本研究根據歐洲椋鳥(Sturnus vulgaris)外型、尺寸及飛行模式設計並製作一翼尖開衩之拍撲實驗機構，利用風洞實驗探討翼尖型態對於飛行過程所造成的阻力變化。此機構模仿椋鳥單邊翅膀結構與動作，由四個可分別操控之自由度，可高度模擬鳥類拍撲過程中羽毛的開合所造成的翼尖型態變化。在低雷諾數條件與高機動性、高穩定性的需求下，翼尖降阻的議題相當重要，本研究挑選具有明顯開衩翼尖的歐洲椋鳥，根據真實椋鳥飛行動作設定其四個關節自由度的運動方式，將影響翼尖間隙大小的羽毛開合角作為應變變因，定義出五種情況之羽毛開合係數(C)，此係數直接影響到羽毛開合速度和羽翼面積極值，並探討羽毛開合角於五種情況時的機構動作驗證與阻力效應。實驗首先將機構拍撲時翅膀上的特徵點，經過直接線性轉換法(Direct Linear Transformation)轉換成四個關節自由度做動作驗證，再來利用Denavit-Hartenberg Convention得到機構拍撲時翅膀的有效攻角理論值，與動作驗證及阻力量測值做比較，緊接著用CATIA機構設計圖和MATLAB邊緣偵測方式，把羽毛翼面積在開合動作下的不規則變化做定量分析，最後，將風洞實驗的量測值扣除真空艙實驗的慣性力後，得到拍撲週期內的阻力變化。結果顯示，四個關節自由度的動作高度相關性表明了此機構之可控程度，且在阻力量測方面，羽毛開合係數 C = 2.5 的情況不但在上下拍反轉期間具有最大推力峰值，更是唯一一個在整個週期平均下具有正推力的情況，因此本研究發現，翼尖開合速度越快的情況可產生較佳的阻力值，且在羽毛開合係數 C = 2.5 的情況為最理想，故推測此飛行模式最接近真實椋鳥情況，然而翼尖開合速度並不能無限上綱地增加，羽毛開合係數 C = 3.0 即為一例。期望未來在仿生拍撲翼微飛行器的發展中，本研究能提供設計參考一個方向，甚至以此為基礎更進一步探討翼尖開衩的暫態氣動力效應。

Recently, several researchers have focused on investigating aerodynamic effects upon different wingtip configurations in order to simulate bird wing in gliding flight to reduce drag and dissipate wingtip vortex. However, the most primary power resource of bird flight is flapping motion, and there are few researches exploring dynamics wingtip motion in flapping state. In this study, a novel flapping-wing robot with slotted wingtip was designed and fabricated to replicate forward motion of European starling (Sturnus vulgaris) for kinematics analysis and drag measurement in wind tunnel. The robot imitated dynamic morphology of starling’s unilateral wing with four degrees of freedom in cruising flight. Five feather-position-coefficients (C) were defined to investigate the aerodynamic effect caused by the different spreading speed of feathers and the distinct variation rate of wing area. The kinematics of the robot was verified using direct linear transformation (DLT) which confirmed that the wing motion had highly correlated with the desired motion. In all cases with different feather-position-coefficients (C), we found the significant drag reduction at the phase of stroke reversal due to the decrease of projected wing area and the backward feather motion. We also found that in the case C = 2.5, the total drag generated by the robot is the least and it’s negative which means it’s the only case provided the net thrust over a whole flapping period. Therefore, we concluded that the increment of feather-position-coefficients should be appropriately not excessively. Case C = 2.5 had the best drag performance, which was also the most similar to starling’s flapping mode. Further investigation such as PIV analysis or elastic effect can be beneficial work to gain insight into unsteady aerodynamics of slotted wingtip.

[1]H. Rajabi, N. Ghoroubi, K. Stamm, E. Appel, and S. Gorb, "Dragonfly wing nodus: A one-way hinge contributing to the asymmetric wing deformation," Acta Biomater, vol. 60, pp. 330-338, Sep 15 2017, doi: 10.1016/j.actbio.2017.07.034.
[2]E. Williams and J. Swaddle, "Moult, flight performance and wingbeat kinematics during take‐off in European starlings Sturnus vulgaris," Journal of Avian Biology, vol. 34, pp. 371-378, 2003, doi: 10.1111/j.0908-8857.2003.02964.x.
[3]J. Dacles-Mariani, G. Zilliac, J. Chow, and P. Bradshaw, "Numerical/experimental study of a wingtip vortex in the near field," AIAA Journal, vol. 33, no. 9, pp. 1561-1568, 1995, doi: 10.2514/3.12826.
