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Research Papers

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

[+] Author and Article Information
Landen Bowen

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: landen.bowen@gmail.com

Kara Springsteen

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: kara.springsteen1@gmail.com

Saad Ahmed

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: sua187@psu.edu

Erika Arrojado

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: eoa5110@psu.edu

Mary Frecker

Fellow ASME
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: mxf36@psu.edu

Timothy W. Simpson

Fellow ASME
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: tws8@engr.psu.edu

Zoubeida Ounaies

Fellow ASME
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: zxo100@engr.psu.edu

Paris von Lockette

Fellow ASME
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: prv2@engr.psu.edu

1Corresponding author.

Manuscript received October 16, 2016; final manuscript received January 29, 2017; published online March 9, 2017. Assoc. Editor: James Schmiedeler.

J. Mechanisms Robotics 9(2), 021012 (Mar 09, 2017) (13 pages) Paper No: JMR-16-1315; doi: 10.1115/1.4035966 History: Received October 16, 2016; Revised January 29, 2017

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.

Copyright © 2017 by ASME
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References

Figures

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Fig. 1

(a) The bifold is designed to fold along two different axes depending on the type of field applied whether, (b) magnetic or, and (c) electric. Note that one crease is outlined with a solid line and the other with a dotted line simply as a reference for which crease is being folded.

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Fig. 2

The stiffness of an origami crease can be approximated by assuming that it behaves as a small length flexural pivot (SLFP). Gray indicates rigid panels and white flexible crease material. Relevant dimensions for the calculation of stiffness are shown.

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Fig. 3

Experimental stress–strain curve for three PDMS samples. Note the large strain prior to failure and the relatively constant slope up to 100% strain.

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Fig. 4

Experimental stress–strain curve for a polypropylene sample. Note the slope changes considerably over a relatively small strain range.

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Fig. 5

Experimental stress–strain curve for three notebook paper samples. Note the slope changes significantly over a relatively small strain range and that failure occurs at a low strain compared to PDMS and polypropylene.

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Fig. 6

Relationship between geometric properties in a cross section of flexible crease material. Note that the neutral axis, indicated by a dotted line, remains the same length during bending.

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Fig. 7

First 11% of the experimental stress–strain curves for the three PDMS samples from Fig. 3. Although the data are noisy, note that the overall slope (and therefore modulus) is nearly constant.

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Fig. 8

Tangent modulus–strain relationship for the polypropylene sample from Fig. 4. Note that the modulus changes by an order of magnitude over the strain range.

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Fig. 9

Tangent modulus–strain relationship for the three notebook paper samples from Fig. 5. Note the change in modulus over the strain range. Also, note the tangent modulus is plotted from 0.5% strain to failure to avoid noisy data at low strains due to the effect of compliance in the tensile grippers.

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Fig. 10

Torsional damping coefficients can be determined by modeling creases and their associated panels as second-order rotational systems. The mass of the panel is assumed to be lumped at its center-of-mass, resulting in a mass moment of inertia of mr2.

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Fig. 11

Upon application of an electric field, the EAP elongates while the passive substrate does not. This causes a strain mismatch between the two materials, resulting in a bending motion.

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Fig. 12

In (a), a 3D image of multilayer bending actuator is presented. Note that in the analytical model, the electrode and adhesive layers are considered as one layer due to the relative thinness of the electrode. In (b), definitions of y and h depicted on a multilayer EAP actuator's cross section are specified. (Reproduced with permission from Ahmed et al. [43]. Copyright 2016 by Elsevier).

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Fig. 13

(a) The crease pattern of the experimental barking dog and (b) placement of four-layer terpolymer actuator (gray) along with the three distinct crease stiffness values. Valley folds are represented by solid lines, and mountain folds by dotted lines.

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Fig. 14

Still frame from a video taken during the barking dog experiment. The measured angle, θ, is indicated.

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Fig. 15

The change in θ (see Fig. 14) as applied electric field strength increases is shown for the same barking dog sample tested at three different frequencies

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Fig. 16

(a) Initial and (b) folded configurations of the barking dog dynamic model

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Fig. 17

The center crease of the barking dog consists of three sections. The effective stiffness of this crease is found by summing the stiffnesses of each of the sections.

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Fig. 18

Comparison between the barking dog experimental data and the dynamic model with the initial stiffness approximation and with calibrated stiffness. The experimental data are the average of the three tests, with one standard deviation represented by the error bars.

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Fig. 19

Design of the bifold. On the top side (left image), thin MAE patches are placed with the indicated poling directions. This configuration results in a fold about the vertical crease line. On the bottom side (right image), four single-layer terpolymer actuators are placed to fold the sample about the horizontal crease line.

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Fig. 20

Four MAE patches (left) and four single-layer terpolymer actuator strips (right) are placed on a PDMS substrate to create a multifield bifold. Since the PDMS is transparent, the sample edges are highlighted in black.

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Fig. 21

The bifold was placed inside of a large, horizontally oriented electromagnet. Upon application of a magnetic field, the MAE patches rotate to fold the PDMS substrate as they attempt to align with the applied field.

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Fig. 22

The bifold was hung from needle nose tweezers and connected to a high-voltage power supply in preparation for electric actuation

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Fig. 23

A camera placed underneath the sample recorded a video of the experiment. Still images from this video were analyzed to measure the fold angle. Sample edges are highlighted with black lines.

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Fig. 24

The magnetic portion of bifold dynamic model utilizes three-component torques on each panel to simulate the effect of MAE patches. One crease is pinned to ground, and the creases not currently being folded are locked to enable simulation of folding from a flat state. Double-headed arrows symbolize torsional springs. Inset is an image of the simulated bifold under these conditions.

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Fig. 25

The electric portion of bifold dynamic model utilizes single component torques on each panel to simulate the effect of terpolymer actuators. One crease is pinned to ground, and the creases not currently being folded are locked to enable simulation of folding from a flat state. Double-headed arrows symbolize torsional springs. Inset is an image of the simulated bifold under these conditions.

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Fig. 26

Comparison between the bifold magnetic experimental data and the dynamic model. The experimental data are the average of the three tests, with one standard deviation represented by the error bars.

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Fig. 27

Comparison between the bifold electric experimental data and the dynamic model. The experimental data are the average of the three tests, with one standard deviation represented by the error bars.

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