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Development of a bio-inspired transformable robotic fin

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2016 Bioinspir. Biomim. 11 056010

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Bioinspir. Biomim. 11 (2016) 056010 doi:10.1088/1748-3190/11/5/056010

PAPER

Development of a bio-inspired transformable robotic fin

YikunYang1, YuXia1, FenghuaQin2,MinXu1,Weihua Li3 and ShiwuZhang1,4

1 Department of PrecisionMachinery and Precision Instrumentation, University of Science andTechnology of China,Hefei, Anhui230027, People’s Republic of China

2 Department ofModernMechanics, University of Science andTechnology of China,Hefei, Anhui 230027, People’s Republic of China3 School ofMechanical,Materials andMechatronic Engineering, University ofWollongong,Wollongong, NSW2522, Australia4 Author towhomany correspondence should be addressed.

E-mail: ykyang@mail.ustc.edu.cn, xy1993@mail.ustc.edu.cn, qfh@ustc.edu.cn, xumin@ustc.edu.cn, weihuali@uow.edu.cn andswzhang@ustc.edu.cn

Keywords: transformable roboticfin, thrust force, efficiency, controllingmode

AbstractFish swimby oscillating their pectoral fins forwards and backwards in a cyclicmotion such that theirgeometric parameters and aspect ratios change according to how fast or slow afishwants to swim;these complexmotions result in a complicated hydrodynamic response. This paper focuses on thedynamic change in the shape of a fin to improve the underwater propulsion of bio-inspiredmechanism. To do this, a novel transformable robotic finhas been developed to investigate how thischange in shape affects the hydrodynamic forces acting on thefin. This robotic fin has amulti-linkframe and aflexible surface skinwhere changes in shape are activated by a purpose designedmulti-linkmechanismdriven by a transformationmotor. A drag platformhas been designed to study theperformance of this variable robotic fin.Numerous experiments were carried out to determine howvarious controllingmodes affect the thrust capability of thisfin. The kinematic parameters associatedwith this roboticfin include the oscillating frequency and amplitude, and the drag velocity. Thefin hasfourmodes to control the cyclicmotion; these were also investigated in combinationwith the variablekinematic parameters. The results will help us understand the locomotion performance of thistransformable robotic fin.Note that different controllingmodes influence the propulsive perfor-mance of this robotic fin, whichmeans its propulsive performance can be optimized in a changingenvironment by adapting its shape. This study facilitates the development of bio-inspired unmannedunderwater vehicles with a very high swimming performance.

1. Introduction

Fish are an intrinsic part of the marine kingdom, so itis no surprise that their graceful swimming hasattracted the attention of researchers while providing avast amount of inspiration and imagination fordesigning and developing robotic fish [1–4]. Notunnaturally, the wide variety of fish and their variousshaped fins were created to perfectly fit their marineenvironment. This wide variety of fin forms wasdesigned for different modes of underwater propul-sion. For instance, the caudal fins act as a dominantpropeller with the pectoral fins, the dorsal fins andother fins assist in the body and caudal fin modes, thepectoral fin is the main propeller for the median and/or paired fin modes, while the dorsal fin and anal finmay be used to assist body position and stability in

motion [5, 6]. Due to their prominent and multipleroles in propulsion and maneuvering, many studieshave been carried out on fins, including their physiol-ogy, morphology, and kinematics, in order to adapttheir structure and propulsive performance [7–12], toroboticfins [13–17].

Fish fins undergo large changes in shape duringswimming. Lauder et al studied theflexible pectoral finand caudal fin of bluegill sunfish during steady for-ward swimming and maneuvering motions [18–20],and found that fins exhibit complicated forms, whe-ther in cruising ormaneuveringmode that may be dueto the active control of the fin ray or the passive altera-tion due to flexibility. Webb studied the form andfunction of fish while swimming and summed up thespecial roles played by caudal fins with differentshapes. For example, a crescent fin is suitable for

RECEIVED

23April 2016

REVISED

16 July 2016

ACCEPTED FOR PUBLICATION

25 July 2016

PUBLISHED

31August 2016

© 2016 IOPPublishing Ltd

cruising; a trapezoid fin is better for accelerating; and afan fin is good at maneuvering [21]. Their researchinspired the development of a new technique for pro-pulsion bymimicking biological fish.