[4]S. Gunasekaran and T. Gerham, "Effect of Chordwise Slots on Aerodynamic Efficiency and Wingtip Vortex," AIAA Journal, vol. 56, no. 12, pp. 4752-4767, 2018, doi: 10.2514/1.J057073.
[5]R. Fox and A. M. Donald, "Introduction to fluid mechanics," 1985.
[6]A. Hedenstrom and F. Liechti, "Field estimates of body drag coefficient on the basis of dives in passerine birds," J Exp Biol, vol. 204, pp. 1167-1175, 2001.
[7]B. Ponitz, A. Schmitz, D. Fischer, and H. Bleckmann, "Diving-flight aerodynamics of a peregrine falcon (Falco peregrinus)," PLoS One, vol. 9, no. 2, p. e86506, 2014, doi: 10.1371/journal.pone.0086506.
[8]B. Ponitz, M. Triep, and C. Brücker, "Aerodynamics of the Cupped Wings during Peregrine Falcon’s Diving Flight," Open Journal of Fluid Dynamics, vol. 04, no. 04, pp. 363-372, 2014, doi: 10.4236/ojfd.2014.44027.
[9]P. Henningsson and A. Hedenström, "Aerodynamics of gliding flight in common swifts," J Exp Biol, vol. 214, no. Pt 3, pp. 382-93, Feb 1 2011, doi: 10.1242/jeb.050609.
[10]M. KleinHeerenbrink, L. C. Johansson, and A. Hedenström, "Multi-cored vortices support function of slotted wing tips of birds in gliding and flapping flight," J R Soc Interface, vol. 14, no. 130, May 2017, doi: 10.1098/rsif.2017.0099.
[11]M. Rosén and A. Hedenstrom, "Gliding flight in a jackdaw - a wind tunnel study," J Exp Biol, vol. 204, pp. 1153-1166, 2001.
[12]D. Chin and D. Lentink, "Flapping wing aerodynamics: from insects to vertebrates," J Exp Biol, vol. 219, no. Pt 7, pp. 920-932, Apr 2016, doi: 10.1242/jeb.042317.
[13]E. Gutierrez, D. B. Quinn, D. D. Chin, and D. Lentink, "Lift calculations based on accepted wake models for animal flight are inconsistent and sensitive to vortex dynamics," Bioinspir Biomim, vol. 12, no. 1, p. 016004, Dec 6 2016, doi: 10.1088/1748-3190/12/1/016004.
[14]P. Phlips, R. East, and N. Pratt, "An unsteady lifting line theory of flapping wings with application to the forward flight of birds," Journal of Fluid Mechanics, vol. 112, pp. 97-125, 1981, doi: 10.1017/S0022112081000311.
[15]J. Birch and M. Dickinson, "Spanwise flow and the attachment of the leading-edge vortex on insect wings," Nature, vol. 412, pp. 729-733, 2001.
[16]J. Birch and W. Dickson, "Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers," J Exp Biol, vol. 207, no. Pt 7, pp. 1063-72, Mar 2004, doi: 10.1242/jeb.00848.
[17]S. Sane and M. Dickinson, "The control of flight force by a flapping wing - lift and drag production," J Exp Biol, vol. 204, pp. 2607-2626, 2001.
[18]J. Birch and M. Dickinson, "The influence of wing-wake interactions on the production of aerodynamic forces in flapping flight," J Exp Biol, vol. 206, no. Pt 13, pp. 2257-72, Jul 2003, doi: 10.1242/jeb.00381.
[19]M. Dickinson, F. Lehmann, and S. Sane, "Wing rotation and the aerodynamic basis of insect flight," Science, vol. 284, no. 5422, pp. 1954-1960, 1999, doi: 10.1126/science.284.5422.1954.
[20]S. Sane and M. Dickinson, "The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight," Journal of Experimental Biology, vol. 205, pp. 1087-1096, 2002.
[21]L. Miller and C. Peskin, "Flexible clap and fling in tiny insect flight," J Exp Biol, vol. 212, no. 19, pp. 3076-90, Oct 1 2009, doi: 10.1242/jeb.028662.
[22]S. Sane, "The aerodynamics of insect flight," J Exp Biol, vol. 206, no. Pt 23, pp. 4191-208, Dec 2003, doi: 10.1242/jeb.00663.
[23]M. Sohn and J. Chang, "Visualization and PIV study of wing-tip vortices for three different tip configurations," Aerospace Science and Technology, vol. 16, no. 1, pp. 40-46, 2012, doi: 10.1016/j.ast.2011.02.005.
[24]D. Miklosovic, "Analytic and Experimental Investigation of Dihedral Configurations of Three-Winglet Planforms," Journal of Fluids Engineering, vol. 130, no. 7, 2008, doi: 10.1115/1.2948372.
