Three-DoF Flapping-Wing Robot with Variable-Amplitude Link ...

Sato, T., Fujimura, A., and Takesue, N.

Paper:

Three-DoF Flapping-Wing Robot withVariable-Amplitude Link MechanismTerukazu Sato, Akihiro Fujimura, and Naoyuki Takesue

Graduate School of Systems Design, Tokyo Metropolitan University6-6 Asahigaoka, Hino-shi, Tokyo 191-0065, JapanE-mail: {sato-terukazu@ed., ntakesue@}tmu.ac.jp

[Received April 2, 2019; accepted October 21, 2019]

This paper describes the development of a three-degrees-of-freedom flapping-wing robot with avariable-amplitude link mechanism for controllingthe lift and thrust forces acting on it. The variable-amplitude link mechanism comprises a lever-crankmechanism driven by a brushless DC motor and a lin-ear actuator to control the amplitude of the flappingangle. The robot also comprises two DC motors withreduction gears for feathering and lead-lag motion.In our experiments, the measurement of force-torquerevealed the effects of the motion of each wing. Wefound that the flapping-amplitude difference betweenthe left and right wings causes a roll and yaw moment.

Keywords: flapping-wing robot, variable-amplitude linkmechanism, biomimetics

1. Introduction

Recently, researches on flapping flight robots that imi-tate insects and birds have been attracting attention. Suchrobots are also called micro aerial vehicles (MAVs), andhave been previously studied extensively. A bird simulta-neously generates a lift force and a thrust force by flappingits wings and is capable of gliding using a lift force evenwithout flapping if it has the airspeed. Flapping flight hasan excellent motion performance in terms of accelerationand turning, and the corresponding running distance fortakeoff and landing is very short or unnecessary. It alsohas many advantages including the ability to fly quietly.

Unmanned aerial vehicles called drones, which havethe function of automatic operation are used in a varietyof fields such as environmental research, situation grasp-ing in the case of disasters, and bridge inspections. As aresult of improvements in battery-energy density, motorperformance, and control technology, it has become pos-sible to fly a drone loaded with cameras and sensors fora long period of time. However, there still exist problemssuch as limitation of payload and cruising distance, noise,and safety in case of crashing. A flapping-wing robot canbe expected to solve such problems. It can realize energysavings during flight by gliding as described above. Itcan suppress unpleasant noise in the high-frequency range

because it does not require propellers rotating at a highspeed. The lack of the requirement of a propeller alsocontributes to an improvement in safety in the case of acrash.

In addition, the flapping-wing robot is not merely a re-placement for the drone but offers many advantages andhas other new potential applications, including natural-environment investigations that require quiet flight. Itsother applications include safely driving away birds bybeing disguised as a bird that is a natural enemy to manybirds, which is especially useful near airports where theoccurrence of a bird strike is a problem.

As a first step, in order to use the flapping-wing robot inapplications similar to those of the currently used drone,the flapping-wing robot is required to take off to a safealtitude by remote control, fly at a certain speed, and re-turn to the takeoff point and land. Owing to energetic re-searches and developments, robots that can fly through theuse of flapping wings have already been realized. How-ever, there are few cases wherein the robot has realizedself-takeoff, landing, as well as gliding flight. It is con-sidered that this is because it is difficult to independentlycontrol the lift and thrust forces generated by the flap-ping motion and to develop a mechanism that is capableof achieving this control.

In order to control the lift and thrust forces, we developa three-degrees-of-freedom (3-DoF) flapping-wing robotwith a variable-amplitude link mechanism for realizingthe flapping motion and confirm its usefulness.

This paper is structured as follows. Section 2 presentsthe approaches of related researches and the positioningof this research. Section 3 provides a detailed descriptionof the flapping mechanism proposed in this research andpresents the fabricated wing. Section 4 presents an expla-nation of the working of the control system and the exper-imental method. Section 5 presents the experiment resultand a discussion. Section 6 presents the effect of the in-ertia force caused by the wing motion. Section 7 presentsthe conclusions of this study and future challenges.

2. Related Researches

The existing researches on the flapping-wing robothave been conducted mainly using following approaches.

894 Journal of Robotics and Mechatronics Vol.31 No.6, 2019

https://doi.org/10.20965/jrm.2019.p0894

© Fuji Technology Press Ltd. Creative Commons CC BY-ND: This is an Open Access article distributed under the terms of the Creative Commons Attribution-NoDerivatives 4.0 International License (http://creativecommons.org/licenses/by-nd/4.0/).

