# Optimal Design and Analysis for a New 1-DOF Compliant Stage Based on Additive Manufacturing Method for Testing Medical Specimens

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Conceptual Design of Compliant 1-DOF Stage

## 3. Proposed Method

- -
- A conceptual design of the 1-DOF stage is predetermined, i.e., built kinematic scheme.
- -
- Predetermine the technical specifications for the 1-DOF stage.
- -
- Establish the dynamic equation for the 1-DOF stage by developing the PRBM and Lagrange’s method.
- -
- Verify the theoretical results by using ANSYS software.
- -
- If the mathematical models are corrected, the process moves to next step. Otherwise, the process turns back the step 1.
- -
- Determine the design variables, objective function, and constraint function.
- -
- Firefly algorithm is utilized for the dynamic response of the proposed stage.
- -
- The optimal results are verified via simulations in ANSYS software.
- -
- The first frequency of the stage is compared with that from the previous studies.

#### 3.1. Overview of Pseudo-Rigid-Body Method

#### 3.2. Lagrange’s Principle

_{eq}depicts the equivalent input stiffness, and m

_{eq}is the equivalent mass.

_{a}is the generalized force.

#### 3.3. Firefly Algorithm

## 4. Results and Discussion

#### 4.1. Dynamic Establishment for 1-DOF Stage

_{c}, the radius of the right circular hinge (r), and the width of the right circular hinge (b

_{c}). Figure 11 shows the thickness of the elliptical hinge (h), the width of the elliptical hinge (w), and the two semi-axes of the elliptical hinge (a and b). In Figure 12, a

_{r}is the thickness of the leaf hinge and b

_{r}is the width of the leaf hinge.

_{in}, d

_{outC}and d

_{outJ}, and d

_{out}, respectively. The output displacement of LAM #1 and LAM #2 is the input displacement of the LAM #3. The dynamic equation of the stage is formed according to the chain of equations as:

_{i}denotes the mass, H

_{i}is the length, and $\phi $

_{j}(i = 1, 2…6, 7), (j = 1, 2, 3, 4) represents the rotary angular of the rigid links.

_{C}) is described in Equation (11). The torsional stiffness of elliptical hinge (K

_{E}) is depicted in Equation (13). The torsional stiffness of leaf hinge (K

_{L}) is formed in Equation (14). The moment of inertia of the rigid links (I

_{j}) are described in Equation (15).

_{in}, the work is defined as:

_{V}, the input force and the input displacement have formed a relation as follows:

_{in}= F

_{in}/d

_{in}) divides both sides by ${d}_{in}^{2}$, the stiffness is determined as:

_{k}) and the elastic energy (E

_{v}) may be conveyed. These two energies are assembled into Lagrange function as L = E

_{k}− E

_{v}.

#### 4.2. Verification of Established Analytical Models

#### 4.3. Parameter Optimization of 1-DOF Stage

**x**) > 200 Hz

**x**) symbolizes the resonant frequency. Meanwhile, x

_{1}, x

_{2}, x

_{3}, and x

_{4}are the dimensions R, G, S, and U, respectively. Especially, the range of design variables depends on the design experiences and the characteristics of different floors. Specifically, the thickness of floor 1 should be more than that of floor 2. In addition, the thickness of floor 2 should be more than that of floor 3. This is needed to permit the strength of the proposed stage as well as reduce the loss of displacement energy. Meanwhile, a suitable thickness of various positions of different floors should be defined by optimization process in order to find the most appropriate values for the proposed structure.