[25]R. Nandi, M. Assad-Uz-Zaman, M. Rabbi, and M. Mashud, "Experimental investigation of an aircraft wing model using slotted winglet," IEEE, 2014.
[26]L. Zhao, S. Shkarayev, and E. Su, "Aerodynamics of a Wing with a Wingtip Flapper," Fluids, vol. 3, no. 2, 2018, doi: 10.3390/fluids3020029.
[27]P. Panagiotou, G. Ioannidis, I. Tzivinikos, and K. Yakinthos, "Experimental Investigation of the Wake and the Wingtip Vortices of a UAV Model," Aerospace, vol. 4, no. 4, 2017, doi: 10.3390/aerospace4040053.
[28]A. Beechook and J. Wang, "Aerodynamic analysis of variable cant angle winglets for improved aircraft performance," 2013.
[29]R. Cosin, F. Catalano, and L. Correa, "Aerodynamic analysis of multi-winglets for low speed aircraft," 2010.
[30]M. Lynch, B. Mandadzhiev, and A. Wissa, "Bioinspired wingtip devices: a pathway to improve aerodynamic performance during low Reynolds number flight," Bioinspir Biomim, vol. 13, no. 3, p. 036003, Mar 20 2018, doi: 10.1088/1748-3190/aaac53.
[31]V. Tucker, "Gliding birds - reduction of induced drag by wing tip slots between the primary feathers," Journal of Experimental Biology, vol. 180, pp. 285-310, 1993.
[32]Y. Inada, D. Watanabe, and J. Kurihara, "Effect of gap between primary feathers on bending moment of a bird-like assembled wing," Journal of Aero Aqua Bio-mechanisms, vol. 3, 2013.
[33]N. Siddiqui, M. Aldeeb, and W. Asrar, "Experimental investigation of a new spiral wingtip," International Journal of Aviation, Aeronautics, and Aerospace, 2018, doi: 10.15394/ijaaa.2018.1213.
[34]G. Sachs and M. Moelyadi, "Effect of slotted wing tips on yawing moment characteristics," J Theor Biol, vol. 239, no. 1, pp. 93-100, Mar 7 2006, doi: 10.1016/j.jtbi.2005.07.016.
[35]B. K. v. Oorschot, H. K. Tang, and B. W. Tobalske, "Phylogenetics and ecomorphology of emarginate primary feathers," J Morphol, vol. 278, no. 7, pp. 936-947, Jul 2017, doi: 10.1002/jmor.20686.
[36]B. v. Oorschot and E. Mistick, "Aerodynamic consequences of wing morphing during emulated take-off and gliding in birds," J Exp Biol, vol. 219, no. Pt 19, pp. 3146-3154, Oct 1 2016, doi: 10.1242/jeb.136721.
[37]B. K. v. Oorschot, R. Choroszucha, and B. W. Tobalske, "Passive aeroelastic deflection of avian primary feathers," Bioinspir Biomim, vol. 15, no. 5, p. 056008, Jul 22 2020, doi: 10.1088/1748-3190/ab97fd.
[38]E. Chang, L. Y. Matloff, A. K. Stowers, and D. Lentink, "Soft biohybrid morphing wings with feathers underactuated by wrist and finger motion," Science Robotics, vol. 5, no. .8, 2020, doi: 10.1126/scirobotics.aay1246.
[39]L. Matloff, E. Chang, T. Feo, L. Jeffries, and A. S. C. T. D. Lentink, "How flight feathers stick together to form a continuous morphing wing," Science, vol. 367, no. 6475, pp. 293-297, 2020, doi: 10.1126/science.aaz3358.
[40]F. Nickols and Y. Lin, "Feathered tail and pygostyle for the flying control of a bio-mimicking eagle bird robot," IEEE, 2017, doi: 10.1109/ICCIS.2017.8274837.
[41]J. Bahlman and S. Swartz, "Design and characterization of a multi-articulated robotic bat wing," Bioinspir Biomim, vol. 8, no. 1, p. 016009, Mar 2013, doi: 10.1088/1748-3182/8/1/016009.
[42]陳威瀚, "以多自由度仿生撲翼機構分析雀類腕關節折曲運動於懸停飛行之氣動力效應," 碩士論文, 2020.
[43]R. George, "Design and analysis of a flapping wing mechanism for optimization," 2011.
[44]R. Hartenberg and J. Denavit, "A kinematic notation for lower pair mechanisms based on matrices," Journal of Applied Mechanics, vol. 77, pp. 215-221, 1955.
[45]Ben-Gida, H. Stalnov, O. Guglielmo, C. G. Kopp, G.A., and G. R., "Unsteady aerodynamics loads during flapping flight of birds; case study - starling and sandpiper," 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, 2016.