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.

Origami-adapted mechanisms form the basis of an increasing number of engineered systems. As most of these systems require the use of non-paper materials, various methods for accommodating thickness have been developed. These methods have opened new avenues for origami-based design. This work introduces approaches for the design of two new classes of thick-origami systems and demonstrates the approaches in hardware. One type of system, called "conceal-and-reveal,'' is introduced, and a method of designing these mechanisms is developed. Techniques are also developed for designing folding printed circuit boards which are fabricated from a single sheet of material. This enables areas of regional flexibility, leaving other areas stiff. This allows components to be attached to stiff regions and folding to occur at flexible regions. An optimization method is presented to design the geometry of surrogate hinges to aid in monolithic origami-based mechanisms such as flexible PCBs. Examples are shown which demonstrate each of these new techniques.

Compliant mechanisms (CMs) take advantage of the deformation of their flexible members to transfer motion, force, or energy, offering attractive advantages in terms of manufacturing and performance over traditional rigid-body mechanisms (RBMs). This dissertation aims to advance the topology optimization (TO) technique (1) to design CMs that are more effective in performing their functions while being sufficiently strong to resist yield or fatigue failure; and (2) to design CMs from the perspective of mechanisms rather than that of structures, particularly with the insight into the concepts of joints, actuations, and functions of mechanisms. The existing TO frameworks generally result in CMs that are much like load-bearing structures, limiting the applications of CMs. These CMs (1) do not have joints, (2) are actuated by a translational force, and (3) can only do simple work such as amplifying motion or gripping. Three TO frameworks for the synthesis of CMs are proposed in this dissertation and they are summarized below. First, a framework was developed for the design of efficient and strong CMs. The widely used stiffness-flexibility criterion for CM design with TO results in lumped CMs that are intrinsically efficient in transferring motion, force, or energy but are prone to high localized stress and thus weak to resist yield or fatigue failure. Indeed, distributed CMs may have a better stress distribution than lumped CMs but have the weakness of being less efficient in motion, force, or energy transfer than lumped CMs. Based on this observation, the proposed framework rendered the concept of hybrid systems, hybrid CMs in this case. Further, the hybridization was achieved by a proposed super flexure hinge element and a design criterion called input stroke criterion in addition to the traditional stiffness-flexibility criterion. Both theoretical exploration and CM design examples are presented to show the effectiveness of the proposed approach. The proposed framework has two main contributions to the field of CMs: (1) a new design philosophy, i.e., hybrid CMs through TO techniques and (2) a new design criterion—input stroke. Second, a systematic framework was developed for the integrated design of CMs and actuators for the motion generation task. Both rotary actuators and bending actuators were considered. The approach can simultaneously synthesize the optimal structural topology and actuator placement for the desired position, orientation, and shape of the target link in the system while satisfying the constraints such as buckling constraint, yield stress constraint and valid connectivity constraint. A geometrically nonlinear finite element analysis was performed for CMs driven by a bending actuator and CMs driven by a rotary actuator. Novel parameterization schemes were developed to represent the placements of both types of actuators. A new valid connectivity scheme was also developed to check whether a design has valid connectivity among regions of interest based on the concept of directed graphs. Three design examples were constructed and a compliant finger was designed and fabricated. The results demonstrated that the proposed approach is able to simultaneously determine the structure of a CM and the optimal locations of actuators, either a bending actuator or a rotary actuator, to guide a flexible link into desired configurations. Third, the concept of a module view of mechanisms was proposed to represent RBMs and CMs in a general way, particularly using five basic modules: compliant link, rigid link, pin joint, compliant joint, and rigid joint; this concept was further developed for the unified synthesis of the two types of mechanisms, and the synthesis approach was thus coined as module optimization technique—a generalization of TO. Based on the hinge element in the finite element approach developed at TU Delft (Netherlands in early 1970), a beam-hinge model was proposed to describe the connection among modules, which result in a finite element model for both RBMs and CMs. Then, the concept of TO was borrowed to module optimization, particularly to determine the “stay” or “leave” of modules that mesh a design domain. The salient merits with the hinge element include (1) a natural way to describe various types of connections between two elements or modules and (2) a provision of the possibility to specify the rotational input and output motion as a design problem. Several examples were constructed to demonstrate that one may obtain a RBM, or a partially CM, or a fully CM for a given mechanical task using the module optimization approach.

