# Survey on Recent Designs of Compliant Micro-/Nano-Positioning Stages

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## Abstract

**:**

## 1. Introduction

## 2. Actuators

#### 2.1. Electromagnetic Actuator

#### 2.2. Electrostatic Actuator

#### 2.3. Electrothermal Actuator

#### 2.4. Piezoelectric Actuator

## 3. Stroke Amplifiers

#### 3.1. Lever-Type Amplifier

#### 3.2. Bridge-Type Amplifier

#### 3.3. Hybrid-Type Amplifier

## 4. Design of a Multi-DOF Stage

#### 4.1. Serial Scheme Design

#### 4.2. Parallel Scheme Design

#### 4.3. Serial-Parallel Scheme Design

## 5. Optimization Methods

#### 5.1. Dimension and Shape Optimization

#### 5.1.1. Non-Heuristic Algorithms

#### 5.1.2. Heuristic Algorithm

#### 5.2. Topology Optimization

## 6. Further Discussion

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Working principles of: (

**a**) electromagnetic actuator (EMA); (

**b**) electrostatic actuator (ESA); (

**c**) electrothermal actuator (ETA); and (

**d**) piezoelectric actuator (PEA).

**Figure 6.**The hybrid amplifier constructed by serially-jointed parallelogram four-bar linkages [73].

**Figure 7.**Schematic diagrams of a serial XY stage with a stacked structure [79].

**Figure 8.**Illustrations of (

**a**) parallelogram flexure (PF), (

**b**) compound parallelogram flexure (CPF) and (

**c**) the Roberts mechanism (RM).

**Figure 9.**A 6-DOF compliant serial-parallel stage [108].

Year | Ref. | Planar Size (mm${}^{2}$) | Actuator | Workspace ($\mathsf{\mu}$m${}^{2}$) | Resolution (nm) | Frequency (Hz) | Decoupler | Coupling Error (%) |
---|---|---|---|---|---|---|---|---|

2007 | [85] | 300 × 300 | PEA | 5 × 5 × 10${}^{6}$ | - | - | CPF | 1 |

2010 | [86] | 385 × 385 | EMA | 10 × 10 × 10${}^{6}$ | 4 | 18 | CPF | - |

2012 | [87] | 214 × 214 | EMA | 10.5 × 10.5 × 10${}^{6}$ | - | 23 | CPF | 1.6 |

2012 | [88] | - | PEA | 41 × 41 | 3 | 340 | CPF | 0.5 |

2013 | [89] | 2.6 × 2.6 | ESA | 225 × 225 | - | 400 | PF | 3 |

2013 | [90] | 230 × 230 | PEA | 8 × 8 | - | 665.4 | PF | 2 |

2013 | [91] | 120 × 120 | EMA | 11.77 × 11.62 × 10${}^{6}$ | 200 | 30 | CPF | 0.55 |

2014 | [92] | - | PEA | 8 × 8 | - | 231 | PF | 0.6 |

2016 | [93] | 130.9 × 130.9 | PEA | 125 × 125 | - | 740 | PF | 0.5 |

2016 | [94] | - | PEA | 100.9 × 100.2 | - | - | PF | 0.4 |

2016 | [95] | 244 × 244 | EMA | 14 × 14 × 10${}^{6}$ | - | 20 | RM | 1.7 |

2016 | [96] | 61 × 61 | PEA | 127 × 127 | 20 | 200 | PF | 4.7 |

Year | Ref. | Planar Size (mm${}^{2}$) | Actuator | Workspace ($\mathsf{\mu}$m${}^{2}$, mrad) | Resolution (nm, $\mathsf{\mu}$rad) | Frequency (Hz) | |
---|---|---|---|---|---|---|---|

Translation | Rotation | ||||||

2014 | [58] | 142 × 110 | PEA | {39.03 × 24.96, -} | - | 1291.4 | 2089.4 |

2015 | [97] | 170 × 170 | PEA | {12.74 × 12.22, 16.67} | - | 1050 | 790 |

2016 | [98] | - | PEA | {6.9 × 8.5, 0.29} | {50, 1.25} | 629.3 | 522.5 |

2016 | [99] | - | PEA | {283.13 × 284.78, 8.73} | {5.7, 1} | 243.09 | 405.52 |

2017 | [57] | 162.7 × 141.7 | PEA | {147.84 × 137.96, 3.75} | - | 199.7 | - |

2017 | [75] | 200 × 200 | PEA | {36.5 × 32, 1.24} | - | 349.8 | - |

Year | Ref. | Prototype | Size (mm${}^{3}$) | Actuator | Workspace ($\mathsf{\mu}$m/axis) | Resolution (nm) | Frequency (Hz) | Decoupler | Coupling Error (%) |
---|---|---|---|---|---|---|---|---|---|

2011 | [100] | Yes | - | PEA | 165 | 180 | - | CPF | 3.6 |

2015 | [101] | No | - | EMA | - | - | 60.6 | RM | 1 |

2015 | [102] | No | - | PEA | 22.32 | - | 106.3 | CPF | 0.5 |

2015 | [68] | No | - | PEA | 153 | - | - | CPF | 0.73 |

2015 | [69] | No | 68.5 × 68.5 × 68.5 | PEA | 120 | - | 226 | PF | 0.75 |

2016 | [63] | No | - | PEA | - | - | 274 | PF | - |

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**MDPI and ACS Style**

Wu, Z.; Xu, Q. Survey on Recent Designs of Compliant Micro-/Nano-Positioning Stages. *Actuators* **2018**, *7*, 5.
https://doi.org/10.3390/act7010005

**AMA Style**

Wu Z, Xu Q. Survey on Recent Designs of Compliant Micro-/Nano-Positioning Stages. *Actuators*. 2018; 7(1):5.
https://doi.org/10.3390/act7010005

**Chicago/Turabian Style**

Wu, Zeyi, and Qingsong Xu. 2018. "Survey on Recent Designs of Compliant Micro-/Nano-Positioning Stages" *Actuators* 7, no. 1: 5.
https://doi.org/10.3390/act7010005