Many bio-inspired and bio-mimetic robotic fisheshave been developed to swim underwater; roboticfishes that mimic fishes from carangiform to ostracii-form are popular where faster swimming is required[22–28]. The propulsive force of these robotic fish ismainly generated by the caudal fin [29], so the shape ofa robotic fin, particularly its aspect ratio, has an enor-mous effect on the propulsive force [30]. These factshave inspired researchers to develop robotic fish thatcan alter the shape of their fins to improve propulsionperformance. The typical attempts include applyingflexible foils on robotic fish [31–35], varying the sur-face area of the fin [36], and imitating structure of thebony fin [37–43], i.e. constructing the robotic fin withfin rays and membrane. The biomimetic structureenables the robotic fins to drive fin rays and perform acomplex three-dimensional deformation during theoscillation to improve propulsion. However, in mostsituations, the shapes of robot fin, especially the aspectratio of the fin, cannot be changed during swimming.In this paper, we report the design and implementa-tion of a transformable robotic fin that can vary itsaspect ratio smoothly and gradually during one cycleof propulsion. The robotic fin can fulfill three kinds oftypical homocercal shapes, that is, fan, trapezoid, andcrescent [21]. The detailed design and experimentscarried out on this robotic fin are presented here.Developing this transformable fin shed light on theapplications of an adaptive robotic fish in complex andchanging environments.

The reminder of the paper is organized as follows:section 2 presents the design of the transformable finthat can synchronously oscillate and transform. Theexperimental platform is explained. Sections 3 and 4present the experimental results of the finwith variouskinematic parameters and controlling modes.Section 5 concludes the study.

2.Materials andmethods

To improve the adaptation of a robotic fish to complexand continuously changing environments, transform-ing the robotic fin is an effective option for underwaterpropulsion.

2.1.Design of the transformable roboticfinThe structure of this robotic fin is shown in figure 1,and indicates how its shape can be changed by pushingor pulling the driving rod. It consists of a rigid multi-link frame and a flexible surface skin. The frame ismade from carbon fiber, because it is light and verystrong. The surface skin is made from a rubbermembrane that can deformwithout rupturing. Thefinchanges shape as the non-elastic cable connected to

the driving rod and transform motor is pulled; theelasticity in the surface skin also provide a restorativeforce as the robotic fin returns to its normal shape.

The design objective here is to gradually andsmoothly transform a robotic fin from a crescent to afan shape via the multi-linked mechanism shown infigure 1(a). As the driving rod moves along the keelrod, themulti-linked structure moves with the drivingrod and changes the shape of the fin. Figure 1(b) showsthis transformation process. The driving rod is drivenby a non-elastic cable that moves smoothly along thekeel rod so the fin can continuously transform fromcrescent to fan.

To calculate the change in the surface area and theaspect ratio of the robotic fin, we divided the fin intofour parts, as shown in figure 2; S1, S2, S3, and S4. Thearea can be calculatedwith the following equations.

aa

a

= + = ´ + +

´= ´ ´

= ´ ´

= + + + ´

S x n b S c b x n

S c d

S e f

S S S S S

1

2;

1

2

sin ,sin

1

2sin ,

2.

1

1 22 2

1

3 2

4 3

1 2 3 4

( ) ( )

( )( )

And the aspect ratio of the transformable fin is definedas:

l = l S, 22 ( )

where x denotes the distance the driving rod moves, ndenotes the distance from the fix block to the hingepoint, b denotes the half length of the driving rod, c, eand f represent the length of the links, respectively, ddenotes the span of the caudal fin, and S represents thetotal area of the fin.

