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The Flight Mechanism of a Bird-like Flapping Wing Robot at a Low Reynolds Number
The Flight Mechanism of a Bird-like Flapping Wing Robot at a Low Reynolds Number
Ding, Changtao;Yao, Xiating;Liu, Chengyao
Hindawi Journal of Robotics Volume 2022, Article ID 6638104, 17 pages https://doi.org/10.1155/2022/6638104 Research Article TheFlightMechanismofaBird-likeFlappingWingRobotataLow Reynolds Number Changtao Ding , Xiating Yao , and Chengyao Liu Zhejiang Industry Polytechnic College, Shaoxing, Zhejiang 312000, China Correspondence should be addressed to Changtao Ding; email@example.com Received 14 November 2020; Revised 13 March 2022; Accepted 30 March 2022; Published 18 April 2022 Academic Editor: Ramadoni Syahputra Copyright © 2022 Changtao Ding et al. (is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (e ﬂight mechanism of a bird-like ﬂapping wing robot at a low Reynolds number was studied in this study for improving the robot performances. Both the physical model and the kinematic model were ﬁrst established. (e dynamic model of the robot at a low Reynolds number was built with the RANS (Reynolds-averaged Navier-Stokes) equations and the Spalart-Allmaras tur- bulence model. (e ﬂight experiments were carried out and the results were discussed. Lift and drag coeﬃcient curves show that it generates upward lift and forward thrust in the phase that the wing ﬂaps downwards, the rate of the coeﬃcient curves is the biggest when the ﬂapping direction changes. Pressure contours indicate that small vortexes with high pressure values appear at the wing edges. (ere are four velocity vortex groups in total at the front and back of the wing in the velocity contours. Some methods for improving the robot ﬂight eﬃciency and the robot strength as well as the stitching position of the robot skin have been obtained from the above results. (e methods provide the important guidance for the stable ﬂights of the ﬂapping wing robot with the high eﬃciency. of platform body and bat-inspired wings as well as SMA 1. Introduction (Shape Memory Alloy) wires, the wings were connected by A bird-like ﬂapping wing robot has many advantages ﬂexible joints . As shown in Figure 1(a), Chirar- compared with a ﬁxed wing robot and a rotary wing robot. attananon et al., designed a ﬂapping wing robot that was Due to “V” formation and some versatile ﬂight modes, it is equipped with two piezoelectric actuators, and the rotational possible for bird-like robots to ﬂy in an energy-saving way motion of the wing was realized by a linear actuator and a [1–3]. A bird-like ﬂapping wing robot has been widely ﬂexure-based four bar transmission . As shown in applied in aerial photography, disaster rescue, military Figure 1(b), Leys et al., designed a ﬂapping wing robot, the operation and the other ﬁelds. For example, due to simi- wing motion was imitated by an artiﬁcial wing, which can larities between a bird-like ﬂapping wing robot and a real generate harmonic strokes with a large amplitude and a high bird, it becomes possible for the robot Robird to chase away frequency . As shown in Figure 1(c), Grand et al., designed a ﬂapping wing robot whose wing can realize an birds from runways by mimicking a predator . Due to its extensive applications, both models and experiments of the arbitrary trajectory with the high eﬃciency . In spite of robot have been widely studied [5–10]. In spite of the fact the fact that some ﬂapping wing robots have been studied, that some studies have been conducted in recent decades, there are less attention on the high ﬂight eﬃciency and the there are still some challenges from the air ﬂow ﬁelds around robot strength as well as the stitching position of the robot the robot, which are vital to reveal the ﬂight mechanism of skin, and it is critical to design the mechanical model of the the robot [6, 10, 11]. robot based on the above aspects . Researchers have extensively studied the mechanical Researchers have established the kinematic model of models of bird-like ﬂapping wing robots. Bunget et al., bird-like ﬂapping wing robots in recent decades. Bunget designed a bat-like ﬂapping wing robot which was composed et al., analyzed the joint data which were mainly from image 2 Journal of Robotics (a) (b) (c) Figure 1: Several ﬂapping wing robots. where (a) :the robot designed by Chirarattananon; (b) :the robot designed by Leys; (c) :the robot designed by Grand. processing and inverse kinematics, and established the ki- CFD method to analyze the laminar and turbulence ﬂows of nematic model of a bat ﬂapping wing . In , Grand a ﬂapping wing robot, and obtained the aerodynamic eﬃ- et al., obtained the kinematic data from the wing movements ciency of some ﬂapping wing motions . In spite of the to characterize the kinematic model of a robot. In , three fact that some studies have been carried out, the