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Flapping-Wing Robot with Variable-Amplitude Link Mechanism

Fig. 1. Relationship between wingspan and body weight of flapping-wing robot [11].

• Visualization of flow field using particle image ve-locimetry.

• Visualization of flow field using numerical analysis.

• Flapping motion of mechanism.

• Flapping motion by programmed control.

• Wing shape and structure design.

The flow field is visualized not only in the case of birdsand insects [1] but also for a robot [2] and there are casesin which the flow field is modeled for performing nu-merical simulations [3, 4]. The analysis of the flow fieldhas indicated that the leading edge vortex (LEV) greatlycontributes to the lift force generated by the flapping ofwings [5]. However, it is difficult to precisely analyze theflapping motion because it requires a coupled problem tobe solved using unsteady aerodynamic dynamics and theelastic deformation of the wing. To perform a flappingmotion using a mechanism, a rocking motion is realizedusing a link mechanism. A link mechanism that generatesthe appropriate motion, the structure of the wing, and amoderately bent shape of the wing in addition to its de-sign method have also been researched [6]. There ex-ists another approach for developing a propeller with highquietness, while focusing on the shape of the wing of aliving body [7]. The flapping motion realized using pro-grammed control includes a flapping motion performedby a servomotor, a variety of types of motions realizedbased on programs, and the verification of the motionbased on the model. An attempt to apply deep-learningto this problem has recently been made [8]. Other at-tempts that have been made include the generation of flap-ping motion using a central pattern generator and adopt-

ing biomimetics, and an approach to handle a nonlinearmodel of flapping flight using adaptive control and a neu-ral network [9, 10].

Herein, the relationship between the wingspan andbody weight of flapping-wing robots is illustrated inFig. 1 [11]. Interestingly, it suggests the existence of acertain relationship and provides reference values, and itcan thus be used as an index for designing flapping-wingrobots. The majority of studies in this field are focused onthe imitation of birds and insects; however, researches onbats, which are vertebrates, and manta rays, which flap inwater, have also been performed [12, 13]．

For a flapping mechanism that can realize flight, thereexist many examples in which a lever-crank mechanism isdriven by a brushless DC motor (BLDC motor), and theresulting rocking motion is used to realize the flappingmotion [6, 14, 15]. Owing to an aerodynamic force gener-ated by the flapping motion, the wing surface is deformedto generate a passive feathering motion, thereby creatinga thrust force and flight. However, the majority of theforce generated using this method comprises the thrustforce, and it is impossible to continue the flight withoutthe airspeed and a steady lift force generated on the wingsurface. Therefore, it is difficult to initiate flight with-out providing an initial velocity via manual throwing, alaunching mechanism, running, and etc.

For the purpose of generating a large lift force, an at-tempt has been made to realize flapping motion by imitat-ing birds that are capable of hovering, such as humming-birds (Nano Hummingbird [16], etc.), which are capableof realizing takeoff and landing without running. In prin-ciple, the mechanism described above is made vertical.However, this method does not allow for gliding, which is

Journal of Robotics and Mechatronics Vol.31 No.6, 2019 895


Fig. 2. Structure of each joint of flapping-wing robot.

one of the advantages of the use of flapping wings. In re-cent years, in order to solve this problem, an attempt hasbeen made to realize self-takeoff without running and hor-izontal flight by controlling the posture of the robot in theair using the center-of-gravity-shifting mechanism [17].Other attempts include researches on a biomimetics ap-proach, such as takeoff by jumping [18, 19].

In order to realize flapping motion that is close to that ofa bird’s, research has been conducted on a multi-degree-of-freedom flapping mechanism [20]. It is a method inwhich each joint is driven by an actuator such as a servo-motor. With three joints, it is capable of realizing flap-ping, feathering, and lead-lag motion. However, it isnecessary to mount a plurality of servomotors, which in-creases the weight of the robot and makes it difficult toobtain sufficient power for flight.

This study is oriented to a design that realizes multi-ple degrees of freedom while securing a power-to-weightratio by using a hybrid configuration of a BLDC-motor-driven lever-crank mechanism and a built-in servomotor.We developed a flapping-wing robot with the objective ofrealizing self-takeoff without running and gliding flightby enabling the control of the thrust and lift forces, andwe evaluated the flapping-wing motion.

