# Directional Stiffness Control Through Geometric Patterning and Localized Heating of Field’s Metal Lattice Embedded in Silicone

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Test Piece Fabrication

#### 2.2. Deriving Forward Kinematics with Changing Axes of Compliance

#### 2.3. Predictive Model

## 3. Results

#### 3.1. Verification from Physical Model

#### 3.2. Successive Melting

#### 3.3. Grid Spacing

## 4. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Predicted bending of Field’s metals (FM) lattice achieved by activating different heating elements shown in red. Mathematical model is based on the product of exponentials method of forward kinematics applied to three cases where (

**a**) shows bending along transverse axes ${w}_{1,3}$, ${w}_{2,3}$, and ${w}_{3,3}$; (

**b**) shows bending along diagonal axes ${w}_{1,1}$, ${w}_{2,1}$, and ${w}_{3,1}$; and (

**c**) shows bending along ${w}_{1,2}$ and ${w}_{3,1}$.

**Figure 2.**The fabrication steps for patterned FM test piece, showing (

**a**) FM injected into the 3D-printed soluble mold; (

**b**) FM lattice with soluble mold material dissolved; (

**c**) layout of Nichrome heating elements; and (

**d**) final casting layer of silicone matrix.

**Figure 3.**The kinematics of 3-segment lattice where the axes of compliance can be chosen through selective melting. Here the kinematics are developed using a product of exponentials formulation and the axis of rotation is defined by the axis of selective melting for each segment, ${w}_{i,p}$. These potential axes of compliance are shown for each segment in red, green, and blue.

**Figure 4.**Development of forward kinematics matrices for specific example case where compliance axes ${\omega}_{1,3}$, ${\omega}_{2,3}$, and ${\omega}_{3,3}$ are selected, allowing bending along the three transverse axes.

**Figure 5.**Bending achieved by FM test piece showing (

**a**) bending along transverse axes ${w}_{1,3}$, ${w}_{2,3}$, and ${w}_{3,3}$; (

**b**) bending along diagonal axes ${w}_{1,1}$, ${w}_{2,1}$, and ${w}_{3,1}$; and (

**c**) bending along ${w}_{1,2}$ and ${w}_{3,1}$.

**Figure 6.**Effects of grid spacing and heating element width on bending axis precision. For this particular heated zone, bending is allowed along any axis between the green and blue axes. This could cause discrepancy between experimental and theoretical results if the analytical model is based on the intended bending axis but actual bending occurs about a different axis within the heated zone.

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**MDPI and ACS Style**

Allen, E.A.; Swensen, J.P.
Directional Stiffness Control Through Geometric Patterning and Localized Heating of Field’s Metal Lattice Embedded in Silicone. *Actuators* **2018**, *7*, 80.
https://doi.org/10.3390/act7040080

**AMA Style**

Allen EA, Swensen JP.
Directional Stiffness Control Through Geometric Patterning and Localized Heating of Field’s Metal Lattice Embedded in Silicone. *Actuators*. 2018; 7(4):80.
https://doi.org/10.3390/act7040080

**Chicago/Turabian Style**

Allen, Emily A., and John P. Swensen.
2018. "Directional Stiffness Control Through Geometric Patterning and Localized Heating of Field’s Metal Lattice Embedded in Silicone" *Actuators* 7, no. 4: 80.
https://doi.org/10.3390/act7040080