We present the mathematical construction of a deployable flasher pattern with near-uniform nonzero thickness in the deployed form and efficient face-to-face packing in the stowed form. We demonstrate its fabrication, deployment, and stowage. The results facilitate the design and manufacture of deployable systems with panels whose substantial thickness is dictated by the end application, with particular utility for space systems.

We analyze the mathematical existence of one of David Huffman’s most prominent curved-crease designs: the Hexagonal Column with Cusps, featuring circular, parabolic, and straight creases. Observations of the physical folded shape suggest that the concave regions between two parabolas form a cylinder, and the regions between the circle and the nearest intersection of the parabolas form a cone. In our analysis, we deduce the remaining rulings that result in a numerically closed hexagonal shape. Finally, we explore other variations of the shape, including those that incorporate only circular creases.

While generative AI has achieved remarkable success in solving problems with verifiable solutions, generating physical art that satisfies both strict geometric constraints and subjective visual aesthetics remains a challenge. This paper presents an approach to tackle these difficulties in the domain of computational origami, a mathematically rigid environment that grounds artistic design within the equations of flat foldability. We present COrigami, an end-to-end AI-driven pipeline that assists the design cycle by generating crease patterns from natural language. Our pipeline involves generating a semantic stick figure, computing a base packing, solving for a flat-foldable crease pattern, shaping the flat-folded crease pattern, and refining the generated model using reinforcement learning driven by an autonomous aesthetic evaluation loop. Our system acts as a highly effective collaborative assistant, generating structural starting points that human artists can further expand and shape. By integrating algorithmic optimisation with autonomous aesthetic critique, this work demonstrates how AI systems can satisfy multi-objective physical constraints to enable reliable, mathematically grounded co-creativity.

This paper introduces bloom patterns as a family of radially expansive, flat-foldable, and developable origami patterns, many of which are rotationally symmetric. Two main definitions are presented for bloom patterns. The generalized definition is a minimum set of conditions based on the most defining characteristics found in bloom patterns, and is designed to minimize the possibility of excluding undiscovered origami patterns that could be classified as bloom patterns. The standardized definition restricts the generalized definition to more specific characteristics of bloom patterns, which enables a systematic framework that describes, analyses, and constructs bloom patterns. A classification scheme for bloom patterns is identified based on their intrinsic characteristics, and several types of bloom patterns are analysed. The distinct helical nature that characterizes bloom patterns is documented with the helical model. A set of compatibility conditions is derived to help determine if a valid bloom pattern can be constructed based on the standardized definition. Finally, applications of bloom patterns are discussed.

Gossamer structures for satellites are large, thin deployable structures that are attractive for space applications because they can be stowed compactly for transportation and deployed to have large functional surface areas. Reflectarray antennas, in particular, are candidates for gossamer structures because they can be realized on thin membranes. However, the efficiency of reflectarray antennas decreases with any deviations from a flat plane, including those induced by plastically deformed creases. Rolling membranes can prevent some plastic deformation, but requires relative slipping between layers that are rolled together. In this work, we describe, analyze, and demonstrate two rolled configurations for deployable gossamer structures based on a combination of rolled and folded membranes and surrogate folds that allow for sliding between layers. Cuts and Step Hinges are used as surrogate folds. Step Hinges connect membranes while limiting slipping motion in a single direction and reducing wrinkling in the structure. The combination of folding, rolling, and sliding connections reduces plastic deformation while providing a highly efficient packing of the stowed form.

This article presents a computational imaging technique by making an interesting connection between two design methodologies namely, origami based shape morphing platforms and metasurfaces. Reconfigurable origami platforms mounted with cavity-backed metasurface antennas have been employed to demonstrate stand-off sparse computational imaging at mi-crowave frequencies (17 - 27 GHz). We use these apertures to perform diffraction-limited RF image reconstructions of 2D and 3D stand-off targets. Such modular, low-cost, conformable aperture find application in remote sensing, stand-off security imagers at checkpoints, automotive radars, and biomedical imaging. We also demonstrate scene adaptive imaging where different origami morphology helps to improve different aspects of imaging metrics like signal-to-noise ratio, cross-range resolution, spatial diversity, and field-of-view.