3. Proposed Flapping-Wing Mechanism andRobot

The flight of a bird consists of flapping, which is themotion of moving a wing up and down; feathering, whichis a motion in which the angle of attack of the wing ischanged; and lead-lag, which is a motion in which thewing is moved back and forth. In this research, we devel-oped a robot that realizes these three DoFs. It was antic-ipated that a flapping mechanism that adopts a variable-amplitude link mechanism would have a comparativelycomplicated structure. Thus, we set the design index ofa wingspan as 1.3 m and body weight of 300 g. Fig. 2presents the structure of each joint, and Fig. 3 presents adiagram of the mechanism of one wing. At the end of theflapping axis, which is driven by the variable-amplitude

Fig. 3. Diagram of flapping mechanism.

Table 1. Specifications of flapping-wing robot.

Wingspan [mm] 1350Wing area [cm2] 1598.5

Weight [g] 383 (not including battery)

Fig. 4. Lever-crank mechanism.

link mechanism, a feathering axis and a lead-lag axis wereprovided in this order. The amplitude of the rocking mo-tion is controlled by changing the length of the output linkusing the linear actuator, and this is used for the flappingmotion. The specifications of the produced flapping-wingrobot are listed in Table 1.

3.1. Variable-Amplitude Link Mechanism forFlapping

In this research, we use the lever-crank mechanism forthe purpose of realizing flapping motion. An example ofthe lever-crank mechanism is presented in Fig. 4. It is afour-bar linkage, in which link A is a fixed link, link B isa driving link, link C is an intermediate link, and link D isa driven link, while it is assumed that the length of link Bis shorter than that of link D. When link B rotates aboutthe axis of the rotation pair with link A, link D is engagedin rocking motion. In this mechanism, the amplitude ofthe rocking motion of an angle θ around the axis of therotation pair of links D and A is controlled by changingthe length of link D in Fig. 4, which is used for the flap-ping motion. As there is no general-solution method forobtaining a link ratio from the amplitude, phase, and ve-locity profiles, an appropriate link ratio was obtained viaa computer-aided design simulation. Its specifications arepresented in Table 2. In addition, the length of link Dbecomes variable between 24.2 mm and 43.2 mm owingto the linear actuator described later, and as a result, therocking amplitude of the angle θ could be controlled in



Table 2. Specifications of variable-amplitude link mechanism.

Link A 48.3 mmLink B 17.0 mmLink C 49.0 mmLink D 24.2–43.2 mm

Amplitude 51.7◦–92.1◦ (0.90–1.61 rad)

Fig. 5. Motion of variable-amplitude link mechanism.

the range of 51.7◦ (0.90 rad) to 92.1◦ (1.61 rad). The op-eration of the variable-amplitude link mechanism is pre-sented in Fig. 5. When the extendable portion of the lin-ear actuator is short, the rocking amplitude becomes large,as presented in the left sub-figure of Fig. 5. In contrast,when it is long, the rocking amplitude becomes small, aspresented in the right sub-figure.

The frame component was fabricated by cutting poly-carbonate resin, and the gear was made by machiningpolyacetal resin. The reduction ratio of the gear reduc-tion mechanism is 1 : 51.7. Components such as thejoints were formed using a 3D printer, and a carbon shaftwas used as the rotating shaft in an attempt to reduce theweight of the body.

3.2. Actuator3.2.1. BLDC Motor

The BLDC motor has a small size, light weight, andlarge output as compared with the brush DC motor. Thereare two types of BLDC motors, an inner-rotor type andan outer-rotor type, according to the rotor structure. TheBLDC with a permanent magnet rotor inside the coil is theinner-rotor type, which has a high responsiveness becauseits inertia is small but its torque is small, and the rota-tional speed is great accordingly. The BLDC with a ro-tor covering the outside of the coil is the outer-rotor type,which has a large torque and low rotation, and therefore,it is suitable for use when a large torque is required. Asthe BLDC motor is electrically rectified, the drive circuithas to detect the position of the rotor, and thus a Hall-effect sensor is usually required for this purpose. How-ever, in the case of an application that does not requirecontrollability in a low-speed, the sensorless control ismainly used, which estimates the rotor position based on

Table 3. Specifications of BLDC motor.

MultiStar VspecModel number 2205-2350KV

Rated voltage [V] 11.1–14.8 (Lipo3–4s)Rotation speed

at no load [rpm] 26085 @11.1V (2350KV)

Coil resistance [Ω] 0.077Maximum output [W] 420

Weight [g] 30

Table 4. Specifications of micro DC gear motor.