#### 4.4. FEA Validation and Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

1-DOF | One degree of freedom |

SEM | Scanning electron microscope |

TEM | Transmission electron microscope |

PRBM | Pseudo-rigid-body model |

ANFIS | Adaptive neuro-fuzzy inference system |

PZT | Piezoelectric actuator |

LAM 1 | Lever displacement amplifier of floor 1 |

LAM 2 | Lever displacement amplifier of floor 2 |

LAM 3 | Lever displacement amplifier of floor 3 |

K_{C} | Stiffness of the semi-circular flexural hinge |

K_{E} | Stiffness of elliptical hinge |

K_{L} | Stiffness of leaf hinge |

FEA | Finite element analysis |

DE | Differential evolutionary algorithm |

NNA | Neural network algorithm |

f | First natural frequency |

## References

- Nowak, J.D.; Rzepiejewska-Malyska, K.A.; Major, R.C.; Warren, O.L.; Michler, J. In-situ nanoindentation in the SEM. Mater. Today
**2010**, 12, 44–45. [Google Scholar] [CrossRef] - Ebenstein, D.M.; Pruitt, L.A. Nanoindentation of biological materials. Nano Today
**2006**, 1, 26–33. [Google Scholar] [CrossRef] - Alderete, N.; Zaheri, A.; Espinosa, H. A Novel In Situ Experiment to Investigate Wear Mechanisms in Biomaterials. Exp. Mech.
**2019**, 59, 659–667. [Google Scholar] [CrossRef] - Hu, Z.; Lynne, K.J.; Markondapatnaikuni, S.P.; Delfanian, F. Material elastic–plastic property characterization by nanoindentation testing coupled with computer modeling. Mater. Sci. Eng. A
**2013**, 587, 268–282. [Google Scholar] [CrossRef] - O’Brien, W. Long-range motion with nanometer precision. Photonics Spectra
**2005**, 39, 80–81. [Google Scholar] - Rabe, R.; Breguet, J.-M.; Schwaller, P.; Stauss, S.; Haug, F.-J.; Patscheider, J.; Michler, J. Observation of fracture and plastic deformation during indentation and scratching inside the scanning electron microscope. Thin Solid Films
**2004**, 470, 206–213. [Google Scholar] [CrossRef] - Ding, B.; Li, Y.; Xiao, X.; Tang, Y.; Li, B. Design and analysis of a 3-DOF planar micromanipulation stage with large rotational displacement for micromanipulation system. Mech. Sci.
**2017**, 8, 117–126. [Google Scholar] [CrossRef][Green Version] - Jiang, C.; Lu, H.; Zhang, H.; Shen, Y.; Lu, Y. Recent Advances on In Situ SEM Mechanical and Electrical Characterization of Low-Dimensional Nanomaterials. Scanning
**2017**, 2017, 1985149. [Google Scholar] [CrossRef] - Gianola, D.S.; Sedlmayr, A.; Mönig, R.; Volkert, C.A.; Major, R.C.; Cyrankowski, E.; Asif, S.A.S.; Warren, O.L.; Kraft, O. In situ nanomechanical testing in focused ion beam and scanning electron microscopes. Rev. Sci. Instrum.
**2011**, 82, 063901. [Google Scholar] [CrossRef][Green Version] - Haque, M.; Saif, M. Application of MEMS force sensors for in situ mechanical characterization of nano-scale thin films in SEM and TEM. Sens. Actuators A Phys.
**2002**, 97–98, 239–245. [Google Scholar] [CrossRef] - Lu, Y.; Ganesan, Y.; Lou, J. A Multi-step Method for In Situ Mechanical Characterization of 1-D Nanostructures Using a Novel Micromechanical Device. Exp. Mech.
**2009**, 50, 47–54. [Google Scholar] [CrossRef] - Xu, Q. Design and testing of a novel multi-stroke micropositioning system with variable resolutions. Rev. Sci. Instrum.
**2014**, 85, 025002. [Google Scholar] [CrossRef] [PubMed][Green Version] - Lu, K.; Zhang, J.; Chen, W.; Jiang, J.; Chen, W. A monolithic microgripper with high efficiency and high accuracy for optical fiber assembly. In Proceedings of the 9th IEEE Conference on Industrial Electronics and Applications, Hangzhou, China, 9–11 June 2014; pp. 1942–1947. [Google Scholar] [CrossRef]
- Putra, A.S.; Huang, S.; Tan, K.K.; Panda, S.K.; Lee, T.H. Design, modeling, and control of piezoelectric actuators for intracytoplasmic sperm injection. IEEE Trans. Control Syst. Technol.
**2007**, 15, 879–890. [Google Scholar] [CrossRef] - Huang, H.; Zhao, H.; Mi, J.; Yang, J.; Wan, S.; Xu, L.; Ma, Z. A novel and compact nanoindentation device for in situ nanoindentation tests inside the scanning electron microscope. AIP Adv.
**2012**, 2, 012104. [Google Scholar] [CrossRef][Green Version] - Huang, H.; Zhao, H.; Mi, J.; Yang, J.; Wan, S.; Yang, Z.; Yan, J.; Ma, Z.; Geng, C. Experimental research on a modular miniaturization nanoindentation device. Rev. Sci. Instrum.
**2011**, 82, 095101. [Google Scholar] [CrossRef] [PubMed] - Zhao, H.; Huang, H.; Fan, Z.; Yang, Z.; Ma, Z. Design, Analysis and Experiments of a Novel in situ SEM Indentation Device. In Nanoindentation in Materials Science; IntechOpen: London, UK, 2012. [Google Scholar] [CrossRef][Green Version]
- Dang, M.P.; Le, H.G.; Le Chau, N.; Dao, T.-P. A multi-objective optimization design for a new linear compliant mechanism. Optim. Eng.
