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The ancient art of ‘origami’ has recently become the source of inspiration for engineers to create structures that can unfold from a compact state to a fully deployed one. For instance, researchers have currently adopted origami designs in various engineering disciplines, including aerospace engineering, robotics, biomedical engineering, and architecture. In particular, architects have been interested in designing origami-inspired rigid walled structures that can be deployed as disaster-relief shelters. This type of design has three main advantages: transportability, constructability, and rigidity. Although there has been increased interests in deployable structures, limited research has been conducted on evaluating their structural performance, specifically the mechanical performance of the hinges that allow for the rotation of the rigid panels. To address the limitation, this thesis proposes a novel design of hinge connections for rigid origami structures. The hinges utilize snap fit connections to allow for the structure to achieve and maintain a locked state once unfolded without the need for any additional connections. Prototypes of the hinge design were fabricated using a 3D printer and their flexural strength was experimentally and computationally studied. It was concluded that the design could resist typical flexural loads for residential structures, and future research should be performed to minimize deflection.

This thesis study addresses the problem of overconstraint via introduction of conformal polyhedral linkages comprising revolute joints only and investigation of special geometric properties for the mobility of such overconstrained linkages. These linkages are of particular interest as deployable structures. First, planar case is issued and conditions for assembling irregular conformal polygonal linkages composed of regular and angulated scissor elements are derived. These planar assemblies are implemented into faces of polyhedral shapes and radially intersecting planes to obtain two different kind of polyhedral linkages. Rest of the thesis work relates to spatial linkages. Identical isosceles Bennett loops are assembled to obtain regular polygonal linkages and many such linkages are assembled to form polyhedral linkages. Then, Fulleroid-like linkages are presented. After these seemingly independent linkage types, Jitterbug-like linkages are introduced. Based on some observations on present linkages in the literature a definition for Jitterbug-like linkages is given first, and then a set of critical properties of these linkages are revealed. This special type of polyhedral linkages is further classified as being homothetic and non-homothetic, and geometric conditions to obtain mobile homothetic Jitterbug-like polyhedral linkages are investigated. Homohedral linkages, linkages with polyhedral supports with 3- and 4-valent vertices only, tangential polyhedral linkages are detailed as special cases and the degenerate case where all faces are coplanar is discussed. Two types of modifications on Jitterbug-like linkages are presented by addition of links on the faces and radial planes of Jitterbug-like linkages. Finally, a special class of Jitterbug-like linkages - modified Wren platforms are introduced as potential deployable structures.

Planar bar-and-joint mechanisms with one degree-of-freedom are widely used in deployable structures and machines. Such mechanisms are designed to undergo a specific motion, which can be described mathematically by plotting out the compatibility conditions, resulting in a curve called compatibility path. It has been observed that compatibility paths can develop singularities similar to that of equilibrium paths of elastic structures. This dissertation studies singularities occurring in compatibility paths with the aid of knowledge in the theory of structural stability. An analogy is set up between the equilibrium path of elastic structures and the compatibility path of mechanisms with a single degree-of-freedom incorporating the different types of bifurcation, effects of imperfections and detection of singularities. It is shown that the fundamentally distinct critical points such as limit points and bifurcation points can also appear in compatibility path. Methods used to singularities for compatibility conditions of mechanisms and equilibrium of structures are unified so that they can be used for both cases. A formulation of potential energy for mechanisms is also proposed in analogy with the potential energy function used in structural analysis. Further analysis of the mechanisms is carried out to demonstrate that singularities of compatibility paths can also be dealt with by the elementary catastrophe theory similar to the stability theory. A relationship is established between the mathematical formulation of different compatibility bifurcations and the canonical forms of catastrophe types. Examples of mechanisms demonstrating the existence of cuspoids of the compatibility conditions are given. An overall classification of the compatibility paths is also proposed.

This dissertation concerns the structural design of medical stent grafts. A new type of an innovative stent graft has been developed. Unlike the conventional stent grafts which consist of a wire mesh and a covering membrane, the proposed stent graft can be made from a single folded sheet of material. Firstly, a detailed symmetric design of a foldable cylindrical tube for the new stent graft has been presented. Folding is achieved by dividing the structure into a series of identical elements with hill and valley folds as in origami (Japanese art of paper folding). The folding patterns allow the stent graft to be folded and expanded both radially and longitudinally. The relationships among the design of the elements, the number of elements in the circumferential and longitudinal directions and the folded dimensions of the stent graft have been derived. It has been found that compact folding in the radial direction can be achieved by increasing the number of circumferential elements. A geometric mismatch during deployment has also been identified. The elements have to deform when the structure is expanded. Optimum designs which minimise the deformation have been found. Secondly, a new stent graft with helical folds has also been designed to improve radial strength and ease the deployment process. Helical folds are introduced by adjusting the joining position of the two edges of a sheet that had been symmetrically jointed in the symmetric design. The relationships among the number of elements in one complete circumference of a helix, the helical angle and the radius of the helical type stent graft have been established. The locations for the helical folds are optimised for easy folding by considering both geometric aspects of folding and the buckling patterns of a thin-walled tube under torsion, which are found analytically. Thirdly, using numerical analysis of the finite element method (FEM) the strain level and overall deformation of the stent graft during deployment has been calculated. Finally, the stent graft has been manufactured to verify the concept. A number of prototypes of the stent graft, which are the same size as standard oesophageal and aortal stent grafts, have been produced successfully using the same materials as current stent grafts of stainless steel and shape memory alloy (SMA) sheets. The patterns of folds on the materials are produced by photochemical etching. It has also been demonstrated that the SMA stent grafts self-expand smoothly and gradually by a near body temperature.

