arXiv subjects

Tomohiro Tachi

Publications and source records attributed to Tomohiro Tachi.

At least 19 recordsLinked to original sources

arXiv2026

Modular fabrication and design of thick rigid-foldable origami metamaterials

Origami metamaterials offer significant potential for stiff deployable structures However, fabricating load-bearing cellular structures from thick panels introduces geometric interference at non-manifold junctions. Conventional thick-panel fabrication often disrupt ideal kinematics, thereby compromising smooth motion and scalability. This study proposes a modular fabrication framework that preserves one-degree-of-freedom rigid-folding kinematics in thick and non-manifold origami metamaterials. By decomposing non-manifold junctions into a hierarchy of stacked, modular hinged panels, our approach successfully accommodates synchronized hinge motions using scissor-like linkages. Exploiting this representation, we implement a graph-based topology optimization framework that tailors macroscopic stiffness while preserving folding connectivity. We demonstrate this approach by fabricating optimized prototypes that deploy seamlessly with a one-degree-of-freedom motion. Furthermore, we demonstrate engineering scalability through the large-scale construction of extensive deployable systems assembled from modular panels, which exhibit high load-bearing capacity. These results pave the way for the practical fabrication of structural, large-scale deployable metamaterials.

cs.CE↗

arXiv2026

Programming sequential deployment of origami via kinematic transition fronts

Propagating transition fronts, in which local interactions sequentially trigger state changes, are widely observed across natural, biological, and engineered systems. While such propagation has been engineered using energy-driven instabilities, front propagation governed purely by geometric constraints remains underexplored and lacks a general design framework. In particular, how to program sequential deployment in origami through such kinematic propagation remains an open challenge. Here, we develop a systematic design framework for kinematic transition fronts based on their correspondence with heteroclinic orbits in discrete dynamical systems. Focusing on strips of developable and flat-foldable degree-4 origami vertices, we show that asymmetric coupling between adjacent creases produces nonlinear recurrence relations whose composition generically gives rise to heteroclinic orbits connecting developed and flat-folded states, enabling domino-like sequential deployment. We further show that macroscopic shape can be programmed independently of propagation behavior by exploiting invariances in the recurrence relation, and illustrate the approach through a representative thick-panel origami prototype. These results enable programmable sequential deployment in origami via transition fronts, while also establishing a general framework for kinematic transition fronts in geometrically constrained systems.

math.DS↗

arXiv2026

Size-Dependent Properties of Miura-ori Tessellations

We investigate the size-dependent behavior of Miura-ori-based origami tessellations by changing the number of origami unit cells. For large tessellations, the Miura-ori sheet generally exhibits a negative in-plane Poisson's ratio, whereas if the size of the Miura-ori tessellations becomes small, the transition between positive and negative Poisson's ratio emerges in the middle of the folding process. Here, we show that such a transitioning point, i.e., zero Poisson's ratio, yields a kinematic locking state. We also experimentally demonstrate the tunable locking behavior altered by tessellation sizes. Extending the analysis to three-dimensional origami tessellations, we find that the direction of kinematic locking changes depending on the tessellation size. Varying tessellation size thus enables control over both the onset and the direction of locking in origami metamaterials.

physics.app-ph↗

arXiv2025

Multistable Curved-Crease Origami Blocks for Reconfigurable Modular Building System

This study proposes a reconfigurable modular building system that assembles multistable curved-crease origami blocks. Curved-crease origami is designed with even-vertex polygonal trajectories and an elastica curvature profile. We then connect the matching ends to impart multistability. Through this design approach, we create various blocks and investigate their snapping and load-bearing behavior using finite element analysis. We design block assemblies of multi-story and quasi-continuous wall surfaces and fabricate a series of desktop and large-scale prototypes to demonstrate the flexibility and adaptability of our system for architectural use. Furthermore, by introducing a tension cable to the assembly, the assembled modules can be snapped into multiple configurations.

physics.app-ph↗

arXiv2024

A Proper Definition of Higher Order Rigidity

[Connelly and Servatius, 1994] shows the difficulty of properly defining n-th order rigidity and flexiblity of a bar-and-joint framework for higher order (n >= 3) through the introduction of a cusp mechanism. The author proposes a "proper" definition of the order of rigidity by the order of elongation of the bars with respect to the arclength along the path in the configuration space. We show that the classic definition using formal n-th derivative of the length constraint is a sufficient condition for the n-th flexiblity in the proposed definition and also a necessary condition only for n = 1, 2.