The objective of this research is to present a new model for predicting the piezoresistive effect in microflexures experiencing bending stresses. A linear model describing piezoresistivity exists for members in pure tension and compression. Extensions of this model to more complex loading conditions do not match experimental results. An accurate model of piezoresistivity in complex loading conditions would expand the design possibilities of piezoresistive devices. A new model to predict piezoresistive effects in tension, compression, and more complex loading conditions is proposed. The focus of this research is to verify a unidirectional form of this proposed model for microflexures in tension and bending. Implementation of the unidirectional form of the model involves geometric design, stress analysis, and electrical analysis. One of the ways to implement the model is with finite-element analysis (FEA). The piezoresistive FEA for flexures (PFF) algorithm is an FEA implementation of the unidirectional form of the model for flexures. A case study is then given in which the resistance curves of two test devices are predicted with the PFF algorithm. Results from the PFF implementation of the unidirectional form of the model show a close comparison between analytical prediction and experimental results. This new model could contribute to optimized sensors, feedback control of microdevices, nanopositioning, and self-sensing microdevices.

Despite many advances in the design methods for compliant mechanisms, it is still not possible to know if a set of user-specifications has a solution. Furthermore, practical considerations such as failure limits and manufacturing limitations cannot be easily incorporated into existing methods. To address these issues, we have recently developed the concept of feasible stiffness and inertia maps. This thesis extends the concept of feasible maps and proposes another kind of maps that comprehensively depict the nonlinear kinetoelastostatic behaviour of compliant mechanisms. Feasible maps drawn as per user-specifications, with compliant mechanisms of the database overlaid on it, instantly inform the reader whether the specifications are feasible; whether the specifications are stringent; whether any mechanisms in the database meet the specifications, and whether any mechanism can be interactively modified to meet the specifications including size, strength and manufacturability. This thesis extends the earlier work on feasible maps by relaxing one condition that all beam segments in a compliant mechanism must retain their relative proportions. This is achieved by using size optimization. Thus, a certain degree of automation is brought into the procedure, which enhances the ease of use of the feasible maps. Illustrative examples are presented and implementation into a software is demonstrated. A major contribution of this work is the development of the concept of kinetoelastostatic maps of compliant mechanisms with fixed topology, shape, and relative proportions of beam segments in them. The map is drawn on a 2D plot using two non-dimensional quantities, one that captures the response of the mechanism and the other that combines the force, geometry, and material parameters. The map encloses a region that indicates the kinetoelastostatic capability of the mechanism. Another contribution of this work is the observation that the enclosed region can be parameterized using average slenderness ratio of the beam segments. The resulting curves help designers in assessing the capability and limits of a mechanism in terms of geometric advantage, mechanical advantage, normalized output displacement, inherent stiffness, etc. Numerous examples are presented to explain various uses of the non-dimensional maps.

This dissertation introduces a novel three-dimensional pseudo-rigid-body model (3-D PRBM) for straight cantilever beams with rectangular cross sections. The model is capable of capturing the behavior of the neutral axis of a beam loaded with an arbitrary force end-load. Numerical integration of a system of differential equations yields approximate displacement and orientation of the beam's neutral axis at the free end, and curvatures of the neutral axis at the fixed end. This data was used to develop the 3-D PRBM which consists of two torsional springs connecting two rigid links for a total of 2 degrees of freedom (DOF). The 3-D PRBM parameters that are comparable with existing 2-D model parameters are characteristic radius factor (mean: γ = 0.8322), bending stiffness coefficient (mean: KΘ = 2.5167) and parametric angle coefficient (mean: cΘ = 1.2501). New parameters are introduced in the model in order to capture the spatial behavior of the deflected beam, including two parametric angle coefficients (means: cΨ = 1.0714; cΦ = 1.0087). The model is verified in a few locations using ANSYSTM and its use in the design of compliant mechanisms is illustrated through spatial compliant versions of crank slider and double slider mechanisms.

