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.

Due to its rigid foldability and predictable kinematics, the reverse fold is the fundamental mechanism behind some of the most well known origami kinematic structures, including the Miura Ori, Yoshimura, and waterbomb patterns. However, the reverse fold only has one parameter to control its behavior: the starting fold angle. In this paper I introduce an alternative to the traditional reverse fold, based on the spring into action pattern, called the spring joint. This novel rigidly foldable mechanism is able to couple multiple reverse folds into a compact space to amplify the kinematic output of a traditional reverse fold by up to ten times, and to add one parameter for each reverse fold, giving more programmatic control of origami structures. Methods of parameterizing both the starting angle, the path of travel, and the axis of motion are also introduced. Unfortunately, this versatility comes at the cost of a large buildup of layers, making the spring joint impractical for thick origami mechanisms. To solve this problem, I also introduce a modular alternative to the spring joint that has no additional layers, with the same kinematic properties. Both of these mechanisms are tested as replacements for the reverse fold in both traditional and custom origami structures.

Origami designs and structures have been widely used in many fields, such as morphing structures, robotics, and metamaterials. However, the design and fabrication of origami structures rely on human experiences and skills, which are both time and labor-consuming. In this paper, we present a rapid design and fabrication method for string-driven origami structures and robots. We developed an origami design software to generate desired crease patterns based on analytical models and Evolution Strategies (ES). Additionally, the software can automatically produce 3D models of origami designs. We then used a dual-material 3D printer to fabricate those wrapping-based origami structures with the required mechanical properties. We utilized Twisted String Actuators (TSAs) to fold the target 3D structures from flat plates. To demonstrate the capability of these techniques, we built and tested an origami crawling robot and an origami robotic arm using 3D-printed origami structures driven by TSAs.

Rigid origami has shown potential in large diversity of practical applications. However, current rigid origami crease pattern design mostly relies on known tessellations. This strongly limits the diversity and novelty of patterns that can be created. In this work, we build upon the recently developed principle of three units method to formulate rigid origami design as a discrete optimization problem, the rigid origami game. Our implementation allows for a simple definition of diverse objectives and thereby expands the potential of rigid origami further to optimized, application-specific crease patterns. We showcase the flexibility of our formulation through use of a diverse set of search methods in several illustrative case studies. We are not only able to construct various patterns that approximate given target shapes, but to also specify abstract, function-based rewards which result in novel, foldable and functional designs for everyday objects.

It was a milestone paper in the field of computational origami, but the algorithm didn't yield very practical folding patterns. Essentially, it took a very long strip of paper and wound it into the desired shape. The resulting structures tended to have lots of seams where the strip doubled back on itself, so they weren't very sturdy. At the Symposium on Computational Geometry in July, Demaine and Tomohiro Tachi of the University of Tokyo will announce the completion of a quest that began with that 1999 paper: a universal algorithm for folding origami shapes that guarantees a minimum number of seams. "In 1999, we proved that you could fold any polyhedron, but the way that we showed how to do it was very inefficient," Demaine says.