This thesis is an exploration in deployable architecture, focusing on long span structural design. The application for the design will be a summer theatre for the Halifax Commons. The deployment of the structure will be for a five month duration, therefore important design considerations will be durability, waterproofing, as well as assembly, disassembly and storage.

Fibre reinforced polymers (FRPs) are currently being used in new bridge construction as a feasible alternative material for corroded bridge deck replacements, footbridges, and emergency vehicle bridges. For both military and civilian applications, there exists a need for bridges that are lightweight and inexpensive, that can be readily transported and easily erected. The 10 m glass FRP deployable box beam presented in this thesis was developed to aid cross-country mobility in areas where infrastructure has been damaged by conflict or natural disasters. The box beam represents one trackway of a dual trackway system. The quasi-static and dynamic behaviour of the box beam was investigated under laboratory and field conditions. Quasi-static tests were conducted to ensure the strength of the steel hinge, the hinge connection to the base plate of the box beam, and the overall box beam would support the vehicle loads in field testing. Data from these tests were used to validate the finite element model. Field testing was conducted to investigate the natural frequencies of the box beam, calculate the dynamic increment of the structure, and confirm the validity of the finite element model created in Matlab. Three vehicles were used to evaluate the response of the box beam to different types of suspension, loads, and number of wheels per trackway. A finite element model was developed to predict the displacement of the bridge under various vehicle loads. The analysis resulted in displacement contours within a reasonable amount of error when compared to those measured in field testing. Recommendations for future research and development of the structure are provided based on this research. / Thesis (Master, Civil Engineering) -- Queen's University, 2008-09-26 22:49:59.077

This thesis presents a dynamic analysis and a control system for a flexible space manipulator, the Deployable Robotic Manipulator or DRM, which has a deployable/retractable link. The link extends (or retracts) from the containing slewing link of the manipulator to change the DRM's length and hence its workspace. This makes the system dynamics time varying and therefore any control strategy has to adapt to this fact. The aim of the control system developed is to slew the manipulator through a predetermined angle given a maximum angular acceleration, to reduce flexural vibrations of the manipulator and to have a certain degree of robustness, all of this while carrying a payload and while the length of the manipulator is changing. The control system consists of a slewing motor that rotates the manipulator using the open-loop assumed torque method and two reaction wheel actuators, one at the base and one at the tip of the manipulator, which are driven by a closed-loop damping control law. Two closed-loop control laws are developed, a linear control law and a Lyapunov based control law. The linear control law is based on collocated output feedback. The Lyapunov control law is developed for each of the actuators using Lyapunov stability theory to produce vibration control that can achieve the objectives stated above for different payloads, while the manipulator is rotating and deploying or retracting. The response of the system is investigated by computer simulation for two-dimensional vibrations of the deployable manipulator. Both the linear and Lyapunov based feedback control laws are found to eliminate vibrations for a range of payloads, and to increase the robustness of the slewing mechanism to deal with uncertain payload characteristics.

Les structures destinées aux applications aérospatiales se doivent d’être légères, rigides et compactes afin de pouvoir être stockées dans la coiffe d’un lanceur. Une solution permettant de déployer automatiquement une ossature rigide à l’aide d’énergie élastique stockée dans des liaisons souples est proposée. La solution retenue, constituant une structure annulaire polygonale, peut être utilisée dans différents types d’applications spatiales, que ce soit pour des voiles solaires, de désorbitation ou des antennes satellite. Elle a fait l’objet d’études géométriques afin d’en optimiser la compacité et la masse. La cinématique et la dynamique du déploiement ont aussi été étudiées et modélisées, à la fois analytiquement et numériquement. L’analyse de la rigidité de la structure en position gerbée (pliée dans la coiffe du lanceur) et en configuration opérationnelle est traitée et confrontée aux expérimentations vibratoires d’un prototype. L’adjonction d’un réseau tridimensionnel permettant de tendre une membrane réflectrice pour des applications de type « antenne »sera proposée, ainsi qu’un dispositif de verrouillage en phase opérationnelle. / The structures intended for the aerospace applications have to be lightweight, stiff and compact to be able to be stored in the fairing of a launcher. A solution is allowing to deploy automatically a stiff skeleton by means of elastic energy stored in flexible connections. The reserved solution, establishing an annular polygonal structure, can be used in various types of space applications, whether it is for solar, deorbiting or satellite antennas. It made the object of geometrical studies to optimize the compactness and the mass. The kinematics and the dynamics of the deployment were also studied and modelled, at the same time analytically and numerically. The analysis of the rigidity of the structure in folded position (folded in the fairing) and in operational configuration is handled and confronted with the vibratory experiments of a prototype. The addition of a three-dimensional network allowing to tighten a reflector membrane for applications of type "antenna" will be proposed, as well as a locking device in operational phase.

