The objective of this thesis is to develop and demonstrate techniques for self-deployment of origami-based mechanical systems achieved through internal strain-energy storage and release, with special application to medical implant devices. The potential of compliant mechanisms and related origami-based mechanical systems to store strain-energy make them ideal candidates forapplications requiring an actuation or deployment process, such as space system arrays and minimally invasive surgical devices. The objective of this thesis is achieved by first categorizing differentdeployment methods in origami-based, deployable mechanisms and then further exploring the use of strain energy to facilitate actuation in deployable mechanisms. With this understanding inplace, there are opportunities using strain energy to develop new approaches to deploy particular mechanical systems. These origami-based mechanisms have the ability to improve devices in themedical field. This work contributes to the knowledge base of self actuating deployable structures in origami-based mechanical systems by developing design concepts and models for strain energystorage and release. By developing the foundational characteristics for self-actuation, the work will be demonstrated thorough applications in medical implant devices.

This work develops models and tools to help designers address the challenges associated with designing origami-based and developable mechanisms. These models utilize strain energy, kinematics, compliant mechanisms, and graphical techniques to make the design of origami-based and developable mechanisms approachable and intuitive. Origami-based design tools are expanded through two methods. First presented is a generalized approach for identifying single-output mechanical advantage for a multiple-input compliant mechanism, such as many origami-based mechanisms. The model is used to predict the force-deflection behavior of an origami-based mechanism (Oriceps) and is verified with experimental data from magnetic actuation of the mechanism. Second is a folding technique for thick-origami, called the regional-sandwiching of compliant sheets (ReCS), which creates flat-foldable, rigid-foldable, and self-deploying thick origami-based mechanisms. The technique is used to create mountain/valley assignments for each fold about a vertex, constraining motion to a single branch of folding. Strain energy in deflected flexible members is used to enable self-deployment. Three physical models, a simple single-fold mechanism, a degree-four vertex mechanism, and a full tessellation, are presented to demonstrate the ReCS technique. Developable mechanism design is further enabled through an exploration of their feasible design space. Terminology is introduced to define the motion of developable mechanisms while interior and exterior to a developable surface. The limits of this motion are identified using defined conditions. It is shown that the more difficult of these conditions may be treated as a non-factor during the design of cylindrical developable mechanisms given certain assumptions. These limits are then applied to create a resource for designing bistable developable mechanisms (BDMs) that reach their second stable positions while exterior or interior to a cylindrical surface. A novel graphical method for identifying stable positions of linkages using a single dominant torsional spring, called the Principle of Reflection, is introduced and implemented. The results are compared with a numerical simulation of 30,000+ mechanisms to identify possible incongruencies. Two tables summarize the results as the guide for designing extramobile and intramobile BDMs. In fulfilling the research objectives, this dissertation contributes to the scientific community of origami-based and developable mechanism design approaches. As a result of this work, practitioners will be better able to approach and design complex origami-based and developable mechanisms.

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.

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.

This thesis addresses the design difficulties encountered when designing deployable origami-based arrays. Specific considerations regarding thickness accommodation, deployment, and parameter modifications are discussed. Patterns such as the Miura-ori, flasher, and hexagon are investigated, with emphasis placed on pattern modification from zero-thickness to finite-thickness. Applying origami principles to form engineering solutions is a complicated task. Competing requirements may create confusion around which pattern is most favorable for the space array application. Implementing origami into a finite-thickness, engineered system poses challenges that are not manifest in a zero-thickness model. As such, it is important to understand and address the limitations of the pattern before implementing it into an engineered system. A preliminary set of approaches to address and mitigate design difficulties is provided. This thesis seeks to improve understanding of design parameters, objectives, and trade offs of origami pattern configurations. Emphasis is placed on finite-thickness models suitable for engineering applications. As a result, engineers and designers should be better prepared to integrate origami principles into space system design.

Origami-based approaches for the folding of thick materials for specific application to large deployable space arrays is explored in this work. The folding approaches presented utilize strain energy, spatial kinematics, membranes, compliant mechanisms, and or in combination together to fold finite-thickness materials viewed through the lens of origami-based engineering. Novel architectures and behaviors of mechanisms are developed to achieve packaging efficiency, deployment, and self-stiffening. A method for the folding of monolithic thick-sheet materials is developed by incorporating compliant mechanisms into the material itself to strategically add degrees of freedom. The design and characterization of the compliant mechanisms with consideration to stress, material selection, and stiffness is given. Other folding approaches developed include a bistable vertex and a double-membrane method.The folding approaches derived are applied to larger tessellations and folding patterns. The fold patterns developed and used lend themselves well to large reconfiguration and the combination of the folding approaches with the patterns create opportunities to fabricate products out of thick, functional materials. Of specific interest is the application of these approaches and patterns to the field of deployable space arrays. Spatial kinematics, computational dynamics, physical tests, and systems engineering are used to develop an array architecture that is self-deployable, self-stiffening, and retractable. This architecture is shown to open the design space of large deployable arrays by increasing packaging efficiency and mass.The method, approaches, and architectures developed by this dissertation contribute to the fields origami-based engineering and deployable space arrays. While a focus of this work is the advancement of space technologies, the depth of the analyses provided are transferable to other origami-based and compliant-mechanism disciplines.