Force-Guiding Particle Chains for Shape-Shifting Displays

We present design and implementation of a chain of particles that can be programmed to fold the chain into a given curve. The particles guide an external force to fold, therefore the particles are simple and amenable for miniaturization. A chain can consist of a large number of such particles. Using multiple of these chains, a shape-shifting display can be constructed that folds its initially flat surface to approximate a given 3D shape that can be touched and modified by users, for example, enabling architects to interactively view, touch, and modify a 3D model of a building.Comment: 6 pages, 5 figure, submitted to IROS 201

The difficulty of folding self-folding origami

Why is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of `distractor' folding branches accessible from a bifurcation at the flat state. Consequently, refolding a sheet requires finding the ground state in a glassy energy landscape with an exponential number of other attractors of higher energy, much like in models of protein folding (Levinthal's paradox) and other NP-hard satisfiability (SAT) problems. As in these problems, we find that refolding a sheet requires actuation at multiple carefully chosen creases. We show that seeding successful folding in this way can be understood in terms of sub-patterns that fold when cut out (`folding islands'). Besides providing guidelines for the placement of active hinges in origami applications, our results point to fundamental limits on the programmability of energy landscapes in sheets.Comment: 8 pages, 5 figure

Minimum Forcing Sets for Miura Folding Patterns

We introduce the study of forcing sets in mathematical origami. The origami material folds flat along straight line segments called creases, each of which is assigned a folding direction of mountain or valley. A subset $F$ of creases is forcing if the global folding mountain/valley assignment can be deduced from its restriction to $F$. In this paper we focus on one particular class of foldable patterns called Miura-ori, which divide the plane into congruent parallelograms using horizontal lines and zig-zag vertical lines. We develop efficient algorithms for constructing a minimum forcing set of a Miura-ori map, and for deciding whether a given set of creases is forcing or not. We also provide tight bounds on the size of a forcing set, establishing that the standard mountain-valley assignment for the Miura-ori is the one that requires the most creases in its forcing sets. Additionally, given a partial mountain/valley assignment to a subset of creases of a Miura-ori map, we determine whether the assignment domain can be extended to a locally flat-foldable pattern on all the creases. At the heart of our results is a novel correspondence between flat-foldable Miura-ori maps and $3$-colorings of grid graphs.Comment: 20 pages, 16 figures. To appear at the ACM/SIAM Symp. on Discrete Algorithms (SODA 2015

Folding and unfolding origami tessellation by reusing folding path

Recent advances in robotics engineering have enabled the realization of self-folding machines. Rigid origami is usually used as the underlying model for the self-folding machines whose surface remains rigid during folding except at joints. A key issue in designing rigid origami is foldability that concerns about finding fold-ing steps from a flat sheet of crease pattern to a desired folded state. Although recent computational methods allow rapid simulation of folding process of certain rigid origamis, these methods can fail even when the input crease pattern is extremely simple. In this paper, we take on the challenge of planning folding and unfolding motion of origami tessellations, which are composed of repetitive crease patterns. The number of crease lines of a tessellation is usually large, thus searching in such high dimensional configuration space with the require-ment of maintaining origami rigidity is nontrivial. We propose a motion planner that takes symmetry into con-sideration and reuses folding path found on the essential crease pattern. Both of these strategies enable us to fold large origami tessellation much more efficiently than the existing methods. Our experimental results show that the proposed method successfully folds several types of rigid origami tessellations that the existing methods fail to fold.

4D Printing: Design and Fabrication of Smooth Curved Surface Using Controlled Self-Folding

Traditional origami structures fold along pre-defined hinges, and the neighboring facets of the hinges are folded to transform planar surfaces into three-dimensional (3D) shapes. In this study, we present a new self-folding design and fabrication approach that has no folding hinges and can build 3D structures with smooth curved surfaces. This four-dimensional (4D) printing method uses a thermal-response control mechanism, where a thermo shrink film is used as the active material and a photocurable material is used as the constraint material for the film. When the structure is heated, the two sides of the film will shrink differently due to the distribution of the constraint material on the film. Consequently, the structure will deform over time to a 3D surface that has no folding hinges. By properly designing the coated constraint patterns, the film can be self-folded into different shapes. The relationship between the constraint patterns and their correspondingly self-folded surfaces has been studied in the paper. Our 4D printing method presents a simple approach to quickly fabricate a 3D shell structure with smooth curved surfaces by fabricating a structure with accordingly designed material distribution

