This thesis addresses a number of challenges designers face when designing deployable origami-based arrays, specifically joint selection, design, and placement within an array. In deployable systems, the selection and arrangement of joint types is key to how the system functions. The kinematics and performance of an array is directly affected by joint performance. This work develops joint metrics which are then used to compare joint performances, constructing a tool designers can use when selecting joints for an origami array. While often a single type of joint is used throughout an array, this work shows how using multiple types of joints within the same array can offer benefits for motion deployment, and array stiffening. Origami arrays are often used for their unique solutions for stowing and deploying large planar shapes. Folds, enabled through joints, within these patterns allow the arrays to fold compactly. However, it can be difficult to fully deploy arrays, particularly array designs with a high number of joints. In addition, it is a challenge to stabilize a fully deployed array from undesired re-folding. This work introduces a strain-energy storing joint that is used to deploy and stiffen foldable origami arrays, the Lenticular Lock (LentLock). Geometry of the LentLock is introduced and the deploying and stiffening performance of the joint is shown. Folds within an origami array create the constraints that link motion between panels, and can be used to create kinematic benefits, such as creating mechanisms with a single degree-of-freedom. While many fold-constraints are required to define motion, this work shows that origami-based system contain many redundant constraints. The removal of redundant joints does not affect the motion of the array nor the observed mobility, but may decrease the likelihood of binding, simplify the overall system and decrease actuation force. This work introduces a visual and iterative approach designers can use to identify redundant constraints in origami patterns, and techniques that can be used to remove the identified redundant constraints. The presented techniques are demonstrated by removing redundant constraints from prototyped origami mechanisms. As a result of this work, designers will be better able to approach and design deployable origami-based mechanisms.

Ces travaux de recherche sont réalisés dans le cadre d’une thèse CIFRE en collaboration entre Schlumberger et le LURPA de l’ENS Cachan. Schlumberger est une entreprise de service pétrolier. Elle développe des outils de mesures fonctionnant sous des conditions sévères de température et pression élevées mais aussi des effets dynamiques tels que des accélérations produisant des chocs entre les différentes pièces.L’objectif de la thèse est de déployer de nouvelles règles de cotation, pour des assemblages hyperstatiques déformables, basées sur la méthode CLIC et les normes ISO. La déformation des pièces dépend considérablement des défauts géométriques. Nous avons donc couplé des modèles de chaînes de cotes 3D avec des modèles RdM de type poutre afin d’optimiser les tolérances. Ces modèles doivent permettre la prise en compte des jeux d’assemblage dans les liaisons, la rigidité des pièces et les différents types de contact entre les sous-ensembles des outils étudiés.Ces modèles multi-physiques ont permis de caractériser le comportement mécanique en fonction des écarts géométriques des pièces. Enfin, pour des études plus complexes, des modélisations et simulations éléments finis, sur Abaqus, ont été réalisés puis validées par une campagne expérimentale de comportement au choc. / This research is carried out within a CIFRE doctoral thesis in collaboration between Schlumberger and the LURPA of ENS Cachan. Schlumberger is an oil service company. It develops measurement tools operating under severe conditions of high temperature and pressure but also dynamic effects such as accelerations producing shocks between the different parts.The objective of the thesis is to deploy new dimensioning and tolerancing rules for deformable hyperstatic assemblies, based on the CLIC method and the ISO standards. The deformation of the parts greatly depends on the geometrical defects. We have coupled 3D dimension chains with beam models to optimize tolerances. These models must allow the taking into account of the assembly clearances between parts, their rigidity and the different types of contact between the subassemblies of the studied tools.These multi-physical models allowed to characterize the mechanical behavior as a function of the geometrical deviations of parts. Finally, for more complex studies, finite element models and simulations on Abaqus were carried out and then validated by an experimental campaign of impact behavior.

Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of deployable structure design. The power of polynomial continuation as a design tool lies in its ability to find all solutions of a system of polynomial equations (even positive dimensional solution sets). A linkage design problem posed in polynomial form can be made to yield every possible feasible outcome, many of which may never otherwise have been found. Methods of polynomial continuation based design are illustrated here by way of various examples. In particular, the types of deployable structures which form planar rings, or frames, in their deployed configurations are used as design cases. Polynomial continuation is shown to be a powerful component of an equation-based design process. A polyhedral homotopy method, particularly suited to solving problems in kinematics, was synthesised from several researchers' published continuation techniques, and augmented with modern, freely available mathematical computing algorithms. Special adaptations were made in the areas of level-k subface identification, lifting value balancing, and path-following. Techniques of forming closure/compatibility equations by direct use of symmetry, or by use of transfer matrices to enforce loop closure, were developed as appropriate for each example. The geometry of a plane symmetric (rectangular) 6R foldable frame was examined and classified in terms of Denavit-Hartenberg Parameters. Its design parameters were then grouped into feasible and non-feasible regions, before continuation was used as a design tool; generating the design parameters required to build a foldable frame which meets certain configurational specifications. Two further deployable ring/frame classes were then used as design cases: (a) rings which form (planar) regular polygons when deployed, and (b) rings which are doubly plane symmetric and planar when deployed. The governing equations used in the continuation design process are based on symmetry compatibility and transfer matrices respectively. Finally, the 6, 7 and 8-link versions of N-loops were subjected to a witness set analysis, illustrating the way in which continuation can reveal the nature of the mobility of an unknown linkage. Key features of the results are that polynomial continuation was able to provide complete sets of feasible options to a number of practical design problems, and also to reveal the nature of the mobility of a real overconstrained linkage.

This thesis comprises a study on the kinematic and force analyses of the overconstrained mechanisms. The scope of the overconstrained mechanisms is too wide and difficult to handle. Therefore, the study is restricted to the planar overconstrained mechanisms. Although the study involves only the planar overconstrained mechanisms, the investigated methods and approaches could be extended to the spatial overconstrained mechanisms as well. In this thesis, kinematic analysis is performed in order to investigate how an overconstrained mechanism can be constructed. Four methods are used. These are the analytical method, the method of cognates, the method of combining identical modules and the method of extending an overconstrained mechanism with extra links. This thesis also involves the force analysis of the overconstrained mechanisms. A method is introduced in order to eliminate the force indeterminacy encountered in the overconstrained mechanisms. The results are design based and directly associated with the assembly phase of the mechanism.

In this dissertation, we explore the possibilities of systematically constructing large structural mechanisms using existing spatial overconstrained linkages with only revolute joints as basic elements. The first part of the dissertation is devoted to structural mechanisms (networks) based on the Bennett linkage, a well-known spatial 4R linkage. This special linkage has been used as the basic element. A particular layout of the structures has been identified allowing unlimited extension of the network by repeating elements. As a result, a family of structural mechanisms has been found which form single-layer structural mechanisms. In general, these structures deploy into profiles of cylindrical surface. Meanwhile, two special cases of the single-layer structures have been extended to form multi-layer structures. In addition, according to the mathematical derivation, the problem of connecting two similar Bennett linkages into a mobile structure, which other researchers were unable to solve, has also been solved. A study into the existence of alternative forms of the Bennett linkage has also been done. The condition for the alternative forms to achieve the compact folding and maximum expansion has been derived. This work has resulted in the creation of the most effective deployable element based on the Bennett linkage. A simple method to build the Bennett linkage in its alternative form has been introduced and verified. The corresponding networks have been obtained following the similar layout of the original Bennett linkage. The second effort has been made to construct large overconstrained structural mechanisms using hybrid Bricard linkages as basic elements. The hybrid Bricard linkage is a special case of the Bricard linkage, which is overconstrained and with a single degree of mobility. Starting with the derivation of the compatibility condition and the study of its deployment behaviour, it has been found that for some particular twists, the hybrid Bricard linkage can be folded completely into a bundle and deployed to a flat triangular profile. Based on this linkage, a network of hybrid Bricard linkages has been produced. Furthermore, in-depth research into the deployment characteristics, including kinematic bifurcation and the alternative forms of the hybrid Bricard linkage, has also been conducted. The final part of the dissertation is a study into tiling techniques in order to develop a systematic approach for determining the layout of mobile assemblies. A general approach to constructing large structural mechanisms has been proposed, which can be divided into three steps: selection of suitable tilings, construction of overconstrained units and validation of compatibility. This approach has been successfully applied to the construction of the structural mechanisms based on Bennett linkages and hybrid Bricard linkages. Several possible configurations are discussed including those described previously. All of the novel structural mechanisms presented in this dissertation contain only revolute joints, have a single degree of mobility and are geometrically overconstrained. Research work reported in this dissertation could lead to substantial advancement in building large spatial deployable structures.