results set kinematic equations were used to describe the motion of obtained with the CFD method are not systematic enough, a ﬂapping wing in the primary and secondary as well as third and the results do not include lift and drag coeﬃcient curves, feathers. Dadashi et al., established the kinematic model of a pressure contours and velocity contours at the same time. Some prototype experiments of ﬂapping wing robots bat-like robot in ﬂight, and represented the kinematics of an articulated ﬂapping wing with the Denavit-Hartenberg have been performed in recent decades [30, 31]. In , the aerodynamic forces of a ﬂapping wing robot were measured convention method . For decades, many researchers have established the in experiments, the results showed that the strong thrust dynamic model of bird-like ﬂapping wing robots. In , the can be obtained by increasing the frequency and reducing averaged dynamic model of a ﬂapping wing robot was the ﬂapping amplitude. Harmon et al., placed some re- established with the force-moment method for describing ﬂective markers on a ﬂapping wing in experiments, and the robot motion. In , the dynamic model of a bird-like used a Vicon measurement system to track the markers for robot was established with the strip theory to calculate the analyzing the wing aerodynamics . In , kinematic data in experiments were obtained by tracking small re- aerodynamic force in the ﬂight. Based on the Euler method, Chirarattananon et al., established the dynamic model of a ﬂective markers on two ﬂapping wings, the data were used to establish ﬂapping membrane wing aerodynamics. In robot to obtain the attitude dynamics, and calculated the total torques imposed on the robot joints . Teoh et al., , the wing shape of a ﬂapping wing robot was optimized considered aerodynamic dampers to establish the improved by taking the overall power eﬃciency as a key objective, and dynamic model of a RoboBee robot . In [22, 23], some the experiments of a 17.2 g robot were used to verify the other methods were also used to establish the dynamic conclusion eﬀectiveness. To date, there are still some model of a ﬂapping wing robot. (e above dynamic models challenges in the ﬂight experiments. For example, it is are mainly applied to the rigid bodies. It is diﬃcult to analyze diﬃcult to measure all the air ﬂow ﬁelds in the robot ﬂights the complex air ﬂow ﬁelds during the robot ﬂight with the due to the lack of a huge equipment. (e experiments are above models. (erefore, it is necessary to establish a dy- usually carried out outdoors, so the environmental pa- rameters usually have some interference to the experiment namic model that is closer to the real ﬂight for obtaining the robot ﬂight mechanism. results. (e complex ﬂight mechanism of a bird-like ﬂapping (e simulation experiments of ﬂapping wing robots have been performed with the CFD (computational ﬂuid dy- wing robot is vital for improving its ﬂight eﬃciency and namics) method. In , air ﬂow ﬁelds of a ﬂapping wing service life as well as stability. It mainly includes two steps to ornithopter were simulated with the CFD method, and the obtain the complex ﬂight mechanism. (e ﬁrst step is to simulation results were consistent with experiments. Su establish the physical model and the kinematic model as well et al., divided the meshes of a bird-like robot and its air ﬂow as the dynamic model of a ﬂapping wing robot. (e second ﬁelds, and used the CFD method to analyze the ground eﬀect step is to conduct simulation experiments and prototype on the robot . Moelyadi et al., obtained the velocity experiments at a low Reynolds number. (e structures of contours of a bird-like robot with the CFD method for this study are as follows: both the physical model and the kinematic model of a bird-like ﬂapping wing robot are analyzing the robot motion characteristics . In , air ﬂow ﬁelds of a robot were simulated with the CFD method, established in Section 2. (e dynamic model of the robot is established in Section 3. In Section 4, the robot ﬂight is and the aerodynamic performances at a low Reynolds number were obtained. In [27, 28], the transient ﬂow ﬁelds simulated with the CFD method, followed by the prototype of ﬂapping wings were analyzed with the CFD method based experiments. Section 5 and Section 6 give the discussion and on an eﬃcient dynamic mesh strategy. Ou et al., used the conclusions of this study respectively. Journal of Robotics 3 2.2. e Kinematic Model. (e movement of the bird-like 2. ThePhysical Modeland theKinematicModel ﬂapping wing robot is shown in Figure 4. (e wings sym- 2.1. e Physical Model. (e physical model of the robot is metrically ﬂap with respect to a middle horizontal plane. (e shown in Figure 2(a). (e robot prototype in Figure 2(b) was wings ﬁrst ﬂap upwards from position 1 (the horizontal built with some outsourced components. (e prototype plane) through position 