#
High-Lift Mechanism Motion Generation Synthesis Using a Metaheuristic^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Position Analysis of Four-Bar Mechanism

_{1}, r

_{2}, r

_{3}, and r

_{4}and other parameters, which are commonly found in standard mechanics of machinery textbooks as mentioned in [6,7,8]. The coupler point (P) in the global coordinate in Figure 2 can be expressed as

_{P}= x

_{O2}+ r

_{2}cos(θ

_{2}+ θ

_{1}) + L

_{1}cos(ϕ

_{0}+ θ

_{3}+ θ

_{1})

_{P}= y

_{O2}+ r

_{2}sin(θ

_{2}+ θ

_{1}) + L

_{1}sin(ϕ

_{0}+ θ

_{3}+ θ

_{1})

_{O}

_{2}and y

_{O}

_{2}are the coordinate positions of the joint O

_{2}in the global coordinates [6]. The relations of the anglesϕ

_{0}, θ

_{3}, θ

_{4}, and γ and the link lengths r

_{1}, r

_{2}, r

_{3}, and r

_{4}at any crank angle (θ

_{2}) can be found using law of cosine.

## 3. Optimization Problem and Constraint Handling

_{d}(x

_{d}, y

_{d}) and the actual points P(x

_{p}, y

_{p}). The second part of the objective function is in terms of the angular error between target angles (θ

_{3d}) and actual angles (θ

_{3p}). This research focuses only on the motion generation problem type, which is called synthesis without prescribed timing. The input set ofθ

_{2}

^{i}values is also assigned as the design variables. The optimization problem without prescribed timing is then written as:

_{1}, r

_{2}, r

_{3}, r

_{4}) = crank(r

_{2})

_{1}, r

_{2}, r

_{3}, r

_{4}) + 2 max(r

_{1}, r

_{2}, r

_{3}, r

_{4}) < (r

_{1}+ r

_{2}+ r

_{3}+ r

_{4})

_{l}≤ x ≤ x

_{u}

_{1}, r

_{2}, r

_{3}, r

_{4}, L

_{1}, L

_{2}, θ

_{0}, x

_{O2}, y

_{O2}, ${\theta}_{2}^{i}$}

^{T}, N is the number of target points, and x

_{l}and x

_{u}are the lower and upper bounds of the design vector x, respectively. This synthesis problem can represent the behaviour of HLM by properly applying the target points and angles.

Design variables for x are | Limits of the variables: |

x = [r_{1}, r_{2}, r_{3}, r_{4}, L_{1}, L_{2}, x_{O}_{2}, y_{O}_{2}, ${\theta}_{1}$] | 0.01 ≤ r_{1} ≤ 0.3 |

Target points are (x_{d}, y_{d}) and ${\theta}_{3d}$ | 0.01 ≤ r_{2}, r_{3}, r_{4} ≤ 0.5 |

(x_{d}, y_{d}) = [(0.059, 0.0032), (0.0642, −0.0455)] * 1.1173 | −0.1 ≤ L_{1}, L_{2} ≤ 0.2 |

${\theta}_{3d}$ = [0, 24.90] * pi/180 for case 1 | x_{O}_{2} = 0 |

(x_{d}, y_{d}) = [(0.059, 0.00032), (0.0703, −0.0454)] * 1.1173 | −0.05 ≤ y_{O}_{2} ≤ 0.05 |