Planning to fold multiple objects from a single self-folding sheet

This paper considers planning and control algorithms that enable a programmable sheet to realize different shapes by autonomous folding. Prior work on self-reconfiguring machines has considered modular systems in which independent units coordinate with their neighbors to realize a desired shape. A key limitation in these prior systems is the typically many operations to make and break connections with neighbors, which lead to brittle performance. We seek to mitigate these difficulties through the unique concept of self-folding origami with a universal fixed set of hinges. This approach exploits a single sheet composed of interconnected triangular sections. The sheet is able to fold into a set of predetermined shapes using embedded actuation. We describe the planning algorithms underlying these self-folding sheets, forming a new family of reconfigurable robots that fold themselves into origami by actuating edges to fold by desired angles at desired times. Given a flat sheet, the set of hinges, and a desired folded state for the sheet, the algorithms (1) plan a continuous folding motion into the desired state, (2) discretize this motion into a practicable sequence of phases, (3) overlay these patterns and factor the steps into a minimum set of groups, and (4) automatically plan the location of actuators and threads on the sheet for implementing the shape-formation control.United States. Defense Advanced Research Projects Agency. Programmable Matter Progra

SELF-FOLDING TRANSFORMER ROBOT BASED ON BIDIRECTIONAL SHAPE MEMORY POLYMER COMPOSITE ACTUATORS

Self-folding is universal in nature. The concept of self-folding has attracted interests from standpoints of both fundamental scientific research and technological innovations due to the advantages of self-folding over traditional manufacturing methods. Driven by the interests in self-folding, people have developed artificial self-folding structures at different length scales based on specific actuators that can realize unidirectional folding movement. To overcome the limitations of unidirectional actuators in fabricating more complex structures, people also developed actuators that can realize bidirectional folding action. Most of these actuators are based on shape memory effects of shape memory polymers and alloys. However, the applicability of these bidirectional actuators is restricted by drawbacks such as complexity in fabrication and programming. We have developed and characterized an easy-to-fabricate and low-cost shape memory polymer composite actuator which could enable bidirectional folding action with adjustable angles by simple programming procedures. Based on analytical, numerical, and experimental analysis, we have shown that we can control the folding angle and the folding force by adjusting the thickness ratio and/or the prestrain of the actuator. To demonstrate the potential application of the actuator, we reported a self-folding transformer robot which folds from two-dimensional (2D) sheet into three-dimensional (3D) configuration by itself and transforms between different 3D shapes via controlled heating of the actuators. Then, we presented the ability of the robot to do obstacle avoidance for practical applications. By combining findings from polymer science and robotics, we envision that the actuator can provide new opportunities for various applications including a soft robot that can transform its shape depending on surrounding environment and navigate itself

Sticker controller and sticker programming for smart sheets (self-folding sheets)

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 265-267).This thesis describes a self-folding sheet that is capable of origami-style autonomous folding. We describe the hardware device we designed and fabricated. This device, called a self-folding sheet, is a sheet with a box-pleat pattern and an integrated electronic substrate and actuators. The sheet is programmed and controlled using a new idea called sticker programming. We describe the architecture of a machine that can be programmed by sticker programming and its instantiation. We also describe planning algorithm and automatic programming algorithm for controlling a given sheet to self-fold into a desired shape. Finally we present experiments with a 4 x 4 hardware device and an 8 x 8 hardware device.by Byoungkwon An.S.M

Kinematics, Structural Mechanics, and Design of Origami Structures with Smooth Folds

Origami provides novel approaches to the fabrication, assembly, and functionality of engineering structures in various fields such as aerospace, robotics, etc. With the increase in complexity of the geometry and materials for origami structures that provide engineering utility, computational models and design methods for such structures have become essential. Currently available models and design methods for origami structures are generally limited to the idealization of the folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures having non-negligible thickness or maximum curvature at the folds restricted by material limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate representations of structural response and a new approach is needed. The first contribution of this dissertation is a model for the kinematics of origami structures having realistic folds of non-zero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of the smooth folds and the constraints on their associated kinematic variables are presented. A numerical implementation of the model allowing for kinematic simulation of structures having arbitrary fold patterns is also described. Examples illustrating the capability of the model to capture realistic structural folding response are provided. Subsequently, a method for solving the origami design problem of determining the geometry of a single planar sheet and its pattern of smooth folds that morphs into a given three-dimensional goal shape, discretized as a polygonal mesh, is presented. The design parameterization of the planar sheet and the constraints that allow for a valid pattern of smooth folds and approximation of the goal shape in a known folded configuration are presented. Various testing examples considering goal shapes of diverse geometries are provided. Afterwards, a model for the structural mechanics of origami continuum bodies with smooth folds is presented. Such a model entails the integration of the presented kinematic model and existing plate theories in order to obtain a structural representation for folds having non-zero thickness and comprised of arbitrary materials. The model is validated against finite element analysis. The last contribution addresses the design and analysis of active material-based self-folding structures that morph via simultaneous folding towards a given three-dimensional goal shape starting from a planar configuration. Implementation examples including shape memory alloy (SMA)-based self-folding structures are provided