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Research Papers

Trade Space Exploration of Magnetically Actuated Origami Mechanisms

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

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

Mary Frecker

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

Timothy Simpson

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

1Corresponding author.

Manuscript received July 5, 2015; final manuscript received December 15, 2015; published online March 7, 2016. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(3), 031012 (Mar 07, 2016) (12 pages) Paper No: JMR-15-1184; doi: 10.1115/1.4032406 History: Received July 05, 2015; Revised December 15, 2015

Self-folding origami has the potential to be utilized in novel areas such as self-assembling robots and shape-morphing structures. Important decisions in the development of such applications include the choice of active material and its placement on the origami model. With proper active material placement, the error between the actual and target shapes can be minimized along with cost, weight, and input energy requirements. A method for creating magnetically actuated dynamic models and experimentally verifying their results is briefly reviewed, after which the joint stiffness and magnetic material approximations used in the dynamic model are discussed in more detail. Through the incorporation of dynamic models of magnetically actuated origami mechanisms into the Applied Research Laboratory's trade space visualizer (atsv), the trade spaces of self-folding dynamic models of the waterbomb base and Shafer's frog tongue are explored. Finally, a design tradeoff is investigated between target shape approximation error and the placement of magnetic material needed to reach a target shape. These two examples demonstrate the potential use of this process as a design tool for other self-folding origami mechanisms.

Copyright © 2016 by ASME
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References

Figures

Grahic Jump Location
Fig. 1

Using adams 2014, a dynamic model of the self-folding waterbomb was created. Key features of the model are noted.

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Fig. 2

Five waterbomb samples were fabricated from polypropylene, upon which permanent magnets were affixed in the orientations shown. Arrows indicate the magnetic poling directions, and gray hatching indicates the panel affixed to ground during the experiment [9].

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Fig. 3

Experimental setup used to obtain folding angle data from magnetically actuated waterbomb samples [9]

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Fig. 4

During the experiment, digital images were taken at known increments of magnetic field strength. From each of these images, the two angles shown were measured using solidworks [9].

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Fig. 11

Upper and lower limits for the ith joint are calculated using the ith initial joint angle

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Fig. 5

A parameter sweep of stiffness in the dynamic waterbomb model was performed to more closely approximate the experimental data for joint G. The experimental data shown are the mean of the five samples, with one standard deviation shown by the error bars. Units for K are in. lb/deg.

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Fig. 6

A parameter sweep of stiffness in the dynamic waterbomb model was performed to more closely approximate the experimental data for joint H. The experimental data shown are the mean of the five samples, with one standard deviation shown by the error bars. Units for K are in. lb/deg.

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Fig. 7

Schematic of the torque, T, generated when magnetic material with remanent magnetization, M, is placed in an applied magnetic field, H [9]

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Fig. 14

The final shape of the model due to the application of magnetically actuated material for (a) design 1, (b) design 2, and (c) design 3

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Fig. 15

Schematic of the identified orientations of magnetic material on the waterbomb base for an applied magnetic field coming out of the page for (a) design 1, (b) design 2, and (c) design 3. The arrows represent the remanent magnetization directions and approximate amounts of the material. Shading indicates the ground panel.

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Fig. 16

Shafer's frog tongue in its (a) open and (b) closed states

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Fig. 17

(a) The labeling scheme for the frog tongue model is presented. Joints are lettered, panels are numbered, and the ground panel is shaded. (b) The initial folded state of the waterbomb is displayed.

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Fig. 18

This 2D scatter plot of 2500 active material design configurations of the frog tongue was generated by the basic and Pareto samplers in atsv. Target shape approximation error and the average torque magnitude for each design are readily obtained from the plot, and the initial error is indicated. Plus symbols represent the Pareto front after trade space exploration. Three designs (D1, D2, and D3) are selected for further investigation.

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Fig. 19

The final shape of the model due to the application of magnetically actuated material for (a) design 1, (b) design 2, and (c) design 3

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Fig. 20

Schematic of the identified orientations of magnetic material on the frog tongue for an applied magnetic field coming out of the page for (a) design 1, (b) design 2, and (c) design 3. The arrows represent the remanent magnetization directions and approximate amounts of the material. Shading indicates the ground panel.

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Fig. 8

Using the AZ function in adams, the angle between the x-axes of two markers, or coordinate systems, is obtained. Marker0, defined by (x0, y0, z0), is attached to ground while Marker1, defined by (x1, y1, z1), is free to move. Note that the y-axis is defined as out of the page. This function is used to obtain the angle, θ, between the applied magnetic field, H, and the remanent magnetization, M, for each magnetic material piece.

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Fig. 9

Comparison of the simulated dynamic model and experimental data for joint G. The experimental data shown are the mean of the five samples, with one standard deviation shown by the error bars. The correlation is best on the higher end of the applied torques.

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Fig. 10

Comparison of the simulated dynamic model and experimental data for joint H. The experimental data shown are the mean of the five samples, with one standard deviation shown by the error bars. The correlation is best on the lower end of the applied torques.

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Fig. 12

(a) The labeling scheme for the waterbomb model is presented. Joints are lettered, panels are numbered, and the ground panel is shaded. (b) The initial folded state of the waterbomb is displayed.

Grahic Jump Location
Fig. 13

This 2D scatter plot of 2500 active material design configurations of the waterbomb was generated by the basic and Pareto samplers in atsv. Target shape approximation error and the average torque magnitude for each design are readily obtained from the plot, and the initial error is indicated. Plus symbols represent the Pareto front after trade space exploration. Three designs (D1, D2, and D3) are selected for further investigation.

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