As figure 2 shows, as the shape changes from cres-cent to fan, the span of the fin does not change much,but the area is more than two times larger, and there-fore the aspect ratio of the finwill be reduced twice.

2.2.Design of the experimental platformTo explore the propulsive performance of this trans-formable fin, theexperimental platform shown infigure 3 was developed. It consists of a synchronousbelt, a towing platform, a driving module, and a two-dimensional force transducer. The driving module,towing platform, and two-dimensional force transdu-cer (JLBS-v, Jnsensor, China) are connected to eachother. A step motor (85BYGH, Shuangjie, China) isused to drive the towing platform at a speed of V tosimulate the drag velocity of the fin under water. Tomimic a caudal fin oscillating under water, the drivingmodule is combined with two motors to oscillate andchange the shape of the roboticfin.

Figure 3(b) illustrates the whole experimentalsetup. To study the individual factors contributing tothe performance of the fin, the experimental platformwas developed without having the confounding

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Bioinspir. Biomim. 11 (2016) 056010 YYang et al

complexity of the whole fish [44]. A carbon fiber tubeconnects the driving module and transformablerobotic fin, through which there is a non-elastic cableconnected to the driving rod of the fin and the cablereel on the drivingmodule. The experiments were car-ried out in a 2 m×1 m×0.8 m transparent tank.The fin sits in the middle of the water tank and even inthe case of the maximum amplitude of 30°, the widthof the transparent tank is still about five times as muchas themoving distance of the distal end of the fin. Thusit can effectively reduce the interference from the wallsand the surface of thewater.

The driving module controls the oscillation andchange in shape of the fin. The oscillating motor pro-vides oscillating motion to the fin as it drives a gear setconnected to the fin via the carbon fiber tube. By con-trolling the motor’s reciprocating rotation we canachieve various oscillating frequencies and amplitudesof the robotic fin. To change the shape of the fin, thetransformation motor drags the non-elastic cablearound the cable reel. The cable bypasses the top and

bottom pulley located in the carbon fiber tube andconnects directly to the driving rod to switch from arotatingmotion to a translational motion. As the cablemoves, the driving rod moves along the keel rod andthe robotic fin changes smoothly from crescent to fan.The rubber membrane provides a restoring force asthe robotic fin returns to its normal shape. The movesin a reciprocating motion along the guiding rod,whereas the oscillating and shape changingmotions ofthe robotic fin are independent of each other. There-fore, the roboticfin can be transformed as it oscillates.

2.3.Design of the experimentThe robotic fin undergoes an oscillating and shapechanging motion, and an arbitrary combination ofoscillation and shape changing, by which we canobtain a large number of controllingmodes. However,this transformable fin has a twofold purpose, (a) toadopt a suitable shape when encountering a changingenvironment; (b) transform itself during an oscillatingcycle to improve propulsion. This robot fin also has

Figure 1.Transformable robotic finwhich can gradually and smoothly change its shape. (a) structure of the transformable fin; (b)transformation process.

Figure 2.Calculation of surface area and aspect ratio of the transformable robotic fin. (a)The length of each rod; (b) the surface areadivision of thefin.

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Bioinspir. Biomim. 11 (2016) 056010 YYang et al

two types of controlling modes, a steady mode and atransformation mode. For steady modes, the shape ofthe fin remains stable during oscillation, but in thetransformation modes, the shape changes during onecycle of oscillation.

To consider biomimetic and practical issues, weselected two typical steady modes and two typicaltransformation modes to explore the propulsive per-formance of the robotic fin. The two steady modesinclude a minimum surface area mode and a max-imum surface area mode, which we called the crescentmode and fan mode respectively. These two transfor-mation modes include a crescent to fan mode, whichmeans the fin transforms from crescent to fan whileoscillating, and fan to crescentmode, whichmeans thefin transforms from fan to crescent.

