Jinkyu Yang

Modern mechanical computing, being envisioned as a pathway toward structure- and material-level processing, holds potential for intelligent metamaterials and robotics in extreme environments. However, current computing architectures remain constrained by binary paradigms. Here, we introduce an origami-inspired modular architecture that encodes logical mappings into its inherent kinematic responses under an input-output decoupled paradigm, enabling both binary and ternary mechanical computing. Within this emerging paradigm, the multi-stable states of two Kresling origami configurations serve as physical carriers for generating discrete signals, while torsional transitions among these states ensure signal switching, supporting operations from logic gates to advanced arithmetic. Based on this mechanical architecture, we systematically demonstrate seven common logic gates and modular arithmetic half- and full-adders in both binary and ternary systems, revealing challenges and opportunities in advancing multi-valued logic through comparative analysis. The physical platform, along with its accompanying response-programming strategy, represents a simplified and generalized paradigm that supports migration to higher-level mechanical computing mechanisms.

Origami-inspired structures with rigid panels now span thick, kirigami, and multi-sheet realizations, making unified kinematic analysis essential. Yet a generalized pipeline that systematically translates their geometric definitions into mathematical loop-closure constraints has been lacking. We present an automated approach that constructs the Pfaffian constraint matrix directly from pattern-level geometric data for a broad class of rigid-foldable structures (RFSs). From a minimally extended data schema, the tool first constructs the facet–hinge graph and extracts a minimum cycle basis to capture all constraints. Subsequently, it employs screw theory to assemble a velocity-level constraint matrix, which encodes coupled rotation-translation loop closure. The framework computes and visualizes deployment and folding motions across diverse RFSs, while eliminating tedious, error-prone constraint calculations.

Interactions between solitary waves are crucial for understanding nonlinear phenomena in systems such as optics, fluid dynamics, and mechanical metamaterials. Rarefaction solitary waves, in particular, offer insight into nonlinear wave dynamics in strain-softening media. Despite their proposed applications in waveguides and energy harvesting, key characteristics—particularly solitonic collisions—are not yet fully understood due to energy dissipation and the need for high-precision measurement techniques. In this work, we introduce an experimental platform for studying pure rarefaction solitons in a strain-softening lattice. Our results show that both symmetric and asymmetric collisions display elastic interactions and amplitude-dependent phase shifts. The experimentally observed dynamics, including soliton speed and phase shifts, closely match numerical simulations and analytical predictions based on the Boussinesq approximation. These findings not only validate our platform but also highlight the potential of mechanical rarefaction solitons for probing nonlinear wave interactions and advancing wave-based computing.

Origami-inspired structures with rigid panels now span thick, kirigami, and multi-sheet realizations, making unified kinematic analysis essential. Yet a general method that consolidates their loop constraints has been lacking. We present an automated approach that generates the Pfaffian constraint matrix for arbitrary rigid foldable structures (RFS). From a minimally extended data schema, the tool constructs the facet-hinge graph, extracts a minimum cycle basis that captures all constraints, and assembles a velocity-level constraint matrix via screw theory that encodes coupled rotation and translation loop closure. The framework computes and visualizes deploy and fold motions across diverse RFS while eliminating tedious and error-prone constraint calculations.

Physics-informed neural networks program full energy landscapes of origami metamaterials directly from governing equations, enabling data-free inverse design and controlled sequential deployment.

This paper introduces a novel approach for designing soft robotic manipulators using origami cylinder modules (OCMs) as building blocks. An OCM is defined as a pneumatically actuated soft robotic unit capable of both linear and bending deformations, contributing to a lightweight and compact robotic system. A rigorous mathematical model was developed to estimate the force and moment outputs of the OCM, with experimental validation confirming the accuracy of the prediction. Multiple OCMs were integrated into a continuum manipulator, and their performance was evaluated by various manipulation tasks. The results demonstrate that the OCM model predicts the behavior of the actuator with a high accuracy in the estimation of force and moment. The origami manipulator also achieves a wide range of motions (ROM) with relatively small errors, showcasing potential for practical applications. These findings introduce a new method for developing soft robotic manipulators made of origami-based air chambers that offer lightweight and compact designs. The mathematical model of the OCM holds implications for simulating actuator behavior in real-world applications, while the performance of the origami manipulator shows the potential for practical implementation. This study provides valuable insights into the advancement of robotic manipulators based on origami structures, allowing a useful set of tools in the field of robotics.

Origami-inspired structures provide unprecedented opportunities for creating lightweight, deployable systems with programmable mechanical responses. However, their design remains challenging due to complex nonlinear mechanics, multistability, and the need for precise control of deployment forces. Here, we present a physics-informed neural network (PINN) framework for both forward prediction and inverse design of conical Kresling origami (CKO) without requiring pre-collected training data. By embedding mechanical equilibrium equations directly into the learning process, the model predicts complete energy landscapes with high accuracy while minimizing non-physical artifacts. The inverse design routine specifies both target stable-state heights and separating energy barriers, enabling freeform programming of the entire energy curve. This capability is extended to hierarchical CKO assemblies, where sequential layer-by-layer deployment is achieved through programmed barrier magnitudes. Finite element simulations and experiments on physical prototypes validate the designed deployment sequences and barrier ratios, confirming the robustness of the approach. This work establishes a versatile, data-free route for programming complex mechanical energy landscapes in origami-inspired metamaterials, offering broad potential for deployable aerospace systems, morphing structures, and soft robotic actuators.