Name Micro metal gearmotorSpeed reduction ratio 1 : 150 (1 : 150.58)

Rated voltage [V] 12Rotation speedat no load [rpm] 200

Stall torque [mNm] 283Maximum output

(theoretical value) [W] 1.5

Encoder resolution [CPR] 12Weight [g] 9.5

the back-electromotive force. Typical applications of thiscontrol are drones and fans.

In light of the above, we selected an outer-rotor-typesensorless BLDC motor for driving the flapping axis.As this type is widely distributed for drones and radio-controlled airplanes, the majority of them are motors thatare designed to be lightweight and large in output. Fromamong them, we selected the one with a large power-to-weight ratio. The specifications of the BLDC motor arepresented in Table 3.

3.2.2. ServomotorIn general, the servomotor is a motor that is feedback-

controlled and follows an angle command. Servomotorsfor robots or radio controllers are usually not designedto drive an object with a large moment of inertia, suchas the wing of a flapping-wing robot. Furthermore, themajority of small-sized robots are incapable of adjustingthe gain and obtaining angle information. Owing to suchconstraints, our original servomotor design comprises aDC gear motor and a potentiometer. The specifications ofthe DC gear motor are listed in Table 4.

3.2.3. Linear ActuatorThe linear actuator is an actuator that is equipped with

a mechanism that converts the rotational motion of themotor into linear motion. The link length is controlled bya small linear actuator in order to change the amplitudeof the lever-crank mechanism that generates the flappingmotion. The specifications of the linear actuator are listedin Table 5.



Table 5. Specifications of linear actuator.

Model number PQ12-100-6-RSpeed at no load [mm/s] 10

Maximum thrust force [N] 50Stroke [mm] 20

Repetition positioning accuracy [mm] ±0.1Rated voltage [V] 6Stall current [mA] 550

Weight [g] 15

Fig. 6. Appearance of produced wing.

3.3. WingAs hawks have an excellent flight performance and

hunting ability, it is highly likely that they have a high-mobility-type design that is sophisticated. Therefore, thewingspan of 100 to 130 cm of the goshawk is used as areference value in the production of the wing of this robot.While referring [21], the frame is fabricated using a car-bon pipe and carbon rod to obtain a lightweight robot, andthe wing is fabricated by a nylon cloth called lip stop. Itsappearance and dimensions are presented in Fig. 6.

4. Control System of Flapping-Wing Robot

The dedicated control board for this system comprisesa power supply circuit, microcomputer, DC motor driver,and BLDC motor drive circuit. The microcomputer per-forms motor control, angle sensor measurement, etc. andtransmits the obtained results to a personal computer (PC)in a 5 ms cycle. A robot operating system (ROS) wasintroduced on the PC side, and thus, a control systemthat uses a data-visualization and recording function and aparameter-management function was constructed. Fig. 7presents the overall configuration of the control system.

4.1. Control System by ROSThe ROS is a middleware used for a robot developed

by the Open Source Robotics Foundation and is a librarytool group operating on Linux. The ROS has been in-troduced in many robot researches in recent years. TheROS was employed in our system in order to utilize the

Fig. 7. Overall configuration of control system.

data visualization and recording function and the param-eter management function, which are the main functions.In the ROS, a program is developed using a unit called anode, and the data are exchanged via TCP-IP based asyn-chronous communication called topic communication.

4.1.1. Joint Control with ros controlThe ROS can execute control via the ros control li-

brary by describing the structure of the robot in the robotdescription language Unified Robot Description Format(URDF) and setting the input and output along with thehardware abstraction interface hardware interface. In ad-dition, a coordinate transformation library tf carries outprocessing based on the basis of URDF, thus allowing therobot model to be visualized in a three-dimensional visu-alization environment RViz. It is designed to allow themodification and change in hardware and software to beflexibly performed with minimal effort.

The controller of ros control has a PID control loop ofthree types of interfaces of position, speed, and force, andsix types of combinations of control input and output areprepared. Each constant of the PID control is read fromthe parameter server of the ROS, and the PID control isperformed through the hardware interface. As each con-stant of the PID control can be adjusted dynamically usingthe rqt reconfigure tool, the adjustment was performed ona rule-of-thumb basis and a trial-and-error basis. Only thespeed control of the DC motor was carried out in the mi-crocomputer.

