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.