2 to position 3. (e wings ﬂap includes a body frame, two ﬂapping wings and a tail as well downwards from position 3 through position 4,5,6 to po- as driving mechanism and transmission mechanism, etc. (e sition 7. In the following the wings ﬂap upwards from aerofoil of the robot is a ﬂat plate. (e mass of the robot is position 7 through position 8 to position 9 (the horizontal nearly 600 g, and the maximum load is 220 g. (e wingspan plane). is 1.26 m and the length from head to tail is 0.5 m. In this study, the movement of the rigid wings is sim- As shown in Figure 3, both the wings and the tail are pliﬁed into only up-down ﬂapping. (e kinematic model of driven independently. (e transmission mechanism of the the robot is given as follows [19, 25]: wings is: motor - gear on the motor—gear A1—gear α(t) � A sin(2πft), (1) A2—gear A3—connecting rod—wing bar. Both the gears and the wing bar ﬁx on the body frame with rotation. (e where α(t) is the ﬂapping angle between the wing and the above transmission mechanism drives the wings to ﬂap horizontal plane, A is the ﬂapping amplitude, f is the repeatedly with the high accuracy. (e wing bar is made of ﬂapping frequency and t is the time. carbon ﬁber spars, which are with high strength for resisting strong impact forces. (e transmission mechanism that 3. The Dynamic Model of the Robot drives the tail to swing upwards and downwards is: motor actuator B - connecting rod B1- connecting rod B2- con- (e Reynolds number of a bird-like ﬂapping wing robot is necting rod B3. (e tail swings leftwards and rightwards by 3 5 usually from 5 × 10 to 5 × 10 during its ﬂights . (e controlling motor actuator C. In addition, an electronic RANS equations have been used to simulate complex tur- speed controller receives signals from remote controller to bulence of the robot. (e average ﬂow can be calculated by control the robot ﬂight. RANS equations due to less amount of calculation. (e Table 1 is the components of the ﬂapping wing robot. Spalart-Allmaras model can be used to close the eddy vis- Numbers 1.1–1.9 are components related to the wing cosity models in RANS equations. In this study, RANS movements. Numbers 2.1–2.9 are components related to the equations can be written in the Cartesian tensor forms tail movements. Number 3 is body frame. Numbers 4.1–4.4 [37, 38]: are battery or control components. zρ z + ρu � 0, (2) zt zx zu z z zp z zu 2 zu z i 1 ′ ′ ρu + ρu u � − + μ + − δ + −ρu u , i i j ij i j (3) zt zx zx zx zx zx 3 zx zx j i j j i 1 j √√ √√√√√√√√√√√√√√√√√√ √√√√√√√√√√√√ √√√√√√√√√√√√√ √ √√√√√√√√√√ (b) (a) (c) (d) u � u + u (i � 1, 2, 3), (4) i i i where (a), (b), (c) and (d) are the inertia force, the pressure, the viscous force and the external force acting on the air ﬂow where u denotes the mean velocity component, and u is the i i respectively. u is the ﬂuid velocity. ρ denotes the ﬂuid ﬂuctuating velocity component. density. p is the pressure. μ denotes the dynamic viscosity. δ In this study, the Spalart-Allmaras model is used to close ′ ′ is a delta function. −ρu u is the Reynolds stresses. the RANS equations at a low Reynolds number. (e Spalart- i j (e velocity component u is given as follows: Allmaras model can be expressed as equation (5) : z z 1 z z v z v ⎣ ⎦ ⎡ ⎤ (ρ v) + ρ vu � P + (μ +ρ v) + C ρ − D + T , (5) i v b2 v v zt zx σ zx zx zx i j j j v where v denotes the modiﬁed turbulent viscosity. P is the destruction. Both σ and C are constants. T is a user- v v b2 v turbulent viscosity production. D is the turbulent viscosity deﬁned source term. v 4 Journal of Robotics (a) (b) Figure 2: A bird-like ﬂapping wing robot. where (a): the physical model of the robot; (b): the robot prototype. skin on tail rib in tail rib in ﬂapping wing remote controller skin on ﬂapping wing (a) connecting connecting 12 bits 6 channel gear on the connecting wing bar rod B2 rod B1 receiver motor rod electronic speed controller connecting frame ball joint tail plate motor connecting motor body battery motor gear A1 gear A2 gear A3 actuator C rod B3 actuator B frame (b) Figure 3: (e components of the ﬂapping wing robot. where (a): the robot in global view; (b): the robot in bottom view. Journal of Robotics 5 Table 1: (e components of the ﬂapping wing robot. Number Component Quantity Descriptions 1.1 Motor 1 It drives the movement of two ﬂapping wings. 1.2 Gear on the motor 1 It coaxially ﬁxes with motor and meshes with gear A1. 1.3 Gear A1 1 It meshes with gear on the motor and coaxially ﬁxes with gear A2. 1.4 Gear A2 2 It coaxially ﬁxes with gear A1 and meshes with gear A3. 1.5 Gear A3 2 It meshes with gear A2 and rotationally connects with connecting rod. It rotationally connects with gear A3 at one end, and it rotationally connects with wing bar by 1.6 Connecting rod 2 a ball joint at the other end. 1.7 Wing bar 2 It rotationally connects with connecting rod and ﬁxes with ribs in ﬂapping wing. 1.8 Rib in ﬂapping wing 10 It ﬁxes at wing bar to prop up skin on ﬂapping wing. 1.9 Skin on ﬂapping wing 1 It is propped up by wing bars and ribs in ﬂapping wing. 2.1 Motor actuator B 1 It ﬁxes in body frame and drives the tail to swing upwards and downwards. 