In the crescent to fanmode, the fin has aminimumarea in two out-strokes and maximum area in two in-strokes. In fan to crescent mode, the fin has a max-imum area in two out-strokes and a minimum area intwo in-strokes. The relationship between the shapechanging motion and oscillating motion of the fourcontrollingmodes is shown infigure 4.

In this study, three kinematic parameters and fourcontrolling modes were combined and investigated.The parameters include the oscillating frequency ( f ),the oscillating amplitude (θ), and the drag velocity (L).This means we can change the controlling modesaccording to different kinematic parameter combina-tions to increase adaptability in a changing environ-ment and improve propulsive performance. The dragvelocity simulates the swimming velocity of fish invarying environments. We selected five drag velocitiesto simulate the performance of the fin in downstreamand counter-currents with different velocities. In thisexperiment, the drag velocity is imitated by the varyingthe movement of the towing platform from −0.5 L to0.5 L, where L represents the total length of the fin setat 170 mm.

To consider the capability of the robot fin and lim-itations of the force transducer, the parameters used inthe experiment are listed below in table 1.

By combining the kinematic parameters and con-trollingmodes, the experiment has 300 cases. To iden-tify how various kinematic parameters and controllingmodes would affect the propulsive performance ofthe fin, we selected typical data for analysis and

Figure 3.The experimental platform and the robotic fin. (a) Sketch of the drivingmodule and the transformable fin. (b)Photographyof the experimental platform.

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Bioinspir. Biomim. 11 (2016) 056010 YYang et al

comparison. The control variable method was used todetermine how each parameter influenced the robotfin [45].

2.4. Evaluation criterionTwo parameters were used to evaluate the propulsiveperformance of the transformable robotic fin, i.e.,thrust force and propulsive efficiency, respectively.Wedefined the propulsive efficiency by the ratio of usefulpower consumption and total consumption of theroboticfin [24], as given below:

h = =-

P

P

P

P P. 3u

w

u

a m

( )

In above equation, all calculations in the functions arefor average power. The useful power consumption ofthe fin within a period is given in equation (4), and thetotal output power of the oscillating motor is definedas equation (5)

= ⋅P F v, 4u ( )

ò w=P

M t t t

T

d, 5

T

a0

( ) ( )( )

where the useful power consumption Pu is defined asthe average thrust force F̄ multiples the drag velocity v.Pa denotes the total output power of the oscillatingmotor, M(t) denotes the output torque of the

oscillatingmotor and ω(t) denotes the angular velocityof the oscillating motor. Pa and the mechanicaltransmission power Pm is obtained as the robotic finundulates in water and air with the same locomotionparameters, and the total consumption of the finmodel underwater Pw is yielded by removing Pm fromthe total power output:

= -P P P . 6w a m ( )

Note that two motors are needed to oscillate andchange the shape of the fin during the transformationmode. In a steady state amotor is not needed to changethe shape, but bothmotors are considered while in thetransformation mode. Propulsive efficiency in thetransformation mode is defined by the total poweroutput and mechanical transmission power from thetwomotors, as shownbelow:

h = =- + -

P

P

P

P P P P, 7u

w

u

a1 m1 a2 m2( ) ( )( )

where Pa1 and Pa2 denote the total output power of theoscillating motor and the transformation motor,respectively, Pm1 and Pm2 denote the mechanicaltransmission power of the oscillating motor and thetransformationmotor, respectively.

3. Experimental results and analysis

The transformable robotic fin and dragging exper-imental platform enable us to explore the propulsiveperformance of the robotic fin in various kinematicparameters and controllingmodes.

Figure 4. Four controllingmodes. (a)Crescentmode; (b) fanmode; (c) crescent to fanmode; (d) fan to crescentmode. A andC standfor out-stoke stages respectively, while B andD stand for in-stroke stages respectively.

