Studies also examined the effect of the distance between the hinges of two wings on enhancing lift and torque generations

. 1986 The generation of circulation and lift in a rigid two-dimensional fling . J. Fluid Mech . 165, 247–272. (doi:/S0022112086003087) Crossref, ISI, Google Scholar

. 2003 Flows around two airfoils performing fling and subsequent translation and translation and subsequent clap . Acta Mech. Sin . 19, 103–117. (doi:/BF02487671) Crossref, ISI, Google Scholar

. 2005 The aerodynamic effects of wing-wing interaction in flapping insect wings . J. Exp. Biol . 208, 3075–3092. (doi:/jeb.01744) Crossref, PubMed, ISI, Google Scholar

. 2007 Development and testing of the Mentor flapping-wing micro air vehicle . J. Aircraft 44, 1701–1711. (doi:/1.28463) Crossref, ISI, Google Scholar

. 2015 Performance tests of a hovering flapping wing micro air vehicle with double wing clap-and-fling mechanism. In IMAV 2015: Proc. Int. Micro Air Vehicle Conf., Aachen, Germany, 15–18 September. Google Scholar

. 2010 Improving flight performance of the flapping wing MAV DelFly: II. In IMAV 2010: Proc. Int. Micro Air Vehicle Conf., Braunschweig, Germany, 6–8 July, pp. 189–205. Google Scholar

Data accessibility

. 2014 Design, fabrication, and performance test of a hovering-based flapping-wing micro air vehicle capable of sustained and controlled flight. In IMAV 2014: Proc. Int. Micro Air Vehicle Conf., Delft, The Netherlands, 12–15 August, pp. 18–25. (doi:/uuid:38f8dd5b-9999-4359-902c-c68ae3e278f8) Google Scholar

2009 Flow visualization and force measurements on a hovering flapping-wing MAV ‘DelFly II’. In The 39th AIAA Fluid Dyna. Conf., San Antonio, Texas, 22—4035) Google Scholar

. 2010 Characteristics of a beetle’s free flight and a flapping wing system that mimics beetle flight . J. Bionic Eng . 7, 77–86. (doi:/S1672-6529(09)60195-5) Crossref, ISI, Google Scholar

. 2012 Flexible wing kinematics of a free-flying beetle (rhinoceros beetle Trypoxylus dichotomus) . J. Bionic Eng . 9, 177–184. (doi:/S1672-6529(11)60113-3) Crossref, ISI, Google Scholar

. 2013 Improvement of the aerodynamic performance by wing flexibility and elytra–hind wing interaction of a beetle during forward flight . J. R. Soc. Interface 10, 20130312. (doi:/rsif.) Link, ISI, Google Scholar

. 2014 Non-jumping take off performance in beetle flight (rhinoceros beetle Trypoxylus dichotomus) . J. Bionic Eng . 11, 61–71. (doi:/S1672-6529(14)60020-2) Crossref, ISI, Google Scholar

. 2011 A modified blade element theory for estimation of forces generated by a beetle-mimicking flapping wing system . Bioinspir. Biomim . 6, 036008. (doi:-3182/6/3/036008) Crossref, PubMed, ISI, Google Scholar

. 2010 Effects of wing deformation on aerodynamic forces in hovering hoverflies . J. Exp. Biol . 213, 2273–2283. (doi:/jeb.040295) Crossref, PubMed, ISI, Google Scholar

. 2009 Details of insect wing design and deformation enhance aerodynamic function and flight efficiency . Science 325, 1549–1552. (doi:/science.1175928) Crossref, PubMed, ISI, Google Scholar

. 2013 Time-varying wing-twist improves aerodynamic efficiency of forward flight in butterflies . PLoS ONE 8, e53060. (doi:/journal.pone.0053060) Crossref, PubMed, ISI, Google Scholar

. 2015 Effect of wing kinematics modulation on aerodynamic force generation in hovering insect-mimicking flapping-wing micro air vehicle . J. Bionic Eng . 12, 539–554. (doi:/S1672-6529(14)60144-X) Crossref, ISI, Google Scholar

. 2008 Software techniques for two- and three-dimensional kinematic measurements of biological and biomimetic systems . Bioinspir. Biomim . 3, 034001. (doi:-3182/3/3/034001) Crossref, PubMed, ISI, Google Scholar