2.2 Connecting rod B1 1 It rotationally connects with motor actuator B and connecting rod B2. 2.3 Connecting rod B2 1 It rotationally connects with connecting rod B1 and connecting rod B3. 2.4 Connecting rod B3 1 It rotationally connects with motor actuator B2 and connecting frame. 2.5 Connecting frame 1 It rotationally connects with connecting rod B3 and body frame. 2.6 Motor actuator C 1 It ﬁxes in connecting frame and drives the tail to swing leftwards and rightwards. 2.7 Tail plate 1 It rotationally connects with motor actuator C, and ﬁxes ribs in tail. 2.8 Rib in tail 4 It ﬁxes at tail plate to prop up skin on tail. 2.9 Skin on tail 1 It is propped up by tail plate and ribs in tail. 3 Body frame 1 It is the robot body that ﬁxes components. 4.1 Battery 1 It provides power for motor and motor actuator B as well as motor actuator C. Electronic speed 4.2 1 It connects with battery and 12 bits 6 channel receiver as well as motor. controller 12 bits 6 channel 4.3 1 It connects with electronic speed controller and motor actuator B as well as motor actuator C. receiver 4.4 Remote controller 1 It remotely sends signals to control the robot movements. Figure 4: (e movement of the bird-like ﬂapping wing robot. (e turbulent viscosity production P is given as follows where both C and k are constants. l is the distance from the v b1 : wall. T denotes a scalar measure of the deformation tensor, and λ ≡ v/v. P � C ρT v, (6) (e mean rate-of-rotation tensor ω is modeled as v b1 ij equation (10): v zu T ≡ T + f , (7) 1 zu v2 i 2 2 ω � − . (10) k l ij 2 zx zx j i ������ T ≡ 2ω ω , (8) ij ij (e viscous damping function f can be written as v1 equation (11): f ≡ 1 − , (9) v2 f � , (11) v1 3 3 1 + λf v1 λ + C v1 6 Journal of Robotics Table 2: Some parameter values. where C is a constant. v1 (e turbulent viscosity destruction D is deﬁned as Parameters C C C C C C σ k b1 b2 w1 w2 w3 v1 v equation (12): Values 0.1355 0.622 3.206 0.3 2.0 7.1 2/3 0.4187 v (12) D � C ρf , v w1 w shown in Figure 5(a), unstructured triangular where: meshes were established which can simulate the 1/6 6 robot movements within a short time, and the ﬁle 1 + C w3 (13) f � g , format was saved as.mesh. Details of “mesh” are g + C w3 shown in Figure 5(b) and 5(c). (4) UDF (User-deﬁned function) codes were pro- g � r + C r − r, (14) w2 grammed based on the kinematic model in Section2. (e parameter values in equation (1) were set as follows: the v r ≡ , (15) ﬂapping amplitude A � π/6, the ﬂapping frequency 2 2 Tk l f � 50Hz. (e ﬂuid velocity u � 5m/s. (e Reynolds number was calculated as Re � 7.22 × 10 . where C , C and C are constants. w1 w2 w3 (5) (e meshes in step (3) were imported to ANSYS C can be calculated by equation (16): w1 FLUENT software, and some options for the robot model C 1 + C b1 b2 were set. In the simulation experiments, it is important to C � + . (16) w1 v select the viscous model of the robot and set its parameters. As shown in Figure 6(a), the Spalart-Allmaras model was (e parameter values C , C , C , C , C , C ,σ and b1 b2 w1 w2 w3 v1 v selected, and the parameters in Table 2 were set. Boundary k are given in Table 2 . conditions of velocity inlet were set as Figure 6(b). Velocity Equations (2)–(4) are RANS equations which have been magnitude was set as 5 m/s, X-component of ﬂow direction used to simulate complex turbulence in the robot ﬂights. was set as 0.9848, Y-component of ﬂow direction was set as equations (5) is the Spalart-Allmaras model which is used to 0.17365, speciﬁcation method of turbulence was selected as close the RANS equations. equation (6)–(16) are the details modiﬁed turbulent viscosity, modiﬁed turbulent viscosity of some variables in equation (5). was set as 0.0001 m /s. Some other options for the model (e Reynolds number is deﬁned by equation (17) were also set as follows: the type of solver was set as pressure- [12, 39]: based, the velocity formulation of solver was set as absolute, ρuL wall motion of both head and tail was selected as stationary Re � , (17) wall, shear condition of both head and tail was selected as no slip, roughness constant of both head and tail was set as 0.5. where L is the chord length of the robot. (e UDF codes in step (4) were imported in ANSYS (us, the dynamic model of the robot was established FLUENT software. based on the RANS equations and the Spalart-Allmaras (6) (e position of the ﬂapping wing at each time step model. was solved for obtaining the results in the transient state and steady state. (e post-processing to the results was carried 4. The Flight Experiments out in ANSYS FLUENT software and TECPLOT software. Some results