This work investigates how curved-crease origami and the developable surfaces which compose it can be transitioned to engineering design. Methods for creating flexible, tailorable-property surfaces that function as thick panels in place of paper are presented. Concepts from curved-crease origami and developable surfaces that can describe and extend engineering applications are discussed and demonstrated. These concepts are particularly beneficial to applications where curved surfaces are integral to the function, deployability is desired, and planar manufacturing could be beneficial.The first part of this work uses arrays of compliant elements to create flexible-tailorable property surfaces. The key feature to these arrays is the alignment of the most flexible bending axis of the individual elements to the ruling line arrangement of a developable surface. This alignment can enable bending of thick panels while maintaining lower stresses, a quality necessary for the transitioning of curved-crease origami into thick materials. The stiffness and stress of these arrays is modeled and physical prototypes are demonstrated. Additionally, shape factors are developed for these compliant arrays (CAs) to facilitate material selection for the panels and understand how the geometry of the array changes the effective properties of the panel. The second part of this work describes and demonstrates several concepts of curved-crease origami and developable surfaces that can benefit mechanism and structure design, particularly in the context of rolling-contact mechanisms. The design of a rolling-contact joint connected by flexible bands similar to a Jacob's Ladder toy is extended through incorporating curved creases into the design. The resulting design is deployable from a compact state to a functional state and can be manufactured from a single plane and folded into shape. Mathematical formulations are presented to describe the classes of developable surfaces in terms of properties which are frequently important in mechanism design. These natural equations for a single class of developable surface are conducive to modeling the folding motion of rigid-ruling developables, developables whose ruling lines do change location in a surface during folding. These formulations are used to generalize the design of rolling-contact joints to a family of joints capable of single degree of freedom spatial motions, being manufactured from a plane, and exhibiting a tailorable force response. Finally practical design suggestions for the implementation of rolling-contact joints is given. These include methodology to create sunken flexures which serve to increase the normal force between rolling bodies to prevent slip.

Origami has become a source of inspiration in a number of engineered systems. In most systems, non-paper materials where material thickness is non-negligible is required. In origami-inspired engineered systems where thickness is non-negligible, thickness-accommodation techniques must be utilized to overcome the issue of self-intersection. Many thickness-accommodation techniques have been developed for use in thick-origami-inspired-engineered systems. In this work several thickness-accommodation techniques are reviewed and discussed. New thickness-accommodation techniques including hybrid thickness-accommodation techniques and the split vertex technique are presented and discussed. These techniques enable new capabilities of thickness-accommodation in origami adapted design. Thickness-accommodation techniques have been developed in the context of developable origami patterns and the application of these techniques to non-developable patterns is introduced here. The capability of non-developable thick origami is demonstrated in an application example of a deployable locomotive nose-fairing.

Traveling to space requires a great deal of energy. This then limits the size of spacecraft accessible to transport to space. An optimization of a flexible tube that could be used as a satellite deployable structure was conducted by varying the cross section of the tube and its composite material properties. The material properties manipulated include the selection of a fiber, matrix, filler volume ratio, and orientation. HEEDS, a commercially available software, conducts the optimization process using the SHERPA algorithm. In the optimization, the finite element code, ABAQUS, iteratively performs two simulations. First, ABAQUS determines the stress distribution along the tube when wrapping the tube in its stored configuration. Second, ABAQUS finds the first natural frequency of the deployed structure. The objective function driving the optimization process is minimizing the weight and strain energy of the tube to create a light but highly flexible tube. This provides benefits of avoiding a violent deployment and lowering the dynamic response of the spacecraft during deployment. Three optimizations were performed with 1000 iterations each, using different initial geometries. While all three produce very similar results, one design converges to a clear best result. Using the best design, a series of deployment simulations are performed, using different boundary conditions to represent various scenarios. These boundary conditions include a free body dynamic response to deployment, a restricted response to only allow for rotation about the direction of deployment, and an increased damping deployment. Energy is dissipated differently comparing the results, showing that the most realistic case, being a free body deployment, has the lowest effect on the system. The spacecraft can dissipate energy by oscillating in the other axis. While damping does reduce the settling time for the deployed tube, there is notable oscillation in the middle of the tube seen in the transient state. / Master of Science / The size and weight of a spacecraft is important when considering its feasibility to launch to space. By creating a spacecraft that can be stowed in a small configuration and deploy, new parameters arise, thus new designs can be created. This paper observes using different shapes and materials to create an expandable tube, providing a support structure for a satellite or spacecraft. HEEDS, an optimization software, uses the SHERPA code to select the shape of the cross section and create a composite material. Composite material selection is comprised of a fiber, a matrix, a filler volume ratio, and an angle for the fibers to lay at. After selecting these parameters, HEEDS calls a finite element software, ABAQUS, to perform two simulations. The first simulation wraps the tube around a central hub and observes stress at each timestep. The second simulation finds the first mode of natural frequency of the deployed model. Using user defined constraints that revolve around the safety factor of the stress and minimum frequency, each iteration is marked as feasible or infeasible. An objective function is used to evaluate the best design. This paper focuses on minimizing the weight of the tube and the strain energy inside of the objective function. By minimizing the strain energy, the tube will deploy less violently and cause less rotation due to deployment. HEEDS performs 1000 iterations on three different initial geometry. While there are similar defining factors of each final design, there is one design that is better than the other two. Using the best design, ABAQUS runs three different deployment simulations to observe the deployment behavior. These scenarios encompass different dynamic simulations and show that a realistic deployment where the spacecraft is free to rotate on all axis is safe.

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.

Because origami has proved to be a tremendously rich source of inspiration in engineering, interest in solving some of the challenges that affect origami-inspired design has been significant. One such challenge involves ensuring that origami-inspired mechanisms are rigid-foldable or capable of moving without requiring links to bend or distort. Because rigid-foldability is essential in mechanisms that are constructed using rigid materials, access to methods of engineering this characteristic are highly desirable. This research addresses this need by developing methods for the design of origami-inspired mechanisms that are rigid-foldable. Methods for modifying crease patterns to achieve this are described and compared. Methods for achieving rigid-foldability using thick materials are also developed. Proofs of a process for generating new variations of existing thick-origami models are developed and demonstrated on multiple models. The possibility of using compliant panels to create rigid-foldability is also studied.Because of the relationship between mechanism stiffness and rigid-foldability, means of managing the pattern stiffness are also examined. The design of compliant, deployable stiffeners is studied to permit a comparison of different stiffener types. This comparison is used to identify dominant configurations that are most advantageous for a deployable mechanism. The use of thick-origami models are also considered. The geometry of two varieties of a cantilever tube are optimized to support a cantilever beam.

No description available.