. 2008 Simulation and parameter variation of flapping-wing motion based on dragonfly hovering . J. AIAA 46, 918–924. (doi:/1.31610) Crossref, Google Scholar

4.5. Discussion

. 2009 Integrated modeling of insect flight: from morphology, kinematics to aerodynamics . Jput. Phys . 228, 439–459. (doi:/j.jcp.) Crossref, ISI, Google Scholar

. 2009 Size effects on insect hovering aerodynamics: an integrated computational study . Bioinspir. Biomim . 4, 015002. (doi:-3182/4/1/015002) Crossref, PubMed, ISI, Google Scholar

. 1984 The aerodynamics of hovering insect flight. IV. Aerodynamic mechanisms . Phil. Trans. R. Soc. Lond. B 305, 79–113. (doi:/rstb.) Link, ISI, Google Scholar

. 2016 Data from: Clap-and-fling mechanism in a www.hookupdate.net/nl/shagle-overzicht/ hovering insect-like two-winged flapping-wing micro air vehicle. Dryad Digital Repository . (doi:/dryad.28713) Google Scholar

Experimental and computational studies have extensively investigated the effect of the clap and fling on the aerodynamic lift generation in insect flight [12,24,33–37]. Miller & Peskin used the immersed boundary method for a low Reynolds number of 10 to investigate the effect of wing flexibility on aerodynamic performance during a clap-and-fling process. The study indicated that the clap-and-fling mechanism in the flexible wing reduced the drag by approximately 50%, while relatively improving the lift when compared with those in a rigid wing. Bennett conducted two-dimensional experiments at a Reynolds number of 83 000 by using a robotic rectangular wing with a vertical wall as a symmetric plane to observe the benefits of the clap-and-fling effect. The measurement indicated that the wing in the presence of vertical plane contributed to an increase of 15% in the total lift when compared with that in the absence of vertical plane. An experimental study on various insects, small birds and bats conducted by Marden reported that flapping wings with the clap-and-fling effect led to an increased lift per unit flight muscle mass of approximately 25% when compared with that of conventional flapping wings without the clap-and-fling motion. Furthermore, a numerical study by Sun & Yu performed a two-dimensional simulation at a Reynolds number of 17 and revealed that the clap-and-fling effect augmented the lift generation when compared with that of a single wing. An increase in the distance from 0.1c to 0.2c (c = wing chord) resulted in a slight decrease in lift but greatly attenuated detrimental torque . The lift and torque enhancements were diminished when the distance approached 1c . Lehmann et al. performed experiments based on the small three-dimensional wing of a Drosophila fruit fly at Reynolds numbers of 100–200, and found that the near-clap-and-fling effect could lead to a lift enhancement of 17% based on wing kinematics.

Figure 1. Snapshot of the kinematics of a rhinoceros beetle’s hind wing at the ends of the upstroke and downstroke during (a) take-off and (b) hovering.

The time histories of the flapping angle and the rotation angles were then obtained from the coordinates of the dots during the flapping motion. The first eight terms of sine and cosine functions were added, and the summation was used as a fitting function to fit the measured time histories of the flapping angle and wing rotation angles, based on the least-square method as expressed below:

Figure 6posite images of two flapping-wing models used for the force measurement. (a) The flapping-wing system with the clap-and-fling effect placed at each stroke reversal and (b) the flapping-wing system with an extended distance between the flapping axes to minimize the effect of the clap and fling.

Figure 8. Distribution of (a) the vertical force or thrust (F_z), (b) horizontal force (F_y) and (c) force in the ?-direction or horizontal drag (F_?) produced by the two flapping-wing systems in a flapping cycle.

Figure 9. Force enhancement due to the clap-and-fling effect in (a) the vertical force or thrust (F_z) and (b) force in the ?-direction or horizontal drag (F_?) in the flapping-wing system.

Figure 11. Plots of swirling strength combined with velocity vector at the wingspan of 0.25R created by the flapping-wing system with the clap-and-fling effect (case A) and without the clap-and-fling effect (case B). LEV, leading edge vortex; TEV, trailing edge vortex; DW, downwash.