L'analyse des tolérances des mécanismes a pour but d'évaluer la qualité du produit lors de sa phase de conception. La technique consiste à déterminer si, dans une production de grandes séries, le taux de rebuts des mécanismes défaillants est acceptable. Deux conditions doivent être vérifiées: une condition d'assemblage et une condition fonctionnelle. La méthode existante se base sur le couplage de la simulation de Monte Carlo avec un algorithme d'optimisation qui est très couteuse en temps de calcul. L'objectif des travaux de thèse est de développer des méthodes plus efficaces basées sur des approches probabilistes. Dans un premier temps, il est proposé une linéarisation des équations non linéaires du modèle de comportement afin de simplifier l'étape faisant appel à l'algorithme d'optimisation. Une étude de l'impact de cette opération sur la qualité de la probabilité est menée. Afin de minimiser l'erreur d'approximation, deux procédures itératives pour traiter le problème d'assemblage sont proposées. Ils permettent de calculer la probabilité de défaillance d'assemblage de façon précise en un temps de calcul réduit. En outre, les travaux de thèse ont permis le développement d'une nouvelle méthode de résolution basée sur la méthode de fiabilité système FORM (First Order Reliability Method) système. Cette méthode permet de traiter uniquement le problème fonctionnel. Elle a nécessité la mise au point d'une nouvelle formulation du problème d'analyse des tolérances sous forme système. La formulation décompose le mécanisme hyperstatique en plusieurs configurations isostatiques, le but étant de considérer les configurations dominantes menant à une situation de défaillance. La méthode proposée permet un gain de temps considérable en permettant d'obtenir un résultat en quelques minutes, y compris pour atteindre des faibles probabilités. / Tolerance analysis of mechanism aims at evaluating product quality during its design stage. Technique consists in computing a defect probability of mechanisms in large series production. An assembly condition and a functional condition are checked. Current method mixes a Monte Carlo simulation and an optimization algorithm which is too much time consuming. The objective of this thesis is to develop new efficient method based on probabilistic approach to deal with the tolerance analysis of overconstrained mechanism. First, a linearization procedure is proposed to simplify the optimization algorithm step. The impact of such a procedure on the probability accuracy is studied. To overcome this issue, iterative procedures are proposed to deal with the assembly problem. They enable to compute accurate defect probabilities in a reduced computing time. Besides, a new resolution method based on the system reliability method FORM (First Order Reliability Method) for systems was developed for the functional problem. In order to apply this method, a new system formulation of the tolerance analysis problem is elaborated. Formulation splits up the overconstrained mechanism into several isoconstrained configurations. The goal is to consider only the main configurations which lead to a failure situation. The proposed method greatly reduces the computing time allowing getting result within minutes. Low probabilities can also be reached and the order of magnitude does not influence the computing time.

Rapidly assembled tent structures are temporary enclosures used to house people or goods. Their uses vary to include recreation, refugee housing, and military shelters. The structural concepts applied in these shelters are as variable as their uses. Some make use of a tensioned fabric and pole system to provide structural strength. Others have a load-bearing frame with attached fabric skin. Further variants make use of inflatable arches or consist of modular containers. Analysis of a number of different types of rapidly assembled tent structures reveals an area where innovation can occur. Conflicts in the last ten years suggest that rapidly assembled shelters for both military purposes and humanitarian relief have the greatest need for innovative solutions. Existing shelters used by the military lack the versatility and speed of deployment necessary in modern conflict. The lack of scalability in the designs makes it difficult to use an existing tent in different situations. They are slow to construct, heavy, and difficult to transport in large numbers. These problems suggest that there is a need for new shelters that better meet the needs of the military. The application of deployable structures technology meets military's needs for structures with the advantages of a small compacted volume, rapid assembly, and ease of deployment. This makes them ideal for application to shelter structures. The aim of this dissertation was to develop a new type of deployable, long-span shelter frame based upon tiled Bennett mechanisms. An overlapping combination of equilateral Bennett mechanisms yields a structure that opens into a half-cylinder shape, providing an enclosed space useful and applicable to the problem of deployable shelters. The specific application considered in the design portion of this process will be a long-span deployable shelter capable of housing military helicopters. This report details the development of the Bennett Shelter concept. Its deployed and compacted geometries are explored, and a procedure for determining structural properties and dimensions is presented. The full concept for the structure, from outer covering to foundation support is then detailed. Loads affecting the structure are determined, and the process of modelling and analysing the structure is then considered. Optimisation of the structure with respect to weight and serviceability requirements is conducted using a number of different materials, and full analysis of the optimal geometries is completed. As no method exists for evaluating the effect of imperfections on the deployment of overconstrained mechanisms, a procedure is derived. The effects of manufacturing imperfections on deployment of the Bennett mechanism are then explored using the method. A full examination of the variation of energy within the Bennett Shelter during deployment provides valuable insight into the performance of the structure. With the above analysis complete, it is shown that the Bennett Shelter is viable as a long-span deployable shelter.

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.