Table 1.Parameters used in experiment.

Parameter Specific value

Frequency, f (Hz) 0.25 0.5 1

Amplitude, θ(degree) 15 20 25 30

Drag velocity, v (L/s) −0.5−0.25 0 0.25 0.5

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Bioinspir. Biomim. 11 (2016) 056010 YYang et al

3.1. Influence of surface areasThe robotic fin can be transformed from a crescent toa fan smoothly, during which time its surface area alsochanges. We first examined how variable surface areasaffected propulsion during a steady swimming state.Figure 5(a) shows the robotic fin in various stages oftransformation where propulsive performance wasstudied in a steady state. Figures 5(b) and (c) presentthe average thrust force and average thrust force perunit area of the fin with respect to displacement of thedriving rod, respectively. Here, x denotes the distancethe driving rod moved while being pulled by the non-

elastic cable, while F/Sdenotes the average thrust forceper unit area of the fin.

Figure 5 also shows how the fin was transformedfrom crescent to fan as the driving rod moved from 0to 51.2 mm. During this process the surface area of therobotic fin increased more than twice its original size.Figure 5(b) shows, during the process of transforma-tion, the surface area and average thrust forceincreased almost synchronously. The thrust force perunit area is extracted to describe the influence of sur-face area defined by F/S, as shown in figure 5(c). Notethat when x is equal to 10.24 mm, the thrust force perunit area is at its maximum, but when the driving rodmoved from 30.72 to 51.2 mm, there was only a smalldeformation and the thrust force per unit arearemained stable.

Although F/S of the moment x at 10.24 mm wasthe maximum value, we still changed the shape fromcrescent to fan to analyze the locomotion performanceaccording to the study ofWebb [21].

3.2. Influence of kinematic parametersThree groups of experiments were carried out toexplore the influence of the kinematic parameters,with the control variable method being used to ensurethat each experiment had a single variable value. Thekinematic parameters used in the experiments arelisted in table 2.

Figure 6 presents a comparison of the thrust force,the average thrust force, and the efficiency by exper-imental measurement. To obtain the condition for asingle variable parameters, we varied the frequency,amplitude, and drag velocity, while keeping the othertwo parameters constant.

The results of varying frequencies are shown infigures 7(a) and (b). In the experiments, the oscillatingamplitude and drag velocity of the fin were constant at30° and 0.25 L/ s, which shows that the peaks and val-leys of the thrust force trajectories increased as the fre-quency increased. Figure 6(b) shows that changes in

Figure 5.Effect of transforming thefinwith f=1 Hz,θ=30° and v=0.25 L. (a) Several intervening states fromcrescent to fanwith differentmoving distance of driving rodx: (I) x=0 mm, (II) x=10.24 mm, (III) x=20.48 mm,(IV) x=30.72 mm, (V) x=40.96 mm, (VI) x=51.2 mm.(b)The dynamics of surface area and average thrust force,alongwith themoving of the driving rod. (c)The dynamics ofthrust force per unit area alongwithmovement of the drivingrod.

Table 2.Parameters used in three groups of experiments.

Parameter Specific value

Change frequency

Oscillating frequency 0.25 Hz 0.5 Hz 1 Hz

Oscillating amplitude 30°Drag velocity 0.25 L

Change amplitude

Oscillating frequency 1 Hz

Oscillating amplitude 15° 20° 25° 30°Drag velocity 0.25 L

Change drag velocity

Oscillating frequency 1 Hz

Oscillating amplitude 30°Drag velocity −0.5 L−0.25 L 0 0.25 L 0.5 L

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Bioinspir. Biomim. 11 (2016) 056010 YYang et al

the average thrust force and its efficiency differed inthat if the frequency increased, the average thrust forceincreased and efficiency decreased. The increasing ofthe oscillating frequency leads to a rapid oscillating ofthe fin and then a larger thrust force. However, thetotal output power consumption Pa and mechanicalenergy consumption Pm both increased during theincreasing of the frequency. And the total consump-tion Pw increased faster than the thrust force did,which leads to a lower propulsive efficiency.