math.AG↗

arXiv2024

Nonlinear Kinematics of Recursive Origami Inspired by the Spidron

Non-periodic folding of periodic crease patterns paves the way to novel nonlinear phenomena that cannot be feasible through periodic folding. This paper focuses on the non-periodic folding of recursive crease patterns generalized from Spidron. Although it is known that the Spidron has a $1$-DOF isotropic rigid folding motion, its general kinematics and dependence on the crease pattern remain unclear. Using the kinematics of a single unit cell of the Spidron and the recursive construction of the folded state of multiple unit cells, we consider the folding of the Spidron that is not necessarily isotropic. We found that as the number of unit cells increases, the non-periodic folding is restricted and the isotropic folding becomes dominant. Then, we analyze the three kinds of isotropic folding modes by constructing $1$-dimensional dynamical systems governing each of them. We show that these systems can possess different recursive natures depending on folding modes even in an identical crease pattern. Furthermore, we show their novel nonlinear nature, including the period-doubling cascade leading to the emergence of chaos.

cond-mat.soft↗

arXiv2023

Stiff deployable structures via coupling of thick Miura-ori tubes along creases

Origami-based structures play an important role in the realization of deployable mechanisms and unique mechanical properties via programmable deformation by folding. Among origami-based structures, tessellation by the coupling of origami tubes enriches the variations in geometry and mechanical properties. However, thickness accommodation is a critical problem in engineering applications involving the coupling of thick origami tubes. To solve this problem, this study proposes the coupling of thick Miura-ori tubes along the creases for facile fabrication, which sustains the one-degree-of-freedom (DOF) motion of thick Miura-ori tubes owing to the local mirror symmetry around the coupling interfaces. Furthermore, the coupling method contributes to the high stiffness of the coupled Miura-ori tubes, as evidenced by the wide gap in the eigenvalues between the one-DOF mode and the elastic modes obtained by the bar-and-hinge models. Finally, meter-scale coupled Miura-ori tubes were fabricated to demonstrate one-DOF motion and high stiffness. The findings of this study enable the rapid construction of structures by one-DOF motion and enhancement of transportability via flat-foldability.

physics.app-ph↗

arXiv2023

Triclinic metamaterials by tristable origami with reprogrammable frustration

Geometrical frustration induced anisotropy and inhomogeneity are explored to achieve unique properties of metamaterials that set them apart from conventional materials. According to Neumann's principle, to achieve anisotropic responses, the material unit cell should possess less symmetry. Based on such guidelines, we present a triclinic metamaterial system of minimal symmetry, which is originated from a Trimorph origami pattern with a simple and insightful geometry: a basic unit cell with four tilted panels and four corresponding creases. The intrinsic geometry of the Trimorph origami, with its changing tilting angles, dictates a folding motion that varies the primitive vectors of the unit cell, couples the shear and normal strains of its extrinsic bulk, and leads to an unusual Poisson's effect. Such effect, associated to reversible auxeticity in the changing triclinic frame, is observed experimentally, and predicted theoretically by elegant math formulae. The nonlinearities of the folding motions allow the unit cell to display three robust stable states, connected through snapping instabilities. When the tristable unit cells are tessellated, phenomena that resembles linear and point defects emerge as a result of geometric frustration. The frustration is reprogrammable into distinct stable and inhomogeneous states by arbitrarily selecting the location of a single or multiple point defects. The Trimorph origami demonstrates the possibility of creating origami metamaterials with symmetries that were hitherto non-existent, leading to triclinic metamaterials with tunable anisotropy for potential applications such as wave propagation control and compliant microrobots.

cond-mat.mtrl-sci↗

arXiv2019

Geodesic Folding of Tetrahedron

In this work, we show the geometric properties of a family of polyhedra obtained by folding a regular tetrahedron along regular triangular grids. Each polyhedron is identified by a pair of nonnegative integers. The polyhedron can be cut along a geodesic strip of triangles to be decomposed and unfolded into one or multiple bands (homeomorphic to a cylinder). The number of bands is the greatest common divisor of the two numbers. By a proper choice of pairs of numbers, we can create a common triangular band that folds into different multiple polyhedra that belongs to the family.

cs.CG↗

arXiv2018

Programming Curvature using Origami Tessellations

Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one degree-of-freedom collapsible structures, we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, and quantify the energetic and material cost of doing so.

cond-mat.soft↗

arXiv2018

A Balloon-Borne Very Long Baseline Interferometry Experiment in the Stratosphere: Systems Design and Developments

The balloon-borne very long baseline interferometry (VLBI) experiment is a technical feasibility study for performing radio interferometry in the stratosphere. The flight model has been developed. A balloon-borne VLBI station will be launched to establish interferometric fringes with ground-based VLBI stations distributed over the Japanese islands at an observing frequency of approximately 20 GHz as the first step. This paper describes the system design and development of a series of observing instruments and bus systems. In addition to the advantages of avoiding the atmospheric effects of absorption and fluctuation in high frequency radio observation, the mobility of a station can improve the sampling coverage (`uv-coverage') by increasing the number of baselines by the number of ground-based counterparts for each observation day. This benefit cannot be obtained with conventional arrays that solely comprise ground-based stations. The balloon-borne VLBI can contribute to a future progress of research fields such as black holes by direct imaging.