${\theta}_{3d}$ = [0, 43.52] * pi/180 for case 2 | −60 ≤ ${\theta}_{1}$ ≤ −45 |

## 4. Design Results

## 5. Conclusions and Discussion

## Acknowledgments

## Conflicts of Interest

## References

- Van Dam, C.P.; Shaw, S.G.; Vander Kam, J.C.; Brodeur, R.R.; Rudolph, P.K.C.; Kinney, D. Aero-Mechanical Design Methodology for Subsonic Civil Transport High-Lift Systems. In Proceedings of the RTO AVT Symposium on “Aerodynamic Design and Optimization of Flight Vehicles in a Concurrent Multi-Disciplinary, Ottawa, QC, Canada, 18–21 October 1999. [Google Scholar]
- Liu, P.; Li, D.; Qu, Q.; Kong, C. Two-Dimensional New-Type High-Lift Systems with Link/Straight Track Mechanism Coupling Downward Defection of Spoiler. J. Aircr.
**2019**, 56, 1524–1533. [Google Scholar] [CrossRef] - Monte, A.D.; Castelli, M.R.; Benini, E. A Retrospective of high-lift device technology. Int. J. Aerosp. Mech. Eng.
**2012**, 6, 2561–2566. [Google Scholar] - Zaccai, D.; Bertels, F.; Vos, R. Design methodology for trailing-edge high-lift mechanisms. CEAS Aeronaut. J.
**2016**, 7, 521–534. [Google Scholar] [CrossRef] - Cabrera, J.A.; Nadal, F.; Muñoz, J.P.; Simon, A. Multiobjective constrained optimal synthesis of planar mechanisms using a new evolutionary algorithm. Mech. Mach. Theory
**2007**, 42, 791–806. [Google Scholar] [CrossRef] - Sleesongsom, S.; Bureerat, S. Four-bar linkage path generation through self-adaptive population size teaching-learning based optimization. Knowl.-Based Syst.
**2017**, 135, 180–191. [Google Scholar] [CrossRef] - Sleesongsom, S.; Bureerat, S. Alternative Constraint Handling Technique for Four-Bar Linkage Path Generation. IOP Conf. Ser. Mater. Sci. Eng.
**2018**, 324, 012012. [Google Scholar] [CrossRef] - Sleesongsom, S.; Bureerat, S. Optimal Synthesis of Four-Bar Linkage Path Generation through Evolutionary Computation with a Novel Constraint Handling synthesis. Mech. Mach. Theory
**2018**, 44, 1784–1794. [Google Scholar] [CrossRef] [PubMed] - Lin, W.Y. A GA–DE hybrid evolutionary algorithm for path synthesis of four-bar linkage. Mech. Mach. Theory
**2010**, 45, 1096–1107. [Google Scholar] [CrossRef] - Peñuñuri, F.; Peón-Escalante, R.; Villanueva, C.; Pech-Oy, D. Synthesis of mechanisms for single and hybrid tasks using differential evolution. Mech. Mach. Theory
**2011**, 46, 1335–1349. [Google Scholar] [CrossRef] - Sleesongsom, S.; Bureerat, S. Optimal synthesis of four-bar linkage path generation through evolutionary computation. Res. Appl. Mech. Eng.
**2015**, 3, 46–53. [Google Scholar] - Nariman-Zadeh, N.; Felezi, M.; Jamali, A.; Ganji, M. Pareto optimal synthesis of four-bar mechanisms for path generation. Mech. Mach. Theory
**2009**, 44, 180–191. [Google Scholar] [CrossRef] - Sleesongsom, S.; Bureerat, S. Alternative Constraint Handling Technique for Four-Bar Linkage Motion Generation. IOP Conf. Ser. Mater. Sci. Eng.
**2019**, 501, 012042. [Google Scholar] [CrossRef] - Phukaokaew, W.; Sleesongsom, S.; Panagant, N.; Bureerat, S. Synthesis of four-bar linkage motion generation using optimization algorithms. Adv. Comput. Des.
**2019**, 4, 197–210. [Google Scholar]

**Figure 1.**Four-bar linkage in the global coordinate system [1].

Case | Position (xi, yi) * 1.1173 | Angle, δi (°) |
---|---|---|

1. Take-off | (0.059,0.0032), (0.0642, −0.0455) | 0, 24.90 |

2. Landing | (0.059,0.00032), (0.0703, −0.0454) | 0, 43.52 |

TLBO | Parameters | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

r_{1} | r_{2} | r_{3} | r_{4} | L_{1} | L_{2} | x_{0} | y_{0} | θ_{1} | Mean | Max | Min | std | |

Case-1 | 0.2997 | 0.0381 | 0.2192 | 0.3989 | 0.0468 | 0.1724 | 0 | −0.0500 | −59.9423 | 0.023221 | 0.023425 | 0.02297 | 7.21 × 10^{−5} |

Case-2 | 0.2999 | 0.0100 | 0.0232 | 0.2993 | −0.0853 | −0.0637 | 0 | −0.0500 | −48.2343 | 0.138061 | 0.138456 | 0.137642 | 0.000243 |

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chabphet, P.; Santichatsak, S.; Thalang, T.N.; Sleesongsom, S.; Bureerat, S.
High-Lift Mechanism Motion Generation Synthesis Using a Metaheuristic. *Proceedings* **2019**, *39*, 5.
https://doi.org/10.3390/proceedings2019039005

**AMA Style**

Chabphet P, Santichatsak S, Thalang TN, Sleesongsom S, Bureerat S.
High-Lift Mechanism Motion Generation Synthesis Using a Metaheuristic. *Proceedings*. 2019; 39(1):5.
https://doi.org/10.3390/proceedings2019039005

**Chicago/Turabian Style**

Chabphet, Poothanet, Supanat Santichatsak, Tunnatorn Na Thalang, Suwin Sleesongsom, and Sujin Bureerat.
2019. "High-Lift Mechanism Motion Generation Synthesis Using a Metaheuristic" *Proceedings* 39, no. 1: 5.
https://doi.org/10.3390/proceedings2019039005