Figures 7(c) and (d) shows the result of varying theoscillating amplitude. Here, the increasing of the

oscillating amplitude also leads to the increasing of theaverage thrust force. Moreover, the change of theoscillating amplitude has smaller effect on the propul-sive efficiency. Hence, the efficiency of different oscil-lating amplitude ranging from15° to 30° kept stable.

The influence of the drag velocity is shown infigures 7(e) and (f). Here the average thrust forcedecreased as the drag velocity ranged from−0.5 L/s to0.5 L/s, while the change in efficiency was opposite.The result also indicates that a higher propulsive effi-ciency and a higher thrust force cannot be achievedsimultaneously.

Figure 6.Comparison of thrust force, average thrust force and efficiency. (a) and (b)Thrust force, average thrust force and efficiency atvariable frequencywith θ=30° and v=0.25 L. (c) and (d)Thrust force, average thrust force and efficiency at different amplitudewith f=1 Hz and v=0.25 L. (e) and (f)Thrust force, average thrust force and efficiency at different drag velocity with f=1 Hz andθ=30°.

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Bioinspir. Biomim. 11 (2016) 056010 YYang et al

It is noted from figures 7(a), (c) and (e) that allthrust force trajectories exhibit fine sine curves, whichindicates that the interference from the wall of thewater tank and the water surface cause a small effect tothe thrust force. From figures 7(b), (d) and (f), it can beseen that the change of the average thrust force and thechange of propulsive efficiency differs, which means itis hard to achieve a higher propulsive efficiency and ahigher thrust force simultaneously just varying thekinematic parameters of the robotic fin. However, theresult also indicates that the robotic fin can vary itskinematic parameters to achieve different perfor-mance to satisfy different requirements.

3.3. Influence of controllingmodesWe also conducted a series of experiments withvariable controllingmodes and the same kinematics inorder to investigate the influence of the controllingmodes, and the results are shown infigure 7.

The thrust force of the fin with four controllingmodes is shown in figure 7(a), and indicates that themaximum thrust force in crescent mode was almostcompletely different to the other modes. The thrustforce of the fin from crescent to fan mode had the

largest peak value and a slightly smaller valley valuethan the fin in crescent mode. Thatmeans the crescentto fanmode can reachmaximum instantaneous thrustforce, whereas the fan to crescent mode is similar tothe crescent to fan mode. Two transformation modescan produce a larger thrust force that will help aroboticfish swim away from a complex environment.

Figure 7(b) shows that crescentmode was themostefficient and fanmode was the least efficient, however,the two transformation modes are still more efficientthan the fan mode. Moreover, the transformationmodes can produce much greater thrust forces thanthe two steady modes. Although the transformationmodes require twomotors, the efficiency is still higherthan the steady state modes due to the higher averagepropulsive thrust. However, the two motors requiremore power for the transformation modes than thetwo steady modes, although different controllingmodes can be selected according to the situation theroboticfish is in.

Comparing to the steady modes, the two transfor-mation modes can generate higher thrust forces. Fur-thermore, the crescent to fan mode produced thelargest thrust force. The reason for this phenomenonlies in that the fin changes shape to crescent duringout-stroke stages (see figure 4), which leads to a smallresistance. Moreover, it changes to fan during in-stroke stages (see figure 4), which leads to a largerthrust force. The average thrust force will thenincrease due to the transformation effect. It is worth tobe noted that the average thrust force of fan to crescentmode is also larger than that of the fan mode. Thephenomenon indicates that the transformation pro-cess alters the flow field to shed an positive impact onthe average thrust force. It should be pointed out thatthe transformation modes can achieve a higher effi-ciency and a higher average thrust force simulta-neously than adjusting the kinematic parameters do,which indicates the unique advantage of the trans-formable robotic fin.