Wearable Health Devices (WHDs) are an emerging technology that enables continuous monitoring of vital signs during daily life. Issues with constant and consistent data acquisition have been found while WHD technology has developed. The force of the measurement area and movement of the sensors are key mechanical issues that need to be solved for WHDs to become a viable way to continuously monitor health conditions. This work explores Constant-Force Mechanisms (CFMs) as a solution to problems the current WHD industry faces. Additionally, the relationship between force provided from the mechanism, sensor pressure on the wrist, patient comfort, and sensor readings quality are explored and analyzed. Design requirements for a constant-force wristband were narrowed down to seven critical requirements (mechanism size vs. allowable travel, ability to be used on a curved surface, works well with existing clasps, ease of assembly, direction of travel, material, and force generation). These key requirements need to be considered for a WHD with an integrated CFM to be designed successfully. Two main concepts (buckling beams and tape springs) were prototyped and evaluated against the seven key requirements. The design and testing of a wrist worn sensing band used to gather relationship data among band tension, sensor pressure, patient comfort, and pulsatile signal quality is also presented. Human subject testing (IRB2020-268) was performed on a wristband with an integrated CFM and the wrist worn sensing band that were developed. The band with an integrated CFM compared pressure on the wrist for both a band with and without an integrated CFM for eight different movement activities. On average the band with the integrated CFM had a lower coefficient of variation for all except one of the activities. The data collected from the wrist worn sensing band shows that tension varies linearly with pressure, and that the pressure vs. tension slope increases with increasing wrist width. There also exists a linear relationship between tension and patient pain/comfort, but pressure does not show an effect on the patient discomfort or pain experienced. Signal quality when measured in the range of of 0-4 N and 0-20 kPa does not have a direct correlation to either tension or pressure.

Compliant mechanisms are useful for improving existing machines and creating new ones that were not previously possible. They also help us to think of new methods and technologies needed to both improve existing systems as well as manufacture systems that have not been done before. The purpose of this thesis is to show novel implementations of compliant mechanisms into folding systems, and to show new methods for fabricating such mechanisms with nontraditional materials and on difficult scales. Folding systems are shown in furniture applications with chairs, stools, and childcare furniture applications as results of research into how such structures could be created with compliant mechanisms to be deployed from a flat state. Compliant mechanisms are also shown to be folded by a laser into simple mechanisms and into a potentially more complex parabolic reflector. Small-scale flexible (or compliant) mechanisms are valuable in replacing rigid components while retaining comparable motion and behavior. However, fabricating such mechanisms on this scale (from 0.01 to 10 cm thick) proves difficult, especially with thin sheet metals. The manufacturing method of laser forming, which uses a laser to cut and bend metal into desired shapes, could facilitate this fabrication. However, specific methods for designing mechanisms formed by lasers need to be developed. This work presents laser forming as a means for creating compliant mechanisms on this scale with thin sheet metal. The unique challenges for designing mechanisms to be laser-formed are explored, and new adaptations of existing designs are fabricated and discussed. The design of basic "building blocks" and features are developed for several mechanisms: a parallel-guided mechanism, a cross-axis flexural pivot, a LET joint array, a split-tube flexure, and a bi-stable switch. These mechanisms are shown to perform repeatable behavior and motion comparable to existing non-laser-formed versions. The further possibilities for fabricating compliant mechanisms with laser forming are explored, as advanced applications can benefit from using lasers to create compliant mechanisms from thin sheet metal. One such possible system is a parabolic reflector, which is useful for making solar collectors and antennas. Such shapes have been developed in various patterns and typically manufactured out of rigid components. Applications for these systems could benefit from paraboloids that can fold up and be deployed into a final shape. This work presents a conceptual method for designing a flat-foldable paraboloid and a means for its fabrication using laser forming.

