This thesis addresses a number of challenges designers face when designing deployable origami-based arrays, specifically joint selection, design, and placement within an array. In deployable systems, the selection and arrangement of joint types is key to how the system functions. The kinematics and performance of an array is directly affected by joint performance. This work develops joint metrics which are then used to compare joint performances, constructing a tool designers can use when selecting joints for an origami array. While often a single type of joint is used throughout an array, this work shows how using multiple types of joints within the same array can offer benefits for motion deployment, and array stiffening. Origami arrays are often used for their unique solutions for stowing and deploying large planar shapes. Folds, enabled through joints, within these patterns allow the arrays to fold compactly. However, it can be difficult to fully deploy arrays, particularly array designs with a high number of joints. In addition, it is a challenge to stabilize a fully deployed array from undesired re-folding. This work introduces a strain-energy storing joint that is used to deploy and stiffen foldable origami arrays, the Lenticular Lock (LentLock). Geometry of the LentLock is introduced and the deploying and stiffening performance of the joint is shown. Folds within an origami array create the constraints that link motion between panels, and can be used to create kinematic benefits, such as creating mechanisms with a single degree-of-freedom. While many fold-constraints are required to define motion, this work shows that origami-based system contain many redundant constraints. The removal of redundant joints does not affect the motion of the array nor the observed mobility, but may decrease the likelihood of binding, simplify the overall system and decrease actuation force. This work introduces a visual and iterative approach designers can use to identify redundant constraints in origami patterns, and techniques that can be used to remove the identified redundant constraints. The presented techniques are demonstrated by removing redundant constraints from prototyped origami mechanisms. As a result of this work, designers will be better able to approach and design deployable origami-based mechanisms.