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.

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.

Origami-based design is increasing in popularity as its benefits and advantages become better understood and explored. However, many opportunities still exist for the application of origami principles to engineered designs, especially in the use of non-paper, thick sheet materials. One specific area utilizing thick sheet materials that is especially promising is origami-based mechanisms that require electrical power transfer applications. Many of these opportunities can be met by the use of surrogate folds. This thesis provides methods and frameworks that can be used by engineers to efficiently select and design surrogate folds for use in origami-based mechanisms and products. Surrogate folds are a means of achieving fold-like behavior, offering a simple method for achieving folding motions in thicker materials. A surrogate fold is a localized reduction in stiffness in a given direction allowing the material to function like a fold. A family of surrogate folds is reviewed, and the respective behaviors of the folds discussed. For a specified fold configuration, the material thickness is varied to yield different sizes of surrogate folds. Constraint assumptions drive the design, and the resultant configurations are compared for bending motions. Finite element and analytical models for the folds are also compared. Prototypes are made from different materials. This work creates a base for creating design guidelines for using surrogate folds in thick sheet materials. As mechanisms with origami-like movement increase in popularity, there is a need for conducting electrical power across folds. Surrogate folds can be used to address this need. Current methods and opportunities for conducting across folds are reviewed. A framework for designing conductive surrogate folds that can be adapted to fit specific applications is presented. Equations for calculating the electrical resistance in single surrogate folds as well as arrays are given. Prototypes of several conductive joints are presented and discussed. The framework is then followed in the design and manufacture of a conductive origami-inspired mechanism.

Continuum manipulators which are robot limbs inspired by trunks, snakes, and tentacles, represent a promising field in robotic manipulation research. They are well known for their compliance, as they can conform to the shape of objects they interact with. Furthermore, they also benefit from improved dexterity and reduced weight compared to traditional rigid manipulators. The current state of the art continuum robots typically consists of a bulky pneumatic or tendon-driven actuation system at the base, hindering their scalability. Additionally, they tend to sag due to their own weight and are weak in the torsional direction, limiting their performance under external load. This work presents an origami-inspired cable-driven continuum manipulator module that offers low-cost, light-weight, and is inherently safe for human-robot interaction. This dissertation includes contributions in the design of the modular and torsionally strong continuum robot, the motion planning and control of the system, and finally the embedded sensing to close the loop providing robust feedback.

Continuum manipulators which are robot limbs inspired by trunks, snakes, and tentacles, represent a promising field in robotic manipulation research. They are well known for their compliance, as they can conform to the shape of objects they interact with. Furthermore, they also benefit from improved dexterity and reduced weight compared to traditional rigid manipulators. The current state of the art continuum robots typically consists of a bulky pneumatic or tendon-driven actuation system at the base, hindering their scalability. Additionally, they tend to sag due to their own weight and are weak in the torsional direction, limiting their performance under external load. This work presents an origami-inspired cable-driven continuum manipulator module that offers low-cost, light-weight, and is inherently safe for human-robot interaction. This dissertation includes contributions in the design of the modular and torsionally strong continuum robot, the motion planning and control of the system, and finally the embedded sensing to close the loop providing robust feedback.

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.

Origami-inspired design is an emerging field capable of producing compact and efficient designs. The object of a surrogate fold is to provide a fold-like motion in a non-paper material without undergoing yielding. Compliant mechanisms provide a means to achieve these objectives as large deflections are achieved. The purpose of this thesis is to present a summary of existing compliant joints suitable for use as surrogate folds. In doing so, motions are characterized which no existing compliant joint provides. A series of compliant joints is proposed which provides many of these motions. The possibility of patterning compliant joints to form an array is discussed. Arrays capable of producing interesting motions are noted.

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.