astro-ph.IM↗

arXiv2018

Rigid Foldability is NP-Hard

In this paper, we show that deciding rigid foldability of a given crease pattern using all creases is weakly NP-hard by a reduction from Partition, and that deciding rigid foldability with optional creases is strongly NP-hard by a reduction from 1-in-3 SAT. Unlike flat foldability of origami or flexibility of other kinematic linkages, whose complexity originates in the complexity of the layer ordering and possible self-intersection of the material, rigid foldability from a planar state is hard even though there is no potential self-intersection. In fact, the complexity comes from the combinatorial behavior of the different possible rigid folding configurations at each vertex. The results underpin the fact that it is harder to fold from an unfolded sheet of paper than to unfold a folded state back to a plane, frequently encountered problem when realizing folding-based systems such as self-folding matter and reconfigurable robots.

cs.CG↗

arXiv2018

Conic Crease Patterns with Reflecting Rule Lines

We characterize when two conic curved creases are compatible with each other, when the rule lines must converge to conic foci and reflect at the crease. Namely, two conics are compatible (can be connected by rule segments in a foldable curved crease pattern) if and only if they have equal or reciprocal eccentricity. Thus, circles (eccentricity 0) and parabolas (eccentricity 1) are compatible with only themselves (when scaled from a focus), and ellipses (eccentricity strictly between 0 and 1) and hyperbolas (eccentricity above 1) are compatible with themselves and each other (but only in specific pairings). The foundation of this result is a general condition relating any two curved creases connected by rule segments. We also use our characterization to analyze several curved crease designs.

cs.CG↗

arXiv2018

An Edge Extrusion-Approach to Generate Extruded Miura-Ori and Its Double Tiling Origami Patterns

This paper proposes a family of origami tessellations called extruded Miura-Ori, whose folded state lies between two parallel planes with some faces on the planes, potentially useful for folded core materials because of face bonding. An extruded Miura-Ori is obtained by cutting Miura-Ori apart along the edges and face diagonals before inserting the extrusion of the section edges. We compute the extrusion direction to obtain a valid extruded Miura-Ori. The extruded Miura-Ori usually has three valid states. We analyse the third state (final folded state) in depth to show that a continuous family of parameters can produce origami tessellations that can completely tile the top and bottom planes.

cs.CG↗

arXiv2018

Self-foldability of monohedral quadrilateral origami tessellations

Using a mathematical model for self-foldability of rigid origami, we determine which monohedral quadrilateral tilings of the plane are uniquely self-foldable. In particular, the Miura-ori and Chicken Wire patterns are not self-foldable under our definition, but such tilings that are rotationally-symmetric about the midpoints of the tile are uniquely self-foldable.

math.MG↗

arXiv2017

Double-line rigid origami

In this paper, we will show methods to interpret some rigid origami with higher degree vertices as the limit case of structures with degree-4 supplementary angle vertices. The interpretation is based on separating each crease into two parallel creases, or \emph{double lines}, connected by additional structures at the vertex. We show that double-lined versions of degree-4 flat-foldable vertices possess a rigid folding motion, as do symmetric degree-$2n$ vertices. The latter gives us a symbolic analysis of the original vertex, showing that the tangent of the quarter fold angles are proportional to each other. The double line method is also a potentially useful in giving thickness to rigid origami mechanisms. By making single crease into two creases, the fold angles can be distributed to avoid $180^\circ$ folds, when panels can easily collide with each other. This can be understood as an extension of the crease offset method of thick rigid origami with an additional guarantee of rigid-foldability.

math.MG↗

arXiv2016

Origami-based tunable truss structures for non-volatile mechanical memory operation

Origami has recently received significant interest from the scientific community as a building block for constructing metamaterials. However, the primary focus has been placed on their kinematic applications, such as deployable space structures and sandwich core materials, by leveraging the compactness and auxeticity of planar origami platforms. Here, we present volumetric origami cells -- specifically triangulated cylindrical origami (TCO) -- with tunable stability and stiffness, and demonstrate their feasibility as non-volatile mechanical memory storage devices. We show that a pair of origami cells can develop a double-well potential to store bit information without the need of residual forces. What makes this origami-based approach more appealing is the realization of two-bit mechanical memory, in which two pairs of TCO cells are interconnected and one pair acts as a control for the other pair. Using TCO-based truss structures, we present an experimental demonstration of purely mechanical one- and two-bit memory storage mechanisms.

cond-mat.mes-hall↗

arXiv2015

Rigid Origami Vertices: Conditions and Forcing Sets

We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as in the unassigned case. We also illustrate the utility of this result by applying it to the new concept of minimal forcing sets for rigid origami models, which are the smallest collection of creases that, when folded, will force all the other creases to fold in a prescribed way.

math.MG↗