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 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.

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.