4. Further analysis of the experimentalresults

In the previous section we examined how a singleparameter and different controlling modes affectspropulsion; here we will explore the propulsiveperformance of the fin with various kinematics in fourcontrolling modes to determine the optimal way ofimproving the performance of a robotic fish in variousenvironments or tasks.

4.1. Influence of oscillating amplitude andcontrollingmodesFigure 8 shows how the oscillating amplitude in fourcontrolling modes performs when the frequency is1 Hz and the drag velocity is 0.25 L/s. Figure 8(a)

Figure 7.Thrust force, average thrust force and efficiency ofvariable controllingmodeswith f=1 Hz, θ=30° andv=0.25 L. (a)Thrust force in one cycle. (b)Average thrustforce and efficiencywith respective to controllingmodes. I, II,III and IV denotes crescentmode, fanmode, crescent to fanmode, and fan to crescentmode, respectively.

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Bioinspir. Biomim. 11 (2016) 056010 YYang et al

shows that the average thrust force increases as theamplitude increases, while the average thrust force ofthe robotic fin in transformation modes has a highervalue than in steady modes. The efficiency shown infigure 8(b) indicates that the crescent mode and fanmode are similar in that the propulsive efficiencyincreases when the oscillating amplitude is below 20°and decreases when the oscillating amplitude is above20°. The efficiency of two transformation modesincreases as the oscillating amplitude increases.

The crescent mode generates a smaller averagethrust force for the least area of the robotic fin, How-ever, it also consumed the least power so that its effi-ciency is the highest. Note that different controllingmodes have different characteristics, so each control-ling mode is suitable for a particular application. Forexample, the crescent to fan mode can be appliedwhen the instantaneous acceleration at a large ampl-itude is needed to obtain the largest thrust force; the

crescentmode is superior in power saving and has bet-ter performance for a long time cruising.

4.2. Influence of oscillating frequency andcontrollingmodesThe oscillating frequency and controlling modes wereinvestigated as shown in figure 9. Figure 9(a) showsthat the average thrust force increased slightly in allcontrolling modes when the frequency increased from0.25 to 0.5 Hz, but when the frequency increased from0.5 to 1 Hz, the average thrust force increased sharply.Moreover, the fan mode generated the largest forcewhen the frequency was 0.25 Hz or 0.5 Hz, whereasthe crescent to fan mode had the largest thrust forcewhen the frequency was 1 Hz.

It can be concluded from figure 9(b) that the twosteady modes became less efficient as the frequencyincreased, but with the two transformationmodes, theefficiency reached its lowest value when the frequency

Figure 8.Effect of amplitude in four controllingmodes with f=1 Hz and v=0.25 L. (a)Average thrust force of different amplitudein four controllingmodes. (b)Efficiency of different amplitude in four controllingmodes.

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Bioinspir. Biomim. 11 (2016) 056010 YYang et al

was 0.5 Hz and the largest value when the frequencywas 1 Hz. From the experimental result, it can be con-cluded that the transformable robotic fin could adoptbetter propulsive performance when the frequency isabout 1 Hz. Note also that the transformation modesusually had better propulsion when the thrust forceand efficiency were considered simultaneously, butthe steady modes can also be applied when the fre-quency is low to help the robotic fish swim moreeffectively.

4.3. Influence of the drag velocity and controllingmodesFigure 10 shows how the drag velocity and controllingmodes affect propulsion; figure 10(a) shows that theaverage thrust force in crescent mode, fan mode, andcrescent to fan mode decreased from −0.5 L/s to0.5 L/s, while the fan to crescent mode had amaximumvalue at 0 drag velocity.

Figure 10(b) shows that the efficiency of two steadymodes were similar, while the two transformationmodes became more efficient from −0.5 L/s to0.25 L/s and less efficient from0.25 L/s to 0.5 L/s.

