Origami has been extensively studied by engineers for its unique motions and ability to collapse to small volumes. Techniques have been studied for replicating origami-like folding motion in thick materials, but limited practical applications of these techniques have been demonstrated. Developable mechanisms are a new mechanism type that has a similar ability to collapse to a low profile. The cylindrical developable mechanism has the ability to emerge from and conform to a cylindrical surface. In this work, a few practical applications of devices with novel expanding motions are presented. The design and testing of an origami-inspired deployable ballistic barrier, which was designed by combining and modifying existing thickness accommodation techniques, is discussed. The properties of cylindrical developable mechanisms are examined and two devices designed for use with minimally invasive surgical tooling are presented. Various hinge options for small-scale cylindrical developable mechanisms are then reviewed and discussed. A planar modeling assumption for curved lamina emergent torsional joints in thin-walled cylinders is then analytically and empirically validated. Conclusions are drawn and recommendations for future work are given.

For origami-based designs to be functional, they need to be stable. Typically, stability is achieved through the introduction of exterior supports or members. This work focuses on incorporating stability into deployable origami-based engineering applications, including the development of deployable stiffeners or hard stops and generating concepts for stable origami-based systems in specific applications. Two types of deployable stiffeners are developed. Models for transcrease hard stops are presented, which can be directly implemented into origami-patterns to block motion at a specified angle. Thickness Utilizing Deployable Hard Stops (ThUDS), adapted from the transcrease hard stop models, can be implemented into thick materials for use in origami-based design. The application of self-deploying, self-locking ThUDS in an origami-based CubeSat reflectarray is shown, designed using optimization principles. Last, various multistable furniture concepts are presented, with stability incorporated into the concept design. These concepts focus on using composite wood as the base material, due to wood's abundance and commonality in furniture design.

Origami can be a powerful source of design inspiration in the creation of reconfigurable systems with unparalleled performance. This thesis provides fundamental tools for designers to employ as origami-based designs are pursued in their respective fields of expertise. The first chapter introduces origami and makes connections between origami and engineering design through a survey of engineered applications and characterizing the relationship between origami and compliant mechanisms. The second chapter evaluates the creasing of non-paper sheet materials, such as plastics and metals, to facilitate origami-based compliant mechanism design. Although it is anticipated that most origami-based design will result from surrogate folds (indirect methods of replacing the crease), it is valuable to provide information that may help in more direct approaches for origami-based design in materials other than paper. Planar sheets of homogeneous material are considered as they maintain the principles fundamental to origami (flat initial state, low cost, readily available). The reduced stiffness along the axis of the crease is an enabling characteristic of origami. Hence a metric based on the deformation of the crease compared to the deformation of the panels enables engineering materials to be evaluated based on their ability to achieve the "hinge-like" behavior observed in folded paper. Advantages of both high and low values of this metric are given. Testing results (hinge indexes, residual angles, localized hinge behavior and cyclic creasing to failure) are presented for various metals and polymers. This methodology and subsequent findings are provided to enable origami-based design of compliant mechanisms. The third chapter proposes a basic terminology for origami-based design and presents areas of considerations for cases where the final engineering design is directly related to a crease pattern. This framework for navigating from paper art to engineered products begins once the crease pattern has been selected for a given application. The four areas of consideration are discussed: 1) rigid foldability 2) crease characterization 3) material properties and dimensions and 4) manufacturing. Two examples are concurrently presented to illustrate these considerations: a backpack shell and a shroud for an adjustable C-Arm x-ray device used in hospitals. The final chapter provides concluding remarks on origami-based design.

published_or_final_version / abstract / Education / Master / Master of Education

<div>Thin walled tubular structures are widely used in the automotive industry because of its weight to energy absorption advantage. A lot of research has been done in different cross sectional shapes and different tapered designs, with design for manufacturability in mind, to achieve high specific energy absorption. </div><div><br></div><div>In this study a novel type of tubular structure is proposed, in which predesigned origami initiators are introduced into conventional square tubes. The crease pattern is designed to achieve extensional collapse mode which results in decreasing the initial buckling forces and at the same time acts as a fold initiator, helping to achieve a extensional collapse mode. The influence of various design parameters of the origami pattern on the mechanical properties (crushing force and deceleration) are extensively investigated using finite element modelling. Thus, showing a predictable and stable collapse behavior. This pattern can be stamped out of a thin sheet of material. </div><div><br></div><div>The results showed that a properly designed origami pattern can consistently trigger a extensional collapse mode which can significantly lower the peak values of crushing forces and deceleration without compromising on the mean values. Also, a comparison has been made with the behavior of proposed origami pattern for extensional mode verses origami pattern with diamond fold.</div>