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 work presents the design and construction of a self-deployable, self-stiffening,and retractable (SDSR) space array from carbon fiber reinforced polymers (CFRP’s) and a working prototype is demonstrated. The effort required developing principles for the design of high-strain composite flexural joints and their integration into angled composite panels. Designing LET arrays in angled panels is explored. Analysis of simple composite LET joints is presented for two degrees of freedom. Validation of the composite LET modeling is sought through numerical methods and empirical testing. Testing of several composite LET joint specimens is conducted and the results are reported. Results indicate that (while not as compact as their isotropic material counterparts) composite laminates can successfully use LET joints as surrogate folds.

Deployable structures serve a large number of space missions. They are vital since spacecraft are launched by placing them inside launch vehicle payload fairings of limited volume. Traditional spacecraft design often involves large components. These components could have power, communication, or optics applications and include booms, masts, antennas, and solar arrays. Different stowing methods are used in order to reduce the overall size of a spacecraft. Some examples of stowing methods include simple articulating, more complex origami inspired folding, telescoping, and rolling or wrapping. Wrapping of a flexible component could reduce the weight by eliminating joints and other components needed to enable some of the other mechanisms. It also is one of the most effective methods at reducing the compaction volume of the stowed deployable. In this study, a generic unfurlable structure is optimized for maximum natural frequency at its fully deployed configuration and minimal strain energy in its stowed configuration. The optimized stowed structure is then deployed in simulation. The structure consists of a rectangular panel that tightly wraps around a central cylindrical hub for release in space. It is desired to minimize elastic energy in the fully wrapped panel and hinge to ensure minimum reaction load into the spacecraft as it deploys in space, since that elastic energy stored at the stowed position transforms into kinetic energy when the panel is released and induces a moment in the connected spacecraft. It is also desired to maximize the fundamental frequency of the released panel as a surrogate for the panel having sufficient stiffness. Deployment dynamic analysis of the finite element model was run to ensure satisfactory optimization formulation and results. / Master of Science / Spacecraft, or artificial satellites, do not fly from earth to space on their own. They are launched into their orbits by placing them inside launch vehicles, also known as carrier rockets. Some parts or components of spacecraft are large and cannot fit in their designated space inside launch vehicles without being stowed into smaller volumes first. Examples of large components on spacecraft include solar arrays, which provide power to the spacecraft, and antennas, which are used on satellite for communication purposes. Many methods have been developed to stow such large components. Many of these methods involve folding about joints or hinges, whether it is done in a simple manner or by more complex designs. Moreover, components that are flexible enough could be rolled or wrapped before they are placed in launch vehicles. This method reduces the mass which the launch vehicle needs to carry, since added mass of joints is eliminated. Low mass is always desirable in space applications. Furthermore, wrapping is very effective at minimizing the volume of a component. These structures store energy inside them as they are wrapped due to the stiffness of their materials. This behavior is identical to that observed in a deformed spring. When the structures are released in space, that energy is released, and thus, they deploy and try to return to their original form. This is due to inertia, where the stored strain energy turns into kinetic energy as the structure deploys. The physical analysis of these structures, which enables their design, is complex and requires computational solutions and numerical modeling. The best design for a given problem can be found through numerical optimization. Numerical optimization uses mathematical approximations and computer programming to give the values of design parameters that would result in the best design based on specified criterion and goals. In this thesis, numerical optimization was conducted for a simple unfurlable structure. The structure consists of a thin rectangular panel that wraps tightly around a central cylinder. The cylinder and panel are connected with a hinge that is a rotational spring with some stiffness. The optimization was solved to obtain the best values for the stiffness of the hinge, the thickness of the panel, which is allowed to vary along its length, and the stiffness or elasticity of the panel's material. The goals or objective of the optimization was to ensure that the deployed panel meets stiffness requirement specified for similar space components. Those requirements are set to make certain that the spacecraft can be controlled from earth even with its large component deployed. Additionally, the second goal of the optimization was to guarantee that the unfurling panel does not have very high energy stored while it's wrapped, so that it would not cause large motion the connected spacecraft in the zero gravity environments of space. A computer simulation was run with the resulting hinge stiffness and panel elasticity and thickness values with the cylinder and four panels connected to a structure representing a spacecraft. The simulation results and deployment animation were assessed to confirm that desired results were achieved.

QC 20100901

This thesis analyses the existing types of polyhedral linkages and presents new linkage types for resizing polyhedral shapes. First, the transformation characteristics, most specifically, magnification performances of existing polyhedral linkages are given. Then, methods for synthesizing single degree-of-freedom planar polygonal linkages are described. The polygonal linkages synthesized are used as faces of polyhedral linkages. Next, the derivation of some of the existing linkages using the method given is presented. Finally, some designs of cover panels for the linkages are given. The Cardan Motion is the key point in both analyses of existing linkages and synthesis of new linkages.