Origami-based mechanisms have unique characteristics that make them attractive for engineering applications. However, origami-based design is still a developing area of design. Continued work to increase general understanding of key design parameters specific to origami-based mechanisms will increase the ability of designers to capture the potential benefits of origami-based mechanisms. This thesis presents a fundamental study of origami to assist designers in gaining a stronger understanding of the key parameters and capabilities of origami-based mechanisms. As a starting point a study of fundamental motions in action origami models (those that exhibit motions in their folded state) is presented to explore fundamental motions and actuation in origami-based mechanisms. Eleven fundamental motions are outlined and defined with the associated actuation forces that drive them. Additionally, considerations for ensuring necessary performance and force transfer characteristics in origami mechanisms are presented. This is done by exploring the effect of surrogate hinge selections, fold pattern modification, and actuation inputs on the final mechanism. A model of mechanical advantage in origami models consisting of N, degree-4, vertices (where N = 1,2,3,...) is developed and explored. From the exploration of the parameters of the mechanical advantage model it is shown that hinge selection can greatly affect the performance of an origami mechanism by determining its range of motion, precision, and mechanical advantage. Therefore, in order to better understand this important design decision, specific considerations for surrogate hinge selection are presented. These considerations discuss methods to increase performance and reduce hinge imprint, as well as develop surrogate hinges in metals. The key design parameters and considerations presented herein as well as study of origami motions serve to lay the groundwork toward the development of analysis tools and design guidelines specifically suited to origami based design.