Orientador: Rita de Cássia Pavani Lamas / Banca: Vanderlei Minori Horita / Banca: Edna Maura Zuffi / O PROFMAT - Programa de Mestrado Profissional em Matemática em Rede Nacional é coordenado pela Sociedade Brasileira de Matemática e realizado por uma rede de Instituições de Ensino Superior. / Resumo: De acordo com as atuais diretrizes pertinentes ao ensino de matemática (Parâmetros Curriculares Nacionais : Matemática e Proposta Curricular do Estado de São Paulo: Matemática), este trabalho baseia-se na Teoria de Van Hiele, visando a aprendizagem de conceitos geométricos, em particular a aprendizagem de poliedros regulares, através da confecção de dobraduras (origami). Iniciando com uma abordagem histórica sobre poliedro, apresenta orientações para o uso de origami em sala de aula, delineia as principais características da Teoria de Van Hiele, além de retomar os principais conceitos matemáticos associados aos poliedros. Utilizando este arcabouço é proposta uma sequência de atividades de sondagem e aplicação de conceitos geométricos respeitando as fases de aprendizagem de Van Hiele, visando a conclusão por parte do aluno, da existência de apenas cinco poliedros regulares. Após a execução das atividades propostas, as demonstrações dos teoremas relacionados aos poliedros apresentados neste trabalho servirão para a sistematização das conclusões feitas pelos alunos, sempre respeitando o nível de Van Hiele em que se encontrem. Apresenta, ainda, atividades de exploração das características dos poliedros através do Teorema de Euler para poliedros convexos / Abstract: According to the current guidelines relevant to teaching mathematics (National Curriculum: Mathematics, and Curricular Proposal of the State of São Paulo: Mathematics) this work is based on Van Hiele, and aimed at learning of geometric concepts, particularly learning regular polyhedra, by paperfolding (origami). Starting with a historical approach of polyhedron, this work presents guidelines for the use of origami in the classroom, outlines the main features of the Van Hiele theory, and resume the main mathematical concepts associated with polyhedra. Using this framework, a sequence of activities is proposed and the applying of geometric concepts respecting the learning phases of Van Hiele, which aims deduction by the student, of the existence of only five regular polyhedra. After execution of the proposed activities, the proof of theorems related to polyhedra presented in this paper will serve to systematize the conclusions made by the students, always respecting the level of Van Hiele who are. It presents further exploration of the characteristics of polyhedra by Euler's theorem for convex polyhedra / Mestre

An important goal of nanoscience is the self-assembly of nanoscale building blocks into complex nanostructures. DNA is an important and versatile building block for nanostructures because of its small size, predictable base pairing, and numerous sequence possibilities. I use DNA origami to design and fold DNA into predesigned shapes, to assemble thin, branched DNA nanostructures as templates for nanoscale metal features. Using a PCR-based scaffold strand generation procedure, several wire-like nanostructures with varying scaffold lengths were assembled. In addition, more complex prototype circuit element structures were designed and assembled, demonstrating the utility of this technique in creating complex templates. My fabrication method for DNA-templated nanodevices involves a combination of techniques, including: solution assembly of the DNA templates, surface orientation and placement, and selective nanoparticle attachment to form nanowires with designed gaps for the integration of semiconducting elements to incorporate transistor functionality. To demonstrate selective surface placement of DNA templates, DNA origami structures have been attached between gold nanospheres assembled into surface arrays. The DNA structures attached with high selectivity and density on the surfaces. In a similar base-pairing technique, 5 nm gold nanoparticles were aligned and attached to specific locations along DNA templates and then plated to form continuous metallic wires. The nanoparticles packed closely, through the use of a high density of short nucleotide attachment sequences (8 nucleotides), enabling a median gap size of 4.1 nm between neighboring nanoparticles. Several conditions, including hybridization time, magnesium ion concentration, ratio of nanoparticles to DNA origami, and age of the nanoparticle solution were explored to optimize the nanoparticle attachment process to enable thinner wires. These small, branched nanowires, along with the future addition of semiconducting elements, such as carbon nanotubes, could enable the formation of high-density self-assembled nanoscale electronic circuits.

