process, the rigid foldability of triangle twist origami pattern is firstly examined based on the kinematics of spherical 4 R linkage network and new overconstrained 6 R linkages are derived by kirigami technique. Then the kinematics of the plane-symmetric Bricard 6 R linkage is analyzed and its bifurcation variations are discussed. After that, the results are applied to study the symmetric folding of six-crease thick-panel waterbomb origami, which is modelled as a network of planesymmetric Bricard 6 R linkages. The motion behaviour of its corresponding tessellation of zerothickness sheet is demonstrated by a network of spherical 6 R linkages. Finally, the motion behaviour of the closed cylindrical form of waterbomb origami is investigated through a parametric study, by means of modelling it as a closed network of spherical 6 R linkages. These studies help to deepen the understanding of spatial linkage kinematics and rigid origami motion, and lay the foundation for engineering applications of spatial linkages and rigid origami patterns.