Origami-inspired mechanisms can transform flat sheets into functional three-dimensional dynamic structures that are lightweight, compact, and capable of complex motion. These properties make origami increasingly valuable in robotic and deployable systems. However, accurately simulating their folding behavior and interactions with the environment remains challenging. To address this, we present a design framework for origami mechanism simulation that utilizes MuJoCo's deformable-body capabilities. In our approach, origami sheets are represented as graphs of interconnected deformable elements with user-specified constraints such as creases and actuation, defined through an intuitive graphical user interface (GUI). This framework allows users to generate physically consistent simulations that capture both the geometric structure of origami mechanisms and their interactions with external objects and surfaces. We demonstrate our method's utility through a case study on an origami catapult, where design parameters are optimized in simulation using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and validated experimentally on physical prototypes. The optimized structure achieves improved throwing performance, illustrating how our system enables rapid, simulation-driven origami design, optimization, and analysis.

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