**2019**, 21, 673–705. [Google Scholar] [CrossRef] - Wang, P.; Xu, Q. Design of a flexure-based constant-force XY precision positioning stage. Mech. Mach. Theory
**2017**, 108, 1–13. [Google Scholar] [CrossRef] - Fan, S.; Liu, H.; Fan, D. Design and development of a novel monolithic compliant XY stage with centimeter travel range and high payload capacity. Mech. Sci.
**2018**, 9, 161–176. [Google Scholar] [CrossRef][Green Version] - Wadikhaye, S.; Yong, Y.; Moheimani, S. Design of a compact serial-kinematic scanner for high-speed atomic force microscopy: An analytical approach. Micro Nano Lett.
**2012**, 7, 309–313. [Google Scholar] [CrossRef][Green Version] - Gauthier, M.; Piat, E. Control of a particular micro-macro positioning system applied to cell micromanipulation. IEEE Trans. Autom. Sci. Eng.
**2006**, 3, 264–271. [Google Scholar] [CrossRef][Green Version] - Ding, B.; Yang, Z.-X.; Zhang, G.; Xiao, X. Optimum design and analysis of flexure-based mechanism for non-circular diamond turning operation. Adv. Mech. Eng.
**2017**, 9, 1687814017743353. [Google Scholar] [CrossRef][Green Version] - Ding, B.; Yang, Z.-X.; Xiao, X.; Zhang, G.; Yangd, Z.-X. Design of Reconfigurable Planar Micro-Positioning Stages Based on Function Modules. IEEE Access
**2019**, 7, 15102–15112. [Google Scholar] [CrossRef] - Ding, B.; Zhao, J.; Li, Y. Design of a spatial constant-force end-effector for polishing/deburring operations. Int. J. Adv. Manuf. Technol.
**2021**, 116, 3507–3515. [Google Scholar] [CrossRef] - Deng, L.; Ling, M. Design and integrated stroke sensing of a high-response piezoelectric direct-drive valve enhanced by push–pull compliant mechanisms. Rev. Sci. Instrum.
**2022**, 93, 035008. [Google Scholar] [CrossRef] [PubMed] - Kim, H.-Y.; Ahn, D.-H.; Gweon, D.-G. Development of a novel 3-degrees of freedom flexure based positioning system. Rev. Sci. Instrum.
**2012**, 83, 055114. [Google Scholar] [CrossRef] - Wang, F.; Liang, C.; Tian, Y.; Zhao, X.; Zhang, D. Design and Control of a Compliant Microgripper With a Large Amplification Ratio for High-Speed Micro Manipulation. IEEE/ASME Trans. Mechatron.
**2016**, 21, 1262–1271. [Google Scholar] [CrossRef] - Chang, S.H.; Du, B.C. A precision piezodriven micropositioner mechanism with large travel range. Rev. Sci. Instrum.
**1998**, 69, 1785–1791. [Google Scholar] [CrossRef] - Ling, M.; Howell, L.L.; Cao, J.; Chen, G. Kinetostatic and Dynamic Modeling of Flexure-Based Compliant Mechanisms: A Survey. Appl. Mech. Rev.
**2020**, 72, 030802. [Google Scholar] [CrossRef][Green Version] - Le Chau, N.; Tran, N.T.; Dao, T.-P. Topology and size optimization for a flexure hinge using an integration of SIMP, deep artificial neural network, and water cycle algorithm. Appl. Soft Comput.
**2021**, 113, 108031. [Google Scholar] [CrossRef] - Dang, M.P.; Le, H.G.; Le, N.N.T.; Le Chau, N.; Dao, T.-P. Multiresponse Optimization for a Novel Compliant Z-Stage by a Hybridization of Response Surface Method and Whale Optimization Algorithm. Math. Probl. Eng.
**2021**, 2021, 9974230. [Google Scholar] [CrossRef] - Dang, M.P.; Le, H.G.; Le Chau, N.; Dao, T.-P. Optimization for a Flexure Hinge Using an Effective Hybrid Approach of Fuzzy Logic and Moth-Flame Optimization Algorithm. Math. Probl. Eng.
**2021**, 2021, 6622655. [Google Scholar] [CrossRef] - Yang, X.S.; He, X. Firefly algorithm: Recent advances and applications. Int. J. Swarm Intell.
**2013**, 1, 36–50. [Google Scholar] [CrossRef][Green Version] - Yildiz, A.R. Hybrid Taguchi-differential evolution algorithm for optimization of multi-pass turning operations. Appl. Soft Comput.
**2013**, 13, 1433–1439. [Google Scholar] [CrossRef] - Dinh, V.B.; Le Chau, N.; Le, N.T.P.; Dao, T.-P. Topology-based geometry optimization for a new compliant mechanism using improved adaptive neuro-fuzzy inference system and neural network algorithm. Eng. Comput.
**2021**, 1–30. [Google Scholar] [CrossRef] - Xu, Q. Design, testing and precision control of a novel long-stroke flexure micropositioning system. Mech. Mach. Theory
**2013**, 70, 209–224. [Google Scholar] [CrossRef] - Li, X.; Tian, Y. The design and new controller of a 1-DOF precision positioning platform. In Proceedings of the 2013 International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale, Suzhou, China, 26–30 August 2013; pp. 190–194. [Google Scholar] [CrossRef]
- Le Chau, N.; Tran, N.T.; Dao, T.-P. An Optimal Design Method for Compliant Mechanisms. Math. Probl. Eng.
**2021**, 2021, 5599624. [Google Scholar] [CrossRef]