4.1.2. Sensor Data Recording by rosbagA rosbag tool is capable of collectively storing and re-

producing all topics of data exchanged on the ROS. Oncombining with RViz, it is possible to efficiently examineand analyze experimental data having been recorded. Italso provides an API for accessing the bag files generatedby rosbag, thereby making data analysis easy.

4.2. Experiment MethodIn the case of self-takeoff without running, we cause

the fixed flapping-wing robot to flap under a variety of



Fig. 8. Appearance of experiment setup.

conditions and examine the effect of each motion andthe usefulness of the variable-amplitude link mechanism.Fig. 8 presents the experiment setup, which includes theflapping-wing robot itself, a force sensor, and a platformon which to fix them. The robot weighs 383 g withoutthe base used for connecting it with the force sensor. Inthe experiment, the PC controls the robot and records thedata. Parameters such as the flapping frequency, feather-ing, and lead-lag amplitude are set by the ROS parameterserver to control each joint. Each joint angle data andforce sensor data are distributed via the topic communi-cation, and all the topic data are recorded by rosbag. Nec-essary data are extracted from the recorded bag file andanalyzed.

The force can be obtained using three components, andin particular, let Fz be the lift force and Fx be the thrustforce observed using the orientation defined in Fig. 2. Asfor the joint angle, the flapping angle is zero when thewing is horizontal with respect to the body, and let the up-stroke direction be positive and the down-stroke directionbe negative. The feathering angle is zero when the wing ishorizontal, and we assume that the direction in which theangle of attack is increased is positive. The lead-lag angleis zero when the leading edge of the wing is parallel withthe Y -axis of the body, and we assume that the directionin which the wing is moved backward is positive.

The flapping-wing robot developed this time exhibitedinsufficient mechanical strength and motor performance,and in the experiment in the next section, we confirmedthe effect of three-DoF by limiting the flapping frequencyto 2 Hz to avoid damaging the mechanism. Experimentsat higher frequencies will be expected to be performed inthe future.

5. Experiment Results and Discussions

5.1. Effect of Flapping Amplitude on Thrust Forceand Lift Force

Figure 9 presents the result obtained on measuring theforce generated on varying the amplitude at a flappingfrequency of 2.0 Hz. The feathering and lead-lag angles

Fig. 9. Thrust and lift forces: flapping amplitude.

Fig. 10. Thrust and lift forces: feathering angle.

were fixed as zero. With an increase in the flapping am-plitude, the change in the lift force Fz was minimal, butthe thrust force Fx increased greatly. The thrust force islikely to be generated mainly by the flapping motion.

5.2. Effect of Feathering Motion on Thrust Forceand Lift Force

In synchronization with the flapping motion at a fre-quency of 2.0 Hz, the flapping motion in which the feath-ering angle was varied from 0 to 1.2 rad in increments of0.2 rad during up-stroke was carried out, and the effectof the feathering motion was examined. The featheringangle during the down-stroke was set as zero. The rela-tionship between the feathering angle and thrust and liftforces is presented in Fig. 10. The average value of thethrust force decreased with a feathering angle of 0.4 radas a peak, while the average value of the lift force exhib-ited an increasing tendency.

Figure 11 presents the time series data of the flappingangle and the thrust and lift forces under the conditions ofthe feathering angle of 0.0 rad and 1.2 rad at up-stroke.It was shown that the negative lift force in the latter halfof the up-stroke, that is, the period in which the flappingangle increases, was suppressed by the feathering motion.

5.3. Effect of Lead-Lag Motion on Thrust and LiftForces

As in the previous section, the lead-lag angle in the up-stroke was varied from 0 to 1 rad in increments of 0.2 rad,and its effect was examined. Fig. 12 indicates that the



(a) Feathering 0.0 rad

(b) Feathering 1.2 rad

Fig. 11. Effect of feathering angle at up-stroke.

Fig. 12. Thrust and lift forces: lead-lag angle.

effect of the lead-lag motion on the thrust and lift forcesis small. Fig. 13 presents the angle of each axis in thelead-lag target angle 0.6 rad plotted in a time series. Atthis time, while the target value of the feathering angleis 0 rad, the feathering angle passively changes approxi-mately −0.1 to 0.2 rad by the effect of the flapping mo-tion. It is considered that the thrust force is generated bythis passive angle change even if the feathering angle tar-get value is zero as presented in Fig. 10.

5.4. Flapping Motion Including Feathering andLead-Lag

We conduct an experiment comprising flapping mo-tion in which the feathering and the lead-lag motion insynchronization with the flapping motion are performed.

Fig. 13. Time series angle data.

