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.

Proteins are made of vast chains of amino acids that twist and fold into intricate designs. These structures are held in place by networks of noncovalent interactions. One of these, the hydrogen bond, forms bridges between adjacent pieces of the protein chain and is one of the most important contributors to the shape and stability of proteins. Hydrogen bonds come in all shapes and sizes and a full understanding of these not only aids in our understanding of proteins in general but can bridge the gap to finding cures to many protein-related diseases, such as sickle-cell anemia. The primary aim of this thesis is to discover if a specific type of hydrogen bond, the N-H···N bond, occurs within proteins and if so, if it contributes to the structure and stability of proteins.

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We work with two different mechanisms to generate geometric frustration on thin elastic sheets; isotropic differential growth and folding. We describe how controlled growth and prescribing folding patterns are useful tools for designing three-dimensional objects from information printed in two dimensions. The first mechanism is inspired by the possibility to control shapes by swelling polymer films, where we propose a solution for the problem of shape formation by asking the question, ``what 2D metric should be prescribed to achieve a given 3D shape?'', namely the reverse problem. We choose two different types of initial configurations of sheets, disk-like with one boundary and annular with two boundaries. We demonstrate our technique by choosing four examples of 3D axisymmetric shapes and finding the respective swelling factors to achieve the desired shape. Second, we present a mechanical model for a single curved fold that explains both the buckled shape of a closed fold and its mechanical stiffness. The buckling arises from the geometrical frustration between the prescribed crease angle and the bending energy of the sheet away from the crease. This frustration increases as the sheet's area increases. Stiff folds result in creases with constant space curvature while softer folds inherit the broken symmetry of the buckled shape. We extend the application of our numerical model to show the potential to study multiple fold structures.

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