My work has been focused on compliant mechanisms, origami engineering, and rapid prototyping. Two of the projects that I worked on were focused on compliant mechanisms and origami engineering. The similar goal of both of those projects was to create an origami membrane whose kinematics mimic that of an existing mechanism. The first project created an origami membrane to mimic the kinematics of a planar shape-changing mechanism. This mechanism was a square shaped unit-cell which could shear, compress, and expand in its own plane. In addition to waterproofing the mechanism, the first project also sought to optimize the dimensions of the mechanism in order to reduce internal stresses during actuation. The results of the optimization portion of this project were a reduction of internal stresses by more than 22%. The results of the origami synthesis portion of the project was the creation of a membrane with an origami pattern whose kinematics mimic that of the shape-shifting surface. The origami membrane is capable of being folded into each of the various positions that the shape-shifting surface is able to fold into. The second project sought to create a similar type of origami fold pattern, but for a Shape Morphing Space Frame (SMSF). This project created an origami membrane designed to mimic the kinematics of a mechanism that had been developed in a different previous project. The mechanism consisted of a series of Linear Bistable Elements (LBEs) which were assembled to form a cylinder. When the LBEs were actuated the cylinder would deform to a hyperboloid. This project created an origami membrane whose kinematics mimic that of the shape-morphing space frame and was able to change side length by more than 30%. The origami membrane was able to fold to each of the SMSF’s states. This project also developed a method for synthesizing an origami fold pattern with shape-morphing triangles. Both of the first two projects that comprise this dissertation sought to develop an origami fold pattern whose kinematics mimic that of an existing mechanism. In each of these projects one of the future goals for the project was to create a prototype where the mechanism and the origami are fabricated together as one integrated prototype. Possible methods of accomplishing this goal include rapid prototyping. Thus, the mechanics of rapid prototyping are of concern for future work on these projects. The third project developed a part which could be printed from a Fused Deposition Modeling (FDM) machine to test certain material properties (yield strength and elastic modulus) after it had been processed through the FDM. This would allow the material properties to be tested without the use of expensive test equipment. This project developed eight parts which could be used to bracket certain material properties of rapid prototyped parts after processing. The parts developed in this project were capable of bracketing the material properties of the materials in question, and were able to do so when tested across multiple FDM machines. The results of this work were stress-strain data which indicates the behavior of the part under load, and a method for inexpensively testing the material properties of rapid prototyped parts after processing.