Self-folding Sheet Research Articles

An End-to-End Approach to Self-Folding Origami Structures

This paper presents an end-to-end approach to automate the design and fabrication process for self-folding origami structures. Self-folding origami structures are robotic sheets composed of rigid tiles and joint actuators. When they are exposed to heat, each joint folds into a preprogrammed angle. Those folding motions transform themselves into a structure, which can be used as body of 3-D origami robots, including walkers, analog circuits, rotational actuators, and microcell grippers. Given a 3-D model, the design algorithm automatically generates a layout printing design of the sheet form of the structure. The geometric information, such as the fold angles and the folding sequences, is embedded in the sheet design. When the sheet is printed and baked in an oven, the sheet self-folds into the given 3-D model. We discuss, first, the design algorithm generating multiple-step self-folding sheet designs, second, verification of the algorithm running in $O(n^2)$ time, where $n$ is the number of the vertices, third, implementation of the algorithm, and finally, experimental results, several self-folded 3-D structures with up to 55 faces and two sequential folding steps.

Shaping the topology of folding pathways in mechanical systems

Disordered mechanical systems, when strongly deformed, have complex configuration spaces with multiple stable states and pathways connecting them. The topology of such pathways determines which states are smoothly accessible from any part of configuration space. Controlling this topology would allow us to limit access to undesired states and select desired behaviors in metamaterials. Here, we show that the topology of such pathways, as captured by bifurcation diagrams, can be tuned using imperfections such as stiff hinges in elastic networks and creased thin sheets. We derive Linear Programming-like equations for designing desirable pathway topologies. These ideas are applied to eliminate the exponentially many ways of misfolding self-folding sheets by making some creases stiffer than others. Our approach allows robust folding by entire classes of external folding forces. Finally, we find that the bifurcation diagram makes pathways accessible only at specific folding speeds, enabling speed-dependent selection of different folded states.

Design, Fabrication, and Modeling of an Electric–Magnetic Self-Folding Sheet

A concept recently proposed by the authors is that of a multifield sheet that folds into several distinct shapes based on the applied field, be it magnetic, electric, or thermal. In this paper, the design, fabrication, and modeling of a multifield bifold are presented, which utilize magneto-active elastomer (MAE) to fold along one axis and an electro-active polymer, P(VDF-TrFE-CTFE) terpolymer, to fold along the other axis. In prior work, a dynamic model of self-folding origami was developed, which approximated origami creases as revolute joints with torsional spring–dampers and simulated the effect of magneto-active materials on origami-inspired designs. In this work, the crease stiffness and MAE models are discussed in further detail, and the dynamic model is extended to include the effect of electro-active polymers (EAP). The accuracy of this approximation is validated using experimental data from a terpolymer-actuated origami design. After adjusting crease stiffness within the dynamic model, it shows good correlation with experimental data, indicating that the developed EAP approximation is accurate. With the capabilities of the dynamic model improved by the EAP approximation method, the multifield bifold can be fully modeled. The developed model is compared to the experimental data obtained from a fabricated multifield bifold and is found to accurately predict the experimental fold angles. This validation of the crease stiffness, MAE, and EAP models allows for more complicated multifield applications to be designed with confidence in their simulated performance.

Design and Optimization of a Shape Memory Alloy-Based Self-Folding Sheet

Origami engineering—the practice of creating useful three-dimensional structures through folding and fold-like operations on two-dimensional building-blocks—has the potential to impact several areas of design and manufacturing. In this article, we study a new concept for a self-folding system. It consists of an active, self-morphing laminate that includes two meshes of thermally-actuated shape memory alloy (SMA) wire separated by a compliant passive layer. The goal of this article is to analyze the folding behavior and examine key engineering tradeoffs associated with the proposed system. We consider the impact of several design variables including mesh wire thickness, mesh wire spacing, thickness of the insulating elastomer layer, and heating power. Response parameters of interest include effective folding angle, maximum von Mises stress in the SMA, maximum temperature in the SMA, maximum temperature in the elastomer, and radius of curvature at the fold line. We identify an optimized physical realization for maximizing folding capability under mechanical and thermal failure constraints. Furthermore, we conclude that the proposed self-folding system is capable of achieving folds of significant magnitude (as measured by the effective folding angle) as required to create useful 3D structures.

Designing and programming self-folding sheets

This paper considers a robot in the form of a self-folding sheet that is capable of origami-style autonomous folding. The sheet is composed of triangular tiles, folding actuators and an integrated electronic substrate, and is formed as an n×m box-pleated crease pattern. The design of the sheet is generated by an automated sheet design algorithm. We control the sheet with a programming method including a hardware model and supporting algorithms. In this paper we present the programming method. We describe and analyze the algorithms that generate designs and programs for the sheet. We finally demonstrate and analyze experiments with 4×4 and 8×8 self-folding sheet devices.

Design and numerical analysis of an SMA mesh-based self-folding sheet

Origami engineering, which is the practice of creating useful three-dimensional structures through folding and fold-like operations applied to initially two-dimensional entities, has the potential to impact several areas of design and manufacturing. In some instances, however, it may be impractical to apply external manipulations to produce the desired folds (e.g., as in remote applications such as space systems). In such cases, self-folding capabilities are valuable. A self-folding material or material system is one that can perform folding operations without manipulations from external forces. This work considers a concept for a self-folding material system. The system extends the ‘programmable matter’ concept and consists of an active, self-morphing sheet composed of two meshes of thermally actuated shape memory alloy (SMA) wire separated by a compliant passive layer. The geometric and power input parameters of the self-folding sheet are optimized to achieve the tightest local fold possible subject to stress and temperature constraints. The sheet folding performance considering folds at different angles relative to the orientation of the wire mesh is also analyzed. The optimization results show that a relatively low elastomer thickness is preferable to generate the tightest fold possible. The results also show that the self-folding sheet does not require large power inputs to achieve an optimal folding performance. It was shown that the self-folding sheet is capable of creating similar quality folds at different orientations.

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

SUMMARYThis 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.