Table 6. Thrust-force-emphasized parameter.

Flapping frequency [Hz] 2.0Flapping amplitude [rad] 1.68

Feathering angle during up-stroke [rad] 0.4Feathering angle during down-stroke [rad] −0.4

Lead-lag angle during up-stroke [rad] 0.4

Average thrust force Fx [N] 1.647Average lift force Fz [N] −0.268

Fig. 14. Time series data of flapping motion with thrust-force-emphasized parameter.

From the previous experiment, the parameter in which thethrust force was obtained the most and the parameter inwhich the lift force was obtained the most are combined,and the experiment and comparison are carried out.

5.4.1. Thrust-Force-Emphasized ParameterWe performed the experiment under the condition of a

combination of the parameter in which the obtained thrustforce was found to be maximum. The condition and theresult are presented in Table 6, and the time series dataare presented in Fig. 14. The average lift force is a neg-ative value, but the average thrust force is 1.6 N, and themaximum thrust force is approximately 7 N.

5.4.2. Lift-Force-Emphasized ParameterWe performed the experiment under the condition of

a combination of parameters for which the obtained lift



Table 7. Lift-force-emphasized parameter and experimentresults.

Flapping frequency [Hz] 2.0Flapping amplitude [rad] 1.70

Feathering angle during up-stroke [rad] 1.2Feathering angle during down-stroke [rad] 0.0

Lead-lag angle during up-stroke [rad] 1.0

Average thrust force Fx [N] 0.540Average lift force Fz [N] 0.449

Fig. 15. Time series data of flapping motion with lift-force-emphasized parameter.

force was the greatest. The condition and result are pre-sented in Table 7, and the time series data are presented inFig. 15. The parameter is intended to reduce the negativelift force and improve the average lift force by the feath-ering and lead-lag motion at the time of up-stroke. How-ever, the result is below the average lift force of 0.52 N inthe case of the feathering angle of 1.2 rad in the experi-ment only in the case of the feathering motion (Fig. 10).Therefore, the effects of the feathering and lead-lag mo-tion are considered to have interfered with each other.

5.4.3. Comparison BetweenThrust-Force-Emphasized Parameter andLift-Force-Emphasized Parameter

A comparison of Figs. 14 and 15 indicates that there aresignificant differences in the generation of the thrust andlift forces. In Fig. 14, a positive thrust force is generatedin both the up-stroke and down-stroke, while in Fig. 15,the thrust force in the up-stroke is small. In addition, inFig. 15, the negative lift force during the up-stroke is sup-pressed. In this manner, it was confirmed that the thrustand lift force changed depending on the feathering andlead-lag angles.

A comparison between the two conditions indicatesthat the thrust and lift forces were +1.1 N and +0.7 N,respectively, but in terms of the magnitude of the gen-erated aerodynamic force, it was 1.67 N in the thrust-force-emphasized parameter and 0.7 N in the lift-force-emphasized parameter, which is a difference of more thantwice. These results suggest that the thrust force is rel-atively more likely to be generated than the lift force is.

(a) t = 0.0 s (b) t = 0.1 s (c) t = 0.2 s

(d) t = 0.3 s (e) t = 0.4 s (f) t = 0.5 s

Fig. 16. Sequence of photographs of flapping motion withlift-force-emphasized parameter.

Fig. 17. Body moment: flapping amplitude difference.

The body is fixed, and under the condition of an airspeedof 0 m/s, and the flapping axis and lift-force direction areorthogonal to each other. When the flapping motion is di-vided into two sections of up-stroke and down-stroke, aforce in the negative-lift-force direction is generated bya change in momentum and the air resistance of the airpushed up by the wing surface at the time of the up-stroke.Hence, it is considered that a force in the positive-lift-force direction is hardly generated at the time of the up-stroke. In contrast, the thrust force is generated in theup-stroke and down-stroke by a passive deformation ofthe wing and a substantial feathering motion due to thedisturbance response of the feathering axis angle. Thus,the thrust force is more likely to be generated than the liftforce.

Figure 16 presents a sequence of photographs underthe condition of Table 7 as representative data of thefeathering and the lead-lag motion. The flapping fre-quency is 1.5 Hz.