There are times when it is desirable for devices to be stowed compactly, ``transported'' to the location of their desired use, and then deployed to another stable shape or configuration to perform their designed function. Origami-based mechanisms are beneficial in these cases due to their compact, folded nature and large deployments. Unlike traditional mechanical design, compliant mechanism and origami-based design approaches inherently have coupled characteristics, creating complex design problems. The research presented here discusses metrics, methods, and designs to aid in the design of origami-adapted and compliant mechanisms, focusing on the design case of deployable space systems. First, the hexagonal twist origami pattern is used to develop performance metrics for next-generation deployable space arrays. These are shown using five different thickness accommodation techniques. The concepts are demonstrated through two applications: a deployable reflectarray antenna and a LiDAR telescope. Second, a highly compact stowable deployment is presented with the Deployable Euler Spiral Connectors (DESCs). These are compliant deployable flexures that can span gaps between segments in a mechanism and then lay flat when under strain in a stowed position. Additionally, a metamaterial is shown based on the combination of Euler spiral flexures (ESFs) to provide unique behaviors difficult to obtain in traditional materials, such as high compactability, decoupled motion and stiffness, tailorable Poisson's ratio, and multi-directional deployment. Third, this work presents a method for creating hinge-like motion for origami-adapted mechanisms using internal membranes attached between rigid panels. The goal is to remove adhesive requirements, preserve panel volume for use as hard stops, and reduce parasitic motion experienced by other membrane joint types, while keeping the stress in the membrane below the stress limits. Lastly, specific applications and examples of each of the above are shown throughout the work with a specific chapter highlighting more concise examples of creating metrics to determine the best origami patterns and to create compatible hinges. The presented techniques stand to greatly benefit the origami-adapted mechanisms design community.

The purpose of this research is to develop fundamentals of compliant mechanisms in deployable space systems. The scope was limited to creating methods for thick origami, developing compliant deployable solar arrays, and developing methods for stowing and deploying the arrays. The research on actuation methods was focused on a one-time deployment of the array. Concepts for both passive and active actuation were considered. The primary objective of this work was to develop approaches to accommodate thickness in origami-based deployable arrays with a high ratio of deployed-to-stowed diameter. The HanaFlex design was derived from the origami flasher model and is developed as a deployable solar array for large arrays (150 kW or greater) and CubeSat arrays (60 W). The origami folding concept enables compact stowage of the array, which would be deployed from a hexagonal prism into a flat array with about a 10-times increase in deployed diameter as compared to stowed diameter. The work on the origami pattern for the solar array was also applied to the folding of 80-100 m2 solar sails for two NASA CubeSat missions, NEA-Scout and Lunar Flashlight. The CubeSat program is a promising avenue to put the solar array or solar sails into space for testing and proving their functionality. The deployable array concept is easily scalable, although application to CubeSats changes some of the design constraints. The thickness-to-diameter ratio is larger, making the issues of thickness more pronounced. Methods of actuation are also limited on CubeSats because of the rigorous size and weight constraints. This dissertation also includes the development of a compact, self-deploying array based on a tapered map fold design. The tapered map fold was modified by applying an elastic membrane to one side of the array and adequately spacing the panels adjacent to valley folds. Through this approach, the array can be folded into a fully dense stowed volume. Potential applications for the array include a collapsible solar array for military or backpacking applications. Additional compliant mechanism design was done in support of the HanaFlex array. This included a serpentine flexure to attach the array to the perimeter truss for deployment, and a bistable mechanism that may be used in the deployment of the array or sail.