We present a compliant joint that gives near-revolute joint motion (stationary instantaneous source) over a large folding angle, suitable for realizing origami and kirigami mechanisms that preserve the kinematic behavior of zero-thickness idealizations based on perfect folds, i.e., pure revolute joints.

This paper presents new kirigami patterns consisting of tiles connected by sub-folds that can approximate multiple specified target surfaces. The curvature of the surfaces approximated by the tiles varies as the patterns are folded, allowing access to a wide range of curvatures. A numerical framework is developed for the synthesis of the fold patterns that approximate a given set of target surfaces. The pattern synthesis process is framed as a tile placement problem, where compatible tile arrangements associated with each target surface are computed by solving a constrained optimization problem. After computing a set of tile arrangements, sub-folds are added to connect adjacent tiles. The resulting patterns are rigid foldable with many kinematic degrees of freedom, allowing them to achieve configurations that approximate the specified target surfaces. Kinematic simulations verify the existence of continuous paths between the target surfaces. A prototype pattern with six target surfaces is fabricated using three-dimensional printed components.

AbstractOrigami is the art of paper folding that allows a single flat piece of paper to assume different 3D shapes depending on the fold patterns and the sequence of folding. Using the principles of origami along with computation imaging technique the authors demonstrate a versatile shape‐morphing microwave imaging array with reconfigurable field‐of‐view and scene‐adaptive imaging capability. Microwave/millimeter‐wave based array imaging systems are expected to be the workhorse for sensory perception of future autonomous intelligent systems. The imaging capability of a planar array‐based systems operating in complex scattering conditions have limited field‐of‐view and lack the ability to adaptively reconfigure resolution. To overcome this, here, deviations from planarity and isometry are allowed, and a shape‐morphing computational imaging system is demonstrated. Implemented on a reconfigurable Waterbomb origami surface with 22 active metasurface panels that radiate near‐orthogonal modes across 17–27 GHz, capability to image complex 3D objects in full details minimizing the effects of specular reflections in diffraction‐limited sparse imaging with scene adaptability, reconfigurable cross‐range resolution, and field‐of‐view is demonstrated. Such electromagnetic origami surfaces, through simultaneous surface shape‐morphing ability (potentially with shape‐shifting electronic materials) and electromagnetic field programmability, opens up new avenues for intelligent and robust sensing and imaging systems for a wide range of applications.

The design and manufacture of an origami-based liver-on-a-chip device is presented, together with demonstrations of the chip's effectiveness at recapitulating some of the liver's key in vivo architecture, physical microenvironment, and functions. Laser-cut layers of polyimide tape are folded together with polycarbonate nanoporous membranes to create a stack of three adjacent flow chambers separated by the membranes. Endothelial cells are seeded in the upper and lower flow chambers to simulate sinusoids, and hepatocytes are seeded in the middle flow chamber. Nutrients and metabolites flow through the simulated sinusoids and diffuse between the vascular pathways and the hepatocyte layers, mimicking physiological microcirculation. Studies of cell viability, metabolic functions, and hepatotoxicity of pharmaceutical compounds show that the endothelialized liver-on-a-chip model is conducive to maintaining hepatocyte functions and evaluation of the hepatotoxicity of drugs. The unique origami approach speeds chip development and optimization, effectively simplifying the laboratory-scale fabrication of on-chip models of human tissues without necessarily reducing their structural and functional sophistication.

The field of foldable and physically reconfigurable antennas has recently attracted significant interest from diverse scientific communities, including researchers on antennas, material science, mechanical engineering and numerical modeling. Deployable, packable and multifunctional systems are very important for many applications, including satellite communications, UAVs, CubeSats as well as airborne and spaceborne communication systems. Foldable and physically reconfigurable antennas, particularly origami-based antennas, can provide new capabilities for the aforementioned applications. In this work, we present emerging research on foldable and physically reconfigurable antennas. Such antennas morph their shape to adapt and reconfigure their EM performance (e.g., frequency of operation, bandwidth, polarization, beamwidth, etc.). Also, origami antennas provide ultra-compact stowage, easy deployment, reduced weight, enhanced EM performance and multifunctional utility.