5.5. Effect of Flapping Amplitude Different onRight and Left

The flapping motion was realized by providing a differ-ence in the flapping amplitude between the right and leftwings. The moment of each axis with respect to the am-plitude difference is presented in Fig. 17. It was indicatedthat the body roll axial moment Mx and the yaw axial mo-ment Mz have an approximately linear relationship with



Fig. 18. Analysis of lever-crank mechanism.

respect to the flapping-amplitude difference Δθ . In gen-eral, the flapping-wing robot realizes turning motion bygenerating a body moment using the orientation of the tailwing, and it is considered that a more agile turning mo-tion can be realized by providing an amplitude differencebetween the right and left wings.

6. Discussions on Effect of Inertia Force

An inertial force is generated by the acceleration in thetranslational direction on a rotating body having a centerof gravity at a position away from the rotation axis center.The effect of the inertial force in the lift-force directionis then examined using a simplified model of the flappingmechanism of this research.

First, we derive the input and output relationship ofthe lever-crank mechanism. As presented in Fig. 18, thelever-crank mechanism is divided into two triangles by anauxiliary line, and the input and output relationship arecalculated using the law of cosines. Let the crank anglebe θ1 as an input, the length of the auxiliary line E isgiven by Eq. (1), and an angle θout of the rocking link asan output is obtained using Eq. (1).

E =√

A2 +B2 −2ABcos(π −θ1) . . . . (1)

θ2 = cos−1(

A2 +E2 −B2

2AE

). . . . . . (2)

θ3 = cos−1(

D2 +E2 −C2

2DE

). . . . . . (3)

θout = θ2 +θ3 . . . . . . . . . . . . . (4)

Next, the flapping motion is discussed. The lever-crankmechanism is installed as presented in Fig. 19. It is fixedat θ0 = 55◦, and θ4 = 125.6◦. As the control system, theflapping angle is defined as zero when the wing is hori-zontal, the flapping angle is offset by π (180◦) to main-tain consistency. The wing having a mass m and centerof gravity rcog from the flapping rotation center performsflapping motion in the Y -Z plane. Here, the wing is a rigidbody, and the moment of inertia and an aerodynamic forceare ignored. The position z of the center of gravity withthe flapping axis as the origin is given by Eq. (5), and theinertia force in the Z-direction is given by Eq. (6).

z = rcog sin (π − (θout −θ0 +θ4)) . . . . . (5)F = mz̈ . . . . . . . . . . . . . . . (6)

Fig. 19. Flapping mechanism using lever-crank mechanism.

Fig. 20. Simulation result of output angle of lever-crankmechanism and inertia force obtained using simple model.

As the wing is installed symmetrically, the force in theY -direction is canceled out, and hence, the inertia forceonly has a component in the Z-direction. We created aprogram using python language and obtained a numericalsolution to Eq. (6). This is presented in Fig. 20. The flap-ping frequency is 2.0 Hz, m = 122 g, and rcog = 68 mmaccording to the parameters of the actual machine. As aresult of the numerical calculation, the maximum value ofthe inertia force was found to be 1.16 N, and the minimumvalue was −2.49 N. The average value was almost zero.

Here, the inertial force was obtained using Eq. (6) onthe basis of the flapping angle measured in the experi-ment. This is presented in Fig. 21. As the inertia force isa second-order differential of the angle data, the noise hasbeen amplified, but the value increases approximately inthe vicinity of the bottom dead center of the down-stroke.The maximum value of the inertia force was 5.62 N, theminimum value was −6.56 N, and the average value wasalmost zero. As there exist a backlash of the gear in anactual mechanism, they become a factor of impact gener-ation at the dead center of a link, and this appears to affectthe inertial force.

From the above discussions, it can be concluded thatthe effect of the inertial force appears superficially in the



Fig. 21. Inertia force calculated from actual flapping angle.

time series data of the lift force but does not affect it onaverage.

In the previous researches such as [22], a passive jointis provided as a flection axis, such that the wing is bentdownward. This is considered to have an effect of moder-ating the speed change of the entire wing when the flap-ping rotation direction changes after the down-stroke. Thebending of the wing is likely to reduce the projection areaof the wing at the time of the up-stroke to suppress thenegative lift force, reduce the moment of inertia of thewing, as well as to suppress the inertial force. If the un-necessary inertia force can be suppressed, it is possible toreduce the load to the motor and reduction gear and to re-duce the design strength of the mechanism. The effect ofthe flection on the inertial force is required to be verifiedthrough a simulation and using an actual machine in thefuture.