**Figure 1.**A scheme of proposed nanoindentation [32].

**Figure 14.**Trends of the frequency based on the alteration of the key stage dimensions: (

**a**) first natural frequency with factors G and R, (

**b**) first natural frequency with factors R and S, (

**c**) first natural frequency with factors S and U, (

**d**) first natural frequency with factors U and R, and (

**e**) first natural frequency with factors G, R, S, and U.

**Figure 15.**Trends of the output displacement (input displacement of 52 µm) based on the alteration of the key stage dimensions: (

**a**) output displacement versus G and R, (

**b**) output displacement versus R and S, (

**c**) output displacement versus S and U, (

**d**) output displacement versus U and R, and (

**e**) output displacement versus G, R, S, and U.

**Figure 16.**Trends of the safety factor (input displacement of 52 µm) based on the alteration of the key stage dimensions: (

**a**) safety factor with factors G and R, (

**b**) safety factor with factors R and S, (

**c**) safety factor with factors S and U, (

**d**) safety factor with factors U and R, and (

**e**) safety factor with factors G, R, S, and U.

Symbol | Value | Symbol | Value | Unit |
---|---|---|---|---|

a | 171 | i | 6 | mm |

b | 108 | j | 10 | mm |

c | 82 | k | 5 | mm |

d | 26 | m | 12 | mm |

e | 16 | G | 0.65 ≤ G ≤ 0.75 | mm |

f | 10 | R | 0.5 ≤ R ≤ 0.7 | mm |

g | 22 | S | 0.5 ≤ S ≤ 0.65 | mm |

h | 26 | U | 0.5 ≤ U ≤ 0.6 |

Response | Theory | FEA | Error (%) |
---|---|---|---|

f (Hz) | 176.96 | 195.07 | 9.28 |

Response | Optimal Result | Initial Design Result | Improvement (%) |
---|---|---|---|

f (Hz) | 226.8458 | 176.96 | 28.19 |

Response | Optimal Design | Simulation | Error (%) |
---|---|---|---|

f (Hz) | 226.8458 | 250.01 | 9.27 |

Response | Presented Method | DE | NNA |
---|---|---|---|

f (Hz) | 226.8458 | 226.8456 | 226.8448 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dang, M.P.; Le, H.G.; Tran, N.T.D.; Chau, N.L.; Dao, T.-P. Optimal Design and Analysis for a New 1-DOF Compliant Stage Based on Additive Manufacturing Method for Testing Medical Specimens. *Symmetry* **2022**, *14*, 1234.
https://doi.org/10.3390/sym14061234

**AMA Style**

Dang MP, Le HG, Tran NTD, Chau NL, Dao T-P. Optimal Design and Analysis for a New 1-DOF Compliant Stage Based on Additive Manufacturing Method for Testing Medical Specimens. *Symmetry*. 2022; 14(6):1234.
https://doi.org/10.3390/sym14061234

**Chicago/Turabian Style**

Dang, Minh Phung, Hieu Giang Le, Nguyen Thanh Duy Tran, Ngoc Le Chau, and Thanh-Phong Dao. 2022. "Optimal Design and Analysis for a New 1-DOF Compliant Stage Based on Additive Manufacturing Method for Testing Medical Specimens" *Symmetry* 14, no. 6: 1234.
https://doi.org/10.3390/sym14061234