Origami robots are machines whose morphologies and functions are created by folding locally flat sheets. This thesis makes three contributions to the design and fabrication of origami robots aimed at the development of an automated computational pipeline for the specification and construction of widely different morphologies and body sizes capable of highly dynamic operation. The initial contribution recruits recent advances in the design of compliant folded structures to build the first soft robots that exhibit highly dynamic behavior. Specifically, the proof-of-concept robots reported here achieve their juggling and hopping behaviors by actuating their origami springs as power-cascading devices. Second, this thesis advances the origami design literature by automating the construction of compliant origami kinematic chains. The “Kinegami” algorithm reported here accepts a Denavit-Hartenberg kinematic specification and uses a catalog of tunably compliant origami modules to generate a crease pattern that folds into the prescribed serial robot mechanism. Finally, the thesis addresses the problem of scalability in general (not just origami) robot design by studying the simultaneous interaction of structural integrity and actuator affordance. Four contrasting abstract task domains impose different scaling criteria that reveal the relative advantages and disadvantages of three distinct structural principles combined with three different actuator types. For example, applying the unloaded dynamic task criterion to a direct drive actuation type reveals that the origami-style shell structure supports superior length scale-up. An accompanying empirical study confirms that structural alternatives cannot achieve a one-degree-of-freedom hopping task at the same five-fold scale-up of the original hopper design exhibited by the shell structure design. Considered in isolation, these contributions advance, respectively, the recent soft robotics literature, the older origami design literature, and the traditional engineering scaling literature. Considered together, they advance the agenda for the rapid, computer-assisted design of customized, high-performance robots.