of the robot at a low Reynolds number are Simulation experiments of the robot were performed at a low shown as Figures 7–11. Reynolds number in Section 4.1. Prototype experiments of As shown in Figure 7, the lift and drag coeﬃcient curves the robot were carried out in Section 4.2. are closed as the wing ﬂaps periodically. Most coeﬃcient values are bigger than zero. (e integral of the lift or the drag 4.1. Simulation Experiments. (e steps of the simulation coeﬃcients with respect to the ﬂapping angle is much bigger experiments are given as follows: than zero within a period, which makes the robot ﬂy stably. (e upper parts of two curves describe the phase of ﬂapping (1) A solid model of the ﬂapping wing robot was built in downwards, which generate the eﬀective aerodynamic SOLIDWORKS software, and the ﬁle format was forces. Moreover, the aerodynamic force coeﬃcients become saved as.xt or.step. bigger while the wing ﬂaps downwards, and they are op- (2) (e model ﬁle in step (1) was imported to ANSYS posite while the wing ﬂaps upwards. From Figure 7, it can be DM software on WORKBENCH platform, and the obtained that the integral of the lift coeﬃcient is bigger than calculation domains of both the robot and the air that of the drag coeﬃcient within a period, which indicates ﬂow ﬁelds were set based on real ﬂight situations. the lift is bigger than the drag. In addition, the rate of (3) (e meshes of both the robot and the air ﬂow ﬁelds aerodynamic force curves reaches the biggest value at the were divided in ANSYS MESHING software on upward-downward or downward-upward transition. An air WORKBENCH platform. (e moving meshes are exhaust mechanism should be designed for improving the required to imitate the movements of the wing. As robot ﬂight eﬃciency. (e curve magnitude in Figure 7 is the Journal of Robotics 7 (a) (b) (c) Figure 5: (e meshes of both the robot and the air ﬂow ﬁelds. (a): unstructured triangular meshes; (b) and (c): details of “mesh”. same as references [40, 41], but the curve shapes are diﬀerent surface and below the lower surface, because the volume with the above references. It expresses the relationship near the wing changed rapidly but the air did not escape in between the aerodynamic force coeﬃcients and the ﬂapping time. (ere are the high pressure values at the wing edges angle in Figure 7 more clearly than that in references [40, 41]. that form a small pressure vortex, which is wrapped by It shows that the pressure contours of two wings are several big vortexes. In Figure 8(d), there are two pressure symmetrical with respect to the middle plane from vortex groups with low values below the head connection Figure 8(a) and 8(b). Most pressure values of the lower and tail connection. In Figure 8(e), the pressure value above surface are higher than zero while those of the upper surface the wing is lower than that below the wing, which results in are lower than zero. (e closer to the head, the pressure an upward lift. As the pressure values are high, the strength value becomes the lower in Figure 8(b). In Figure 8(c), there of the wing edges and the head connection as well as the tail are several ellipsoidal pressure vortexes above the upper connection should be increased in order to resist the high ﬂap upwards ﬂap downwards 8 Journal of Robotics (a) (b) Figure 6: (e settings of viscous model and velocity inlet in ANSYS FLUENTsoftware. (a): the settings of viscous model; (b): the settings of velocity inlet. ﬂap downwards ﬂap upwards -1 -2 -30 -20 -10 0 10 20 30 Flapping angle (deg) drag coeﬃcient Li coeﬃcient Figure 7: Lift and drag coeﬃcient curves of the bird-like ﬂapping wing robot. pressure, which has not been mentioned in previous re- ring shapes, and the iso-surfaces in Figures 9(f)–9(h) and search results. (ere are some similar vorticity contours in 9(j)–9(l) resemble the spherical shapes. reference , but it has not mentioned vorticity contours of (ere are several arcs in Figure 10(a), and the air velocity below the wing is much lower than that above the wing. It the robot surfaces, and the speciﬁc values of the vorticity contours have not been given in reference . also shows that the air velocity near the upper surface of the (e shapes of pressure iso-surfaces in Figures 9 are wing is low, which is attributed to the air adhesion to the bilaterally symmetrical with respect to the middle plane. (e wing. (e air velocity gradually becomes lower from the pressure iso-surfaces in Figures 9(a) and 9(b) are similar to inner layer to the outer layer. (e robot is surrounded by the smooth cylinders that are above the ﬂapping wing. (e velocity contours in Figure 10(b). From Figure 10(c), three iso-surfaces in Figures 9(a) and 9(b) are nearly symmetrical velocity vortexes with high values appear above the front of with those in Figures 9(d) and 9(c). (e pressure iso-surfaces the wing, two velocity vortexes