7. Conclusions

In this research, we developed a three-DoF flapping-wing robot having a variable-amplitude link mechanismwith the objective of controlling the lift and thrust forces.We have successfully confirmed the improvement in thethrust force due to the increase in the flapping amplitudeand the improvement in the lift force due to the featheringmotion being in synchronization with the flapping motion.However, the majority of the aerodynamic force generatedwas obtained mainly as the thrust force by the flappingmotion, and it became clear that it was difficult to obtaina lift force exceeding its own weight by controlling thefeathering and lead-lag.

It is successfully demonstrated that the variable-amplitude link mechanism proposed in this research is ca-pable of controlling the amplitude independently on theright and left wings even though it is a lever-crank mech-anism and is capable of moment control of the body byproviding a difference in the flapping amplitude of theright and left wings. In addition, it has been successfullyconfirmed that the thrust force increases on increasing theamplitude in a stationary state.

The observation of real birds tells us that they spreadtheir wings at the time of takeoff and immediately afterthat, and they have a relatively small amplitude during

flight. This mechanism, which is capable of controllingthe flapping amplitude, is capable of properly using theflapping amplitude like a bird.

The flapping-wing robot requires machine rigidity thatcan withstand an impact force of the flapping motionwhile it needs to be light in weight. Polycarbonate, knownas a high strength engineering plastic, is used as the mainframe material, but the rigidity of the material itself is nothigh because it is a resin. In the design, the minimumrigidity is ensured by increasing the width and thicknessof the member. To further reduce the weight and increasethe rigidity, it is essential to re-examine the material andstructure.

The flapping-wing robot developed in this research wasnot capable of generating an aerodynamic force exceedingits own weight. Too many degrees of freedom was a factorof the resulting high own weight. In addition, at present,the robot only has the flapping mechanism and the wingdoes not have a tail wing and the fuselage necessary forflight. Thus, it is impossible to compare it with otherflapping-wings of robots and birds, but it is anticipatedthat this robot would become heavier than its present statewhen their weight is also taken into consideration. Fu-ture policies include weight reduction and simplification,which have been attempted by placing emphasis on thethrust force in the aerodynamic force generation and lim-iting it to the flapping motion and the feathering motion.The body attitude is changed by the motion of the wing,the control of the tail wing, etc., which thereby controlthe aerodynamic force vector, and the possibility of therealization of self-takeoff without running and horizontalflight can be examined.

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Name:Terukazu Sato

Affiliation:Master Course Student, Graduate School of Sys-tems Design, Tokyo Metropolitan University

Address:6-6 Asahigaoka, Hino-shi, Tokyo 191-0065, JapanBrief Biographical History:2018- Master Course Student, Graduate School of Systems Design, TokyoMetropolitan University

Name:Akihiro Fujimura

Affiliation:Master Course Student, Graduate School of Sys-tems Design, Tokyo Metropolitan University

Address:6-6 Asahigaoka, Hino-shi, Tokyo 191-0065, JapanBrief Biographical History:2017- Master Course Student, Graduate School of Systems Design, TokyoMetropolitan University2019- Topcon Corporation

Name:Naoyuki Takesue

Affiliation:Associate Professor, Faculty of Systems Design,Tokyo Metropolitan University

Address:6-6 Asahigaoka, Hino-shi, Tokyo 191-0065, JapanBrief Biographical History:2000- Research Associate, Osaka University2003- Assistant Professor, Nagoya Institute of Technology2005- Associate Professor, Nagoya Institute of Technology2008- Associate Professor, Tokyo Metropolitan UniversityMain Works:• “Scissor lift with real-time self-adjustment ability based on variablegravity compensation mechanism,” Advanced Robotics, Vol.30, Issue 15,pp. 1014-1026, 2016.• “Development of Power Assist Crane Operated by Tensional Informationof Dual Wire,” J. Robot. Mechatron., Vol.25, No.6, pp. 931-938, 2013.• “Design and Prototype of Variable Gravity Compensation Mechanism(VGCM),” J. Robot. Mechatron., Vol.23, No.2, pp. 249-257, 2011.• “Kinesthetic Assistance for Improving Task Performance – The Case ofWindow Installation Assist –,” Int. J. Automation Technol., Vol.3, No.6,pp. 663-670, 2009.Membership in Academic Societies:• The Society of Instrument and Control Engineers (SICE)• The Japan Society of Mechanical Engineers (JSME)• The Robotics Society of Japan (RSJ)• The Institute of Electrical Engineers of Japan (IEEJ)• The Japan Society for Precision Engineering (JSPE)• The Institute of Electrical and Electronics Engineers (IEEE)


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