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Research Papers

Development and Validation of a Dynamic Model of Magneto-Active Elastomer Actuation of the Origami Waterbomb Base

[+] Author and Article Information
Landen Bowen, Kara Springsteen

Mechanical Engineering,
The Pennsylvania State University,
University Park,
State College, PA 16802

Hannah Feldstein

The Pennsylvania State University,
University Park,
State College, PA 16802

Mary Frecker

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

Timothy W. Simpson

Fellow ASME
Professor of Mechanical
and Industrial Engineering,
The Pennsylvania State University,
University Park,
State College, PA 16802

Paris von Lockette

Mem. ASME
Associate Professor of Mechanical Engineering,
The Pennsylvania State University,
University Park,
State College, PA 16802

1Corresponding author.

Manuscript received September 26, 2014; final manuscript received November 22, 2014; published online December 31, 2014. Assoc. Editor: Thomas Sugar.

J. Mechanisms Robotics 7(1), 011010 (Feb 01, 2015) (10 pages) Paper No: JMR-14-1264; doi: 10.1115/1.4029290 History: Received September 26, 2014; Revised November 22, 2014; Online December 31, 2014

Of special interest in the growing field of origami engineering is self-folding, wherein a material is able to fold itself in response to an applied field. In order to simulate the effect of active materials on an origami-inspired design, a dynamic model is needed. Ideally, the model would be an aid in determining how much active material is needed and where it should be placed to actuate the model to the desired position(s). A dynamic model of the origami waterbomb base, a well-known and foundational origami mechanism, is developed using adams 2014, a commercial multibody dynamics software package. Creases are approximated as torsion springs with both stiffness and damping. The stiffness of an origami crease is calculated, and the dynamic model is verified using the waterbomb. An approximation of the torque produced by magneto-active elastomers (MAEs) is calculated and is used to simulate MAE-actuated self-folding of the waterbomb. Experimental validation of the self-folding waterbomb model is performed, verifying that the dynamic model is capable of accurate simulation of the fold angles.

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References

Figures

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Fig. 4

The waterbomb geometry was modeled in ADAMS in a folded state

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Fig. 3

Waterbomb crease pattern. Dashed lines indicate mountain folds, while solid lines indicate valley folds.

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Fig. 2

The waterbomb base can be viewed as a spherical 8 bar change point mechanism. Joints are represented by rectangles and are lettered, while links are numbered. Hatching on link 1 indicates ground.

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Fig. 1

Origami waterbomb base (paper) in its (a) first stable state and (b) second stable state

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Fig. 5

A SLFP was chosen to model creases, allowing for the determination of stiffness. In terms of the waterbomb, l is the width of a crease, t is the thickness of the sheet of material, and c is the length of a crease.

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Fig. 6

While it is possible that the panels (the white triangles) are flexible, for modeling purposes they are assumed to be rigid, with flexible material (gray) connecting each panel. Key dimensional parameters are called out.

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Fig. 7

The waterbomb is (a) displaced from equilibrium and released, returning to (b) the first stable state

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Fig. 8

The (a) displacement (angle) and (b) potential energy of each torsion spring as a function of time. In (c) the summation of each torsion spring energy is plotted as a function of time. Note that all displacements and energies settle to zero. This corresponds to the first stable state, or the position in which all torsion springs are undeflected.

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Fig. 9

The waterbomb is (a) displaced from equilibrium and released, returning to (b) the second stable state

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Fig. 10

The (a) displacement (angle) and (b) potential energy of each torsion spring as a function of time. In (c), the summation of each torsion spring energy is plotted as a function of time. Note that all displacements and energies reach a nonzero equilibrium, corresponding to the second stable state.

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Fig. 18

Two angles were measured at each magnetic field increment for each sample. The angle on the left corresponds to joint H  in the model, and the angle on the right to joint G.

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Fig. 19

A comparison between the simulated and experimental self-folding waterbomb for joint G. Note that the initial angle is subtracted out, leaving only the joint rotation. The experimental data are the mean of four samples, and the error bars indicate the standard deviation.

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Fig. 12

MAE patches (represented here with arrows in the direction of magnetization) of the same size and orientation were simulated on the waterbomb in three separate configurations. This was done to examine the effect of the location of the torque on a panel. All three simulations returned the same data, confirming that torque location does not change motion. Note that the magnetic field is going into the page.

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Fig. 13

A sample MAE actuation configuration. MAE patches are represented here with arrows in the direction of magnetization. Note that the magnetic field is going into the page.

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Fig. 14

The MAE configuration from Fig. 13 tested at the (a) first value, (b) second value, and (c) third value of torque in Table 3. Note that as the magnitude of the torques increases, displacement also increases.

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Fig. 15

The equilibrium state of the waterbomb subject to the second value of torque from Table 3

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Fig. 16

Polypropylene waterbomb samples were created with a laser cutter. Gray hatching indicates the ground panel. Permanent magnets with magnetization direction marked with black arrows were attached to each ungrounded panel to match the configuration determined from the dynamic model in Fig. 13.

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Fig. 17

The experimental setup used to induce and measure the change in angle of various joints of the polypropylene waterbomb samples due to a change in applied magnetic field.

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Fig. 11

Schematic of torque, T, generated by placing a MAE patch with magnetization direction, M, in a magnetic field, H

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Fig. 20

A comparison between the simulated and experimental self-folding waterbomb for joint H. Note that the initial angle is subtracted out, leaving only the joint rotation. The experimental data is the mean of four samples, and the error bars indicate the standard deviation.

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