with low values locate below in Figures 9(e)–9(h) are nearly symmetrical with those in the front of the wing. (ere are four velocity vortex groups in Figures 9(i)–9(l) due to the opposite ﬂapping direction. (e Figure 10(d) when the wing ﬂaps upwards. Two groups with pressure iso-surfaces in Figures 9(e) and 9(i) resemble the low values locate above the front of the wing and below the Drag and li coeﬃcients Journal of Robotics 9 Z Y -5 -5 -10 -10 -15 -15 -20 -20 -25 -25 -30 -35 -30 -40 -35 -45 -40 -45 (a) (b) 1769.1 1765.57 1580.8 1510.63 1488.71 1471.46 1448.77 1445.4 0.446031 1436.81 -0.297458 1339.49 -1.08815 1332.66 -1.73317 -500 -5 -1000 -10 -1500 -15 -1540.86 -20 -2000 -25 -2500 -30 -3000 -35 -3500 -40 -4000 -45 -4500 -5000 (c) (d) Figure 8: Continued. 10 Journal of Robotics 3151.96 2338.61 2224.3 1838.07 1464.55 1357.5 1270.04 1230.62 933.137 -500 -1000 -1500 -2000 -2500 -3000 -3500 (e) Figure 8: Pressure contours of the ﬂapping wing robot. (a) and (b): the lower and upper surfaces of the robot in the steady state; (c): 3D view along the symmetrical plane in the steady state; (d): 3D view in the transient state when the wing ﬂaps upwards; (e): 3D view in the transient state when the wing ﬂaps downwards. 5 10 10 Y 4 9 9 3 8 8 Y Y 2 7 7 X Z 1 6 6 0 5 5 -1 4 4 -2 3 3 -3 2 2 -4 1 1 -5 0 0 -6 -1 -1 -7 -2 -2 -8 -3 -3 -9 -4 -4 -10 -5 -5 -6 -6 (a) (b) (c) Y Y 9 2000 Z 8 1500 X Z 1000 X 500 5 0 4 -500 -500 3 -1000 -1000 -1500 -1500 -2000 -2000 -2500 -2500 -1 -3000 -3000 -2 -3500 -3500 -3 -4000 -4000 -4 -4500 -4500 -5 -5000 -5000 -6 (d) (e) (f) Figure 9: Continued. Journal of Robotics 11 Y Y -500 -500 -1000 -1000 -1500 -1500 -2000 -2000 -2500 -2500 -500 -3000 -3000 -1000 -3500 -3500 -1500 -4000 -4000 -2000 -4500 -4500 -2500 -5000 -5000 -3000 (g) (h) (i) 5000 5000 5000 4500 4500 4500 4000 4000 4000 3500 3500 3500 3000 3000 3000 X X Z Z 2500 2500 2500 2000 2000 2000 1500 1500 1500 1000 1000 1000 500 500 500 0 0 0 -500 -500 -500 -1000 -1000 -1000 -1500 -1500 -1500 -2000 -2000 -2000 -2500 -2500 -2500 -3000 -3000 -3000 (j) (k) (l) Figure 9: Pressure iso-surfaces of the ﬂapping wing robot. (a), (b), (c) and (d):static pressure P � −4, −1, 1, and 4 (Pa) in the steady static; (e), (f), (g) and (h): static pressure P � 0, 1200, 1850 and 2000 (Pa) when the wing ﬂaps upwards; (i), (j), (k) and (l): static pressure P � 0, 1000, 2000 and 3000 (Pa) when the wing ﬂaps downwards. 7.5 7.5 7 7 6.5 6.5 6 6 5.5 5.5 5 5 4.83111 4.5 4 4 3.5 3.5 3 3 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 0 -0.5 -0.5 -1 -1 -1.5 -1.5 -2 -2 -2.5 -2.5 (a) (b) Figure 10: Continued. 12 Journal of Robotics 7.5 Y 60 6.5 5.5 Z 20 12.5624 4.5 8.78818 1.24908 3.5 0.945573 0.658521 2.5 -1.66106 -1.86795 1.5 -3.92593 -4.46399 0.5 -10 -20 -0.5 -30 -1 -40 -1.5 -50 -2 -60 -2.5 (c) (d) 14.1691 7.6215 6.9974 2.98293 -10 -20 -30 -40 -50 -60 -70 (e) Figure 10: Velocity contours of the ﬂapping wing robot. (a), (b) and (c): right view, top view and front view of the robot in the steady state; (d): front view in the transient state when the wing ﬂaps upwards; (e): front view in the transient state when the wing ﬂaps downwards. at the back of the wing in Figure 11(d). Figures 11(e)– back of the wing. (e other groups with high values are nearly symmetrical with the above groups with respect to the wing. (e 11(h) are velocity iso-surfaces when the wing ﬂaps up- centers of the above vortex groups are closed to the wing. (ere wards. (e shape of the iso-surface in Figure 11(e) likes are also four vortex groups in Figure 10(e) when the wing ﬂaps two silkworms, which locate above the front of the robot downwards, but the positions of the vortex groups are opposite and below the back of the robot. (ere is a very large iso- to those in Figure 10(d). (e robot skin where appears four surface in Figure 11(f). (e iso-surfaces in Figures 11(g) velocity vortex groups should avoid stitching for preventing air and 11(h) also like silkworms, which locate above the back leakages, which has not been proposed in other references. of the robot and below the front of the robot. (e velocity Some velocity contours were given in references [16, 42], but iso-surfaces in Figures 11(i)–11(l) like silkworms, which there were few ﬁgures or lack of speciﬁc velocity values. appear when the wing ﬂaps downwards. (e iso-surfaces In Figure 11(a), there is a long cylindrical iso-surface in Figures 11(i) and 11(j) locate above the back of the robot and below the front of the robot. (e iso-surfaces in above the front of the wing. (e robot is wrapped by a sphere iso-surface in Figure 11(b). (e robot is covered by Figures 11(k) and 11(l) locate above the front of the robot a ﬂat iso-surface in Figure 11(c). (ere is a ﬂat iso-surface and below the back of the robot. Journal of Robotics 13 6 5 6 5.8 X 4.85 5.8 5.6 4.7 5.6 5.4 4.55 5.4 5.2 5.2 4.4 Z 5 4.25 5 4.8 4.1 4.8 4.6 3.95 4.6 4.4 3.8 4.4 4.2 3.65 