Reconfigurable surfaces are useful in many applications. This paper proposes a type of reconfigurable surfaces that consist of rigid elements (tiles) connected by novel compliant joints. Depending on the actuation, these novel connecting joints can either operate as torsional hinges, which create isometric transformation (like origami folding) between connected tiles, or bistable translational springs, which accommodate metric-changing transformation between connected tiles. A specific example of a reconfigurable surface with square tile shape that can morph into flat, cylindrical (in two different directions), and spherical configurations with simple actuation is given.

We present new families of thick origami mechanisms that achieve rigid foldability and parallel stacking of panels in the flat-folded state using linkages for some or all of the hinges between panels. A degree-four vertex results in a multi-loop eight-bar spatial mechanism that can be analyzed as separate linkages. The individual linkages are designed so that they introduce offsets perpendicular to the panels that are mutually compatible around each vertex. This family of mechanisms offers the unique combination of a planar unfolded state, parallel-stacked panels in the flat folded state, and kinematic single-degree-of-freedom motion from the flat-unfolded to the flat-folded state.

Origami design principles are scale invariant and enable direct miniaturization of origami structures provided the sheets used for folding have equal thickness to length ratios. Recently, seminal steps have been taken to fabricate microscale origami using unidirectionally actuated sheets with nanoscale thickness. Here, we extend the full power of origami-inspired fabrication to nanoscale sheets by engineering bidirectional folding with 4 nm thick atomic layer deposition (ALD) SiNx-SiO2 bilayer films. Strain differentials within these bilayers result in bending, producing microscopic radii of curvature. We lithographically pattern these bilayers and localize the bending using rigid panels to fabricate a variety of complex micro-origami devices. Upon release, these devices self-fold according to prescribed patterns. Our approach combines planar semiconductor microfabrication methods with computerized origami design, making it easy to fabricate and deploy such microstructures en masse. These devices represent an important step forward in the fabrication and assembly of deployable micromechanical systems that can interact with and manipulate micro- and nanoscale environments.

Abstract. The ability of origami to alter its properties and behaviors with its shape makes it an elegant source of inspiration for many engineering designs challenges. Fold states specify the shape of the origami – its facets, creases, and fold angles. Origami research recognizes several acknowledged fold states: the unfolded, fully folded, and flat-folded states. However, these fold states are not comprehensive, excluding some of the most predominant fold states in origami-based devices. In this paper we propose a comprehensive list of fold states based on fold angles. We support the method of categorizing fold states by evaluating the functions and fold states of a large sample of origami-based devices. These correlations provide insight for selecting fold states for origami-based design. We discuss properties and behaviors of the fold states individually and provide a process for fold-state selection.

Deployable mechanical systems such as space solar panels rely on the intricate stowage of passive modules, and sophisticated deployment using a network of motorized actuators. As a result, a significant portion of the stowed mass and volume are occupied by these support systems. An autonomous solar panel array deployed using the inherent material behavior remains elusive. In this work, we develop an autonomous self-deploying solar panel array that is programmed to activate in response to changes in the surrounding temperature. We study an elastic "flasher" origami sheet embedded in a circle of scissor mechanisms, both printed with shape memory polymers. The scissor mechanisms are optimized to provide the maximum expansion ratio while delivering the necessary force for deployment. The origami sheet is also optimized to carry the maximum number of solar panels given space constraints. We show how the folding of the "flasher" origami exhibits a bifurcation behavior resulting in either a cone or disk shape both numerically and in experiments. A folding strategy is devised to avoid the undesired cone shape. The resulting design is entirely 3D printed, achieves an expansion ratio of 1000% in under 40 seconds, and shows excellent agreement with simulation prediction both in the stowed and deployed configurations.

The trend toward smaller mechanism footprints and volumes, while maintaining the ability to perform complex tasks, presents the opportunity for exploration of hypercompact mechanical systems integrated with curved surfaces. Developable surfaces are shapes that a flat sheet can take without tearing or stretching, and they represent a wide range of manufactured surfaces. This work introduces "developable mechanisms" as devices that emerge from or conform to developable surfaces. They are made possible by aligning hinge axes with developable surface ruling lines to enable mobility. Because rigid-link motion depends on the relative orientation of hinge axes and not link geometry, links can take the shape of the corresponding developable surface. Mechanisms are classified by their associated surface type, and these relationships are defined and demonstrated by example. Developable mechanisms show promise for meeting unfilled needs using systems not previously envisioned.