The technique of DNA origami utilizes the specific and limited bonding properties of DNA to fold single stranded DNA sequences of various lengths to form a predesigned structure. One longer sequence is used as a scaffold and numerous shorter sequences called staples, which are all complementary to the scaffold sequence, are used to fold the scaffold into intricate shapes. The most commonly used scaffold is derived by extracting the genome of the M13 phage and the staples are usually chemically synthesized oligonucleotides. Longer single stranded sequences are difficult to synthesize with high specificity, which limits the choices of scaffold sequences available. In this project two main methods of single stranded amplification, Rolling Circle Amplification (RCA) and the usage of helper phages, were explored with the goal to produce both a 378 nt scaffold and staple sequences needed for folding a DNA origami structure. To facilitate imaging by Transmission Electron Microscopy (TEM) of this small structure, the DNA origami structure was created to form a polymer structure. Production of the scaffold sequence in high yield was unsuccessful and no well-defined polymers were found in the folded samples, though a few results showed promise for further studies and optimizations. Due to time constraints of this project, only production of the scaffold sequence was tested. Unfortunately the scaffold produced by the helper phages was of the complementary strand to that used to design the DNA origami structure, and could therefore not be used for folding. The correct strand was produced by the RCA where the yield was too low when using Phi29 DNA polymerase for proper folding to take place, though small scale RCA by Bst DNA polymerase on the other hand showed promising results. These results indicate that the scaffold production may not be far off but still more experience in producing intermediate size oligonucleotides may be necessary before succeeding in high yield production of this 378 nt long sequence. The promise given by this production is to enable high yield, high purity, low cost and also an easily scalable process set-up. This would be an important step in future DNA nanotechnology research when moving from small scale laboratory research to large scale applications such as targeted drug delivery systems.

An outstanding challenge in modern medicine is the safe and efficient delivery of drugs. One approach to improve drug delivery yield and increase specificity towards diseased cells, is to employ a drug carrier to facilitate transport. Promising steps towards developing such a carrier have been taken by the nascent field of nanomedicine: nanometer-sized particles designed to evade premature excretion, non-specific absorption, and the body’s immune response, can reduce undesired drug loss, while also increasing specific drug uptake into diseased cells through targeting surface modifications. However, progress is limited by incomplete knowledge of the ‘ideal’ nanoparticle design as well as a lack of appropriate high resolution construction methods for its implementation. DNA origami, a modular, nanometer-precise assembly method that would enable the rapid testing of particle properties as well as massively parallel fabrication, could provide an avenue to address these needs. In this thesis, I employed the DNA origami method to investigate how nanoscale shape and ligand functionalization affect nanoparticle uptake into cultured endothelial cells. In the first part, I evaluated the uptake yield of a series of eight shapes that ranged from 7.5 nm to 400 nm in their individual dimensions. The best performing shape of that study, a 15 × 100 nm DNA origami nanocylinder, was internalized 18-fold better than a dsDNA control of the same molecular weight. In a follow up study, I decorated this nanocylinder with integrin-targeting cyclic RGD peptides. This surface functionalization increased cellular uptake another 13-fold. In addition, uptake yield and the ratio of internalized versus surface-bound particles depended on the number of ligands present on the nanoparticle surface. This work represents a significant first step towards attaining the ability to design and implement an 'ideal' nanoparticle drug carrier. In the future, the DNA origami method can be used as a platform technology to further expand our understanding of transport properties of drug carriers and achieve safer and more efficient drug delivery.

In this thesis, the folding process of the de novo designed polypeptide chignolin was elucidated through atomic-scale Molecular Dynamics (MD) computer simulations. In a series of long timescale and replica exchange MD simulations, chignolin’s folding and unfolding was observed numerous times and the native state was identified from the computed Gibbs free-energy landscape. The rate of the self-assembly process was predicted from the replica exchange data through a novel algorithm and the structural fluctuations of an enzyme, lysozyme, were analyzed. DNA’s structural flexibility was investigated through experimental structure determination methods in the liquid and gas phase. DNA nanostructures could be maintained in a flat geometry when attached to an electrostatically charged, atomically flat surface and imaged in solution with an Atomic Force Microscope. Free in solution under otherwise identical conditions, the origami exhibited substantial compaction, as revealed by small angle X-ray scattering. This condensation was even more extensive in the gas phase. Protein folding is highly reproducible. It can rapidly lead to a stable state, which undergoes moderate fluctuations, at least for small structures. DNA maintains extensive structural flexibility, even when folded into large DNA origami. One may reflect upon the functional roles of proteins and DNA as a consequence of their atomic-level structural flexibility. DNA, biology’s information carrier, is very flexible and malleable, adopting to ever new conformations. Proteins, nature’s machines, faithfully adopt highly reproducible shapes to perform life’s functions robotically.