4.2 4 4 3.5 3.8 3.35 3.8 3.6 3.2 3.6 3.4 3.05 3.4 3.2 2.9 3.2 3 2.75 3 2.8 2.6 2.8 (a) (b) (c) Y Y 5.95 5.9 5.85 Z 5.8 5.75 5.7 -10 5.65 -20 5.6 -30 5.55 -40 5.5 -50 5.45 -60 -10 5.4 -20 5.35 -30 5.3 -40 5.25 -50 5.2 -60 (d) (e) (f) Y Y Y X 40 X 50 40 40 30 30 20 20 10 -10 -20 -10 -30 -10 -20 -40 -20 -30 -50 -30 -40 -60 -40 -50 -60 -50 -70 -60 (g) (h) (i) 80 80 Y 70 70 60 60 50 50 40 40 Z 30 30 20 20 10 10 0 0 -10 -10 -10 -20 -20 -20 -30 -30 -30 -40 -40 -40 -50 -50 -50 -60 -60 -60 -70 -70 -70 (j) (k) (l) Figure 11: Velocity iso-surfaces of the ﬂapping wing robot. (a), (b), (c) and (d): air velocity v � 6, 5, 4.8 and 3 in the steady state; (e), (f), (g) and (h): air velocity v � 0, 5, 6 and 10 in the transient state when the wing ﬂaps upwards; (i), (j), (k) and (l): air velocity v � 0, 4, 6 and 10 in the transient state when the wing ﬂaps downwards. 14 Journal of Robotics 4.2. Prototype Experiments. (e robot prototype experi- wing edges. (ere are four velocity vortex groups in total at ments mainly include the following steps: (1) Before the the front and back of the wing in the velocity contours. With ﬂight experiments of the robot, the mass center of the robot some results in this study, some methods have been obtained was adjusted for ensuring the balance between left part and for improving the robot ﬂight performances. right part, and the tail was kept upwards 30 . (2) When the Referring to references [19, 37–39], the physical model, robot took oﬀ, the wing ﬂapped with the highest frequency, the kinematic model and the dynamic model were separately and the robot ﬂied against the wind to generate the maxi- established in this study. (e 3D physical model with the mum aerodynamic force for taking oﬀ successfully. (3) same parameters as the robot prototype was built in this When the robot ﬂied stably in the sky, the ﬂapping frequency study, which is much nearer to real robots compared with of the wing turned to 1/2 or 2/3 of that in taking oﬀ phase. 1D or 2D model in references [14, 39, 43, 44] (e same as (e robot ﬂied towards diﬀerent direction by adjusting its references [17, 19, 40, 41], the kinematic model of the robot tail. (e robot would turn left or right when the tail turned was established in this study. (e dynamic model was left or right. (4) (e robot ﬂoated down freely at the end of established based on the RANS equations and the Spalart- Allmaras model in this study, which can eﬀectively describe the ﬂight for avoiding severe impacts with the ground. (e ﬂight experiments of the robot are shown in Fig- the air ﬂow ﬁelds around the robot. (e strip method was ure 12, the robot ﬂied stably and freely in the sky at a low used to establish the dynamic model of ﬂapping wing robots Reynolds number. During the ﬂight, the robot repeatedly in references [19, 34, 40, 41, 45, 46], by which the aerody- ﬂapped its wings to generate enough aerodynamic forces, namic forces have been approximately calculated, but the and the robot turned left or right by turning its tail left or results are less accurate than that in this study. In references right. [20, 43, 47, 48], the dynamic model of ﬂapping wing robot (e Reynolds number is mainly determined by ρ u, L, μ was established with the moment equilibrium method, from equation (17). Both the ﬂuid densityρ and the dynamic which can approximately analyze the complex dynamic viscosityμ depend on the external environment. A sunny characteristics, but it is diﬃcult to simulate the air ﬂow ﬁelds environment was chosen in the prototype experiments. An around ﬂapping wings in realities. In summary, both the physical model and the dynamic model are developed in this anemometer was used to measure wind speed and tem- perature. (e ﬂight velocity of the robotu was kept at 5 m/s study compared with the previous research results. by adjusting the remote controller. (e chord length of the (e simulation experiments were carried out in this robot L is a constant. (e parameters ρ u, μ had no big study. (e lift and drag coeﬃcient curves within a period deviation in spite of the fact that there were some small were obtained to describe the aerodynamic forces, both the changes of the external environment, therefore the robot pressure contours and the velocity contours were used to ﬂied at a low Reynolds number. analyze the complex ﬂight mechanism in this study. Some (e remote controller controlled the robot ﬂight by simulation results in this study are similar to those in ref- sending signals to the electronic speed controller at the erence . (e aerodynamic forces of the robot were ground station. (e motor drove the movements of the obtained with some non ﬂuid simulation methods in ref- wings. (e motor was controlled by a handle on the remote erences [19, 34, 40, 41, 45, 46, 49], which have not described the air ﬂow ﬁelds and been less accurate than the results in controller to realize the robot ﬂight in a straight line. (e faster the motor, the faster the robot ﬂied. (e motor ac- this study. In addition, some experiments were performed in tuators drove the movements of the tail. (e motor actuators references [16, 42, 50] but which did not study steady sit- were remotely controlled by another handle to realize the uations and transient situations as well as prototype ex- robot turning. (e faster the motor actuators, the faster the periments together. (e simulation experiments were robot turned a corner. explored more in this study compared with the previous (e robot ﬂight eﬀects were mainly qualitatively eval- research results.