Folding and Unfolding Linkages, Paper, and Polyhedra

Demaine, Erik D.

doi:10.1007/3-540-47738-1_9

Cited by 22 publications

(18 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In origami, a goal shape is achieved from an initially planar sheet exclusively through folding. In this context, a fold is any deformation of the sheet in which the in-surface distance between any two points in the sheet is constant and the sheet does not self-intersect [2,3].…”

Section: Introductionmentioning

confidence: 99%

Kinematics of Origami Structures With Smooth Folds

Hernandez

Hartl

Lagoudas

2016

Journal of Mechanisms and Robotics

View full text Add to dashboard Cite

Origami provides both inspiration and potential solutions to the fabrication, assembly, and functionality of various structures and devices. Kinematic modeling of origamibased objects is essential to their analysis and design. Models for rigid origami, in which all planar faces of the sheet are rigid and folds are limited to straight creases having only zeroth-order geometric continuity, are available in the literature. Many of these models include constraints on the fold angles to ensure that any initially closed strip of faces is not torn during folding. However, these previous models are not intended for structures with non-negligible fold thickness or with maximum curvature at the folds restricted by material or structural limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate idealizations of structural response, and a new approach is needed. In this work, a novel model analogous to those for rigid origami with creased folds is presented for sheets having realistic folds of nonzero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of smooth folds and constraints on their associated shape variables are presented. A numerical implementation of the model allowing for kinematic simulation of sheets having arbitrary fold patterns is also described. Simulation results are provided showing the capability of the model to capture realistic kinematic response of origami sheets with diverse fold patterns.

show abstract

Section: Introductionmentioning

confidence: 99%

Kinematics of Origami Structures With Smooth Folds

Hernandez

Hartl

Lagoudas

2016

Journal of Mechanisms and Robotics

View full text Add to dashboard Cite

show abstract

“…In general, the problem of interest is how a particular object (e.g., a piece of paper, a linkage, or a polyhedron) can be folded subject to some natural constraints. For general surveys on folding and unfolding, see [7,30].…”

Section: Related Problems In Folding and Unfoldingmentioning

confidence: 99%

“…However, if cuts are allowed interior to the faces of the polygon, there is a one-piece unfolding without overlap. See [7,30] for details.…”

Section: Folding and Unfolding Polyhedramentioning

confidence: 99%

Recent Results in Computational Origami

Demaine¹,

Demaine²

2002

Origami^{3}

View full text Add to dashboard Cite

Computational origami is a recent branch of computer science studying efficient algorithms for solving paper-folding problems. This field essentially began with Robert Lang's work on algorithmic origami design [25], starting around 1993. Since then, the field of computational origami has grown significantly. The purpose of this paper is to survey the work in the field, with a focus on recent results, and to present several open problems that remain. The survey cannot hope to be complete, but we attempt to cover most areas of interest. OverviewMost results in computational origami fit into at least one of three categories: universality results, efficient decision algorithms, and computational intractability results.A universality result shows that, subject to a certain model of folding, everything is possible. For example, any tree-shaped origami base (Section 2.1), any polygonal silhouette (Section 2.3), and any polyhedral surface (Section 2.3) can be folded out of a large-enough piece of paper. Universality results often come with efficient algorithms for finding the foldings; pure existence results are rare.When universality results are impossible (some objects cannot be folded), the next-best result is an efficient decision algorithm to determine whether a given object is foldable. Here "efficient" normally means "polynomial time." For example, there is a polynomialtime algorithm to decide whether a "map" (grid of creases marked mountain and valley) can be folded by a sequence of simple folds (Section 3.4).Not all paper-folding problems have efficient algorithms, and this can be proved by a computational intractability result. For example, it is NP-hard to tell whether a given crease pattern folds into any flat origami (Section 3.2), even when folds are restricted to simple folds (Section 3.4). These results mean that there are no polynomial-time algorithms for these problems, unless some of the hardest computational problems can also be solved in polynomial time, which is generally deemed unlikely.We further distinguish computational origami results as addressing either origami design or origami foldability. Basically, in origami design, some aspects of the target configuration are specified, and the goal is to design a suitable target that can be folded out of paper. In

show abstract

“…Origami art presents many creative concepts for reconfigurable design [1]. A single sheet of material (paper) undergoes folding to create a unique design without assembly.…”

Section: Introductionmentioning

confidence: 99%

Evaluating Compliant Hinge Geometries for Origami-Inspired Mechanisms

Delimont

Magleby

Howell

2015

Journal of Mechanisms and Robotics

View full text Add to dashboard Cite

Origami-inspired design is an emerging field capable of producing compact and efficient designs. Compliant hinges are proposed as a way to replicate the folding motion of paper when using nonpaper materials. Compliant hinges function as surrogate folds and can be defined as localized reduction of stiffness. The purpose of this paper is to organize and evaluate selected surrogate folds for use in compliant mechanisms. These surrogate folds are characterized based on the desired motion as well as motions typically considered parasitic. Additionally, the surrogate folds' ability to rotate through large deflections and their stability of center of rotation are evaluated. Existing surrogate folds are reviewed and closed-form solutions presented. A diagram intended as a straightforward design guide is presented. Areas for potential development in the surrogate fold design space are noted.

show abstract

Folding and Unfolding Linkages, Paper, and Polyhedra

Cited by 22 publications

References 26 publications

Kinematics of Origami Structures With Smooth Folds

Kinematics of Origami Structures With Smooth Folds

Recent Results in Computational Origami

Evaluating Compliant Hinge Geometries for Origami-Inspired Mechanisms

Contact Info

Product

Resources

About