# Modeling of a Symmetric Five-Bar Displacement Amplification Compliant Mechanism for Energy Harvesting

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## Abstract

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## 1. Introduction

## 2. Displacement Amplification

## 3. Experimental Validation

_{2}laser cutting machine. The material has a Young’s modulus (E) of 3.2 GPa, and Poisson’s ratio ($\nu $) of 0.327. The input displacements ${X}_{in}$ were provided using two micrometer actuators, with 0.05 mm accuracy, applied in the opposite directions. ${X}_{in}$ was varied between 0.1 mm and 0.5 mm (at 0.1 mm increments), while the external load ${F}_{L}$ was applied to the top of the mechanism using weights that were varied between 1 N to 5 N (at 1 N increments). A dial indicator, with an accuracy of 0.01 mm, was used to measure the output displacements. Figure 4 shows the setup for the experimental validation. Six strain gauges were fixed at the middle of each flexure hinge (Segments 1, 4, and 6), at the locations shown in Figure 4. These locations were selected for being the mechanism’s weakest segments. The strain gauges were connected to strain meters (DP25B-S, Omega, CT, USA), which were calibrated to provide the average strain.

## 4. Energy Harvesting Using a Unimorph Piezoelectric Cantilever

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AR | Amplification ratio |

PMMA | Poly(methyl methacrylate) |

PRBM | Pseudo-rigid-body models |

PZT | Lead Zirconate Titanate (piezoelectric ceramic material) |

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**Figure 3.**Free body diagram of the mechanism, showing dimensions, forces, and mechanism segments “i”.

**Figure 5.**Effect of the input displacement ${X}_{in}$ and the external load ${F}_{L}$ on the output displacement.

Segments 1, 2, and 3 | ${\mathit{N}}_{\mathit{i}}=-\frac{{\mathit{F}}_{\mathit{L}}}{2}$ |

Segments 4, 5, and 6 | ${N}_{i}={A}_{x}\phantom{\rule{0.166667em}{0ex}}cos\phantom{\rule{0.166667em}{0ex}}{\theta}_{i}+\frac{{F}_{L}}{2}\phantom{\rule{0.166667em}{0ex}}sin\phantom{\rule{0.166667em}{0ex}}{\theta}_{i}$ |

Segment 7 | ${N}_{i}={A}_{x}$ |

Hinges | ${t}_{rc}$ | ${r}_{rc}$ | ${t}_{cf}$ | ${r}_{cf}$ | ${l}_{cf}$ |

3.75 | 5 | 3.75 | 2 | 15 | |

Links | ${l}_{1}$ | ${l}_{2}$ | ${l}_{3}$ | ${l}_{4}$ | ${l}_{5}$ |

10 | 85 | 15 | 85.5 | 15 | |

Others | w | ${\theta}_{5}$ | |||

8 | 15° |

Material | ${d}_{31}$ | ${E}_{P}$ | ${E}_{m}$ | |||||||||

125 × 10^{−9} mm/V | 80 GPa | 200 GPa | ||||||||||

Dimensions | ${t}_{P}$ | ${t}_{m}$ | ${L}_{b}$ | ${w}_{b}$ | ||||||||

0.24 mm | 0.16 mm | 33 mm | 2 mm |

Parameter | X_{in}(mm) | Y_{ex}(mm) | F_{L}(N) | Y_{L}(mm) | Y_{out}(mm) | AR | V (V) |
---|---|---|---|---|---|---|---|

Value | 0.16 | 1.787 | 0.289 | 0.133 | 1.654 | 10.33 | 0.1884 |

Equation | (4) | (6) | (5) | (1) | (2) | (13)–(15) |

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**MDPI and ACS Style**

Elsisy, M.M.; Arafa, M.H.; Saleh, C.A.; Anis, Y.H.
Modeling of a Symmetric Five-Bar Displacement Amplification Compliant Mechanism for Energy Harvesting. *Sensors* **2021**, *21*, 1095.
https://doi.org/10.3390/s21041095

**AMA Style**

Elsisy MM, Arafa MH, Saleh CA, Anis YH.
Modeling of a Symmetric Five-Bar Displacement Amplification Compliant Mechanism for Energy Harvesting. *Sensors*. 2021; 21(4):1095.
https://doi.org/10.3390/s21041095

**Chicago/Turabian Style**

Elsisy, Moataz M., Mustafa H. Arafa, Chahinaz A. Saleh, and Yasser H. Anis.
2021. "Modeling of a Symmetric Five-Bar Displacement Amplification Compliant Mechanism for Energy Harvesting" *Sensors* 21, no. 4: 1095.
https://doi.org/10.3390/s21041095