(e prototype experiments were carried out uated due to the limitation of experimental conditions. It in this study similar to references [32, 33, 35], and the robot was considered that the robot ﬂight eﬀects were good when ﬂied stably at a low Reynolds number. However, the air ﬂow the robot realized stable ﬂight, otherwise it was considered ﬁelds around the robot have not been measured in the that the ﬂight eﬀects were poor. prototype experiments, and the robot has not ﬂied in some complex situations, e.g., severe weathers. Some methods for improving the robot ﬂight performances have been pro- 5. Discussion posed in this study, which have not been given in the It is important to obtain the complex ﬂight mechanism at a previous research results. In spite of the fact that the complex ﬂight mechanism of low Reynolds number for realizing the stable ﬂights of the robot. Some interesting results have been obtained from the the robot has been analyzed in this study, the following ﬂight experiments. For example, most values of aerodynamic challenges should be further explored: (1) A bird-like robot force coeﬃcient are bigger than zero that generate the prototype should be further optimized with bionics and upward lift and forward thrust. (e eﬀective aerodynamic biomimetics, and a more complex kinematic model includes forces mainly generate in the phase that the wing ﬂaps the relative incidence angle should be established for imi- downwards instead of ﬂapping upwards. (e pressure tating the movement of real birds. (2) Some ﬂight experi- ments should be improved with advanced instruments and contours show the big vortexes wrap the small vortexes, which are usually with high pressure values and closed to the methods, e.g., a camera measurement or a wind tunnel Journal of Robotics 15 Figure 12: Prototype experiments of the robot. should be used to measure the air ﬂow ﬁelds in prototype Some methods for improving the robot ﬂight per- experiments. A quantitative measurement method should be formances have been obtained from the ﬂight experi- adopted to accurately evaluate the robot ﬂight eﬀects. (3)(e ments. (1) As the upward or downward lift mainly complex ﬂight mechanism of the robot under severe generates in the phase that the wing ﬂaps downwards or weathers should be further studied in the future. upwards, an air exhaust mechanism should be designed for improving the robot ﬂight eﬃciency. (2) (e strength of the wing edges and the head connection as well as the 6. Conclusions tail connection should be increased for resisting the high pressure. (3) (e robot skin where appears four velocity (e complex ﬂight mechanism of a bird-like ﬂapping wing vortex groups should avoid stitching in order to prevent robot at a low Reynolds number was studied in this study. air leakages. Both the physical model and the kinematic model of the robot were ﬁrst built, and the dynamic model was also established based on the RANS equations and the Spalart- Data Availability Allmaras turbulence model. (e ﬂight experiments of the robot were performed. (e ﬁgures and estimation results data used to support the Some important results have been obtained from the ﬂight ﬁndings of this study are included within the article. experiments: (1) (e robot ﬂies upwards and forwards mainly because aerodynamic force coeﬃcient is bigger than Conflicts of Interest zero within a period. It is the upward lift and forward thrust when the wings ﬂap downwards. (e rate of the coeﬃcient (e authors declare that there is no conﬂict of interest re- curves reaches the biggest value when the ﬂapping direction garding the publication of this paper. changes. (2) (ere are several pressure vortexes near to the ﬂapping wing, the big vortexes wrapped the small vortexes, Acknowledgments which are with the high pressure values and usually appear at the wing edges. (e above pressure vortexes make the robot (is research was supported by the Joint Funds of the ﬂy forwards. 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Journal of Robotics
Hindawi Publishing Corporation
The Flight Mechanism of a Bird-like Flapping Wing Robot at a Low Reynolds Number
Journal of Robotics
, Volume 2022 –
Apr 18, 2022
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