The result of the experiment shows that the trans-formable robotic fin can achieve an optimal thrustforce or efficiency by changing the controlling modeswhen encountering a changing environment withvariableflow speed or a changing task.

5.Discussions

In one cyclic movement, a fish fin oscillates backwardsand forwards to propel the fish forwards. Researchershave put forward several basic patterns in order tosimplify these complex movements [46–48]. Unlikethe shape of a single fin, a transformable robotic fincan adapt better to different environments andgenerate better propulsion. A novel transformablerobotic fin has been developed where the shape can bechanged by a drivingmotor, and so too can the surfacearea and aspect ratio.

This transformable fin can change from crescentto fan shape with various features; it can change shapewhile swimming to adapt to changing environments;it can also change shape in one oscillating cycle toimprove propulsion. It is worth emphasizing that thisrobotic fin was not developed to fully replicate themorphology of a fin but to verify how to perform withan optimal way in various environment by changingshape of the fin during swimming.

The experimental result indicates that the trans-formation modes of the robotic fin can achieve higherpropulsive performance, especially the crescent to fanmode and fan to crescent mode can generate higherthrust forces. However, the mechanism of the trans-formation propulsion still remains unknown, whichneeds the study of the hydrodynamics during transfor-mation propulsion. The transformable fin performstransformation during oscillating, so the simulation ofthe process is quite difficult. Furthermore, the com-plex flow field caused by the shape change of the finduring oscillating is difficult to be measured experi-mentally. The hydrodynamic mechanism of trans-form modes of the robotic fin needs to be studied inthe future.

The experimental results revealed that thedynamic change in the shape of the fin has a significanteffect on how the surrounding fluid responds. How-ever, one deformation mode did not always have thebest effect for various kinematic parameters because asthe amplitudes varied the crescent mode was the mostefficient, and as the frequencies varied, the fan modedelivered themaximum average thrust force at 0.5 Hz.With the drag velocity, the fan to crescent mode had amaximum average thrust force at 0 l s−1 and a uniquerule of efficiency, therefore different controllingmodes must be applied at different kinematic para-meters and environmental parameters to optimizeswimming in full operating conditions for changingtasks.

Figure 9. Influence of frequency in four controllingmodeswith θ=30° and v=0.25 L. (a)Average thrust force ofdifferent frequency in four controllingmodes. (b)Efficiencyof different frequencies in four controllingmodes.

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Bioinspir. Biomim. 11 (2016) 056010 YYang et al

6. Conclusions

This paper proposes a novel transformable fish fininspired by the ability of fish to change the shape oftheir fins while swimming. Although the frame of thisfin is rigid, the skin is flexible. Amulti-linkmechanismdriven by a motor was used to change the fin fromcrescent to fan while swimming. The surface area andaspect ratio of the fin also changes. Two motors wereused to synchronize and realize the oscillating andshape changing motions. We investigated the charac-teristics of various fin shapes, and the influence hemain kinematic parameters and controlling modeshad on the thrust force and propulsive efficiency. Wefound that transformation modes in a cyclic motioncan influence the hydrodynamic response in differentways. The oscillating kinematic parameters indicatedthat these parameters coupled with the controllingmodes in a complicated way, but they did improvepropulsion when the parameters were combinedproperly. These results delivered a comprehensiveunderstanding of the complex deformation of the finand its effect on the hydrodynamic forces, which canguide future designs of novel underwater robotic

propulsive systems. Future work includes an accuratemeasurement of theflowfield as thefin is transformed,in order to obtain an overall understanding of thepropulsive performance of this transformable fin.

Acknowledgments

This research is supported byNationalNatural ScienceFoundation of China (No. 51375468) and ARCDiscovery Grant (DP150102636). The authors wouldlike to thank Mr Yun Qian and Mr Dongqi Gao fortheir helpful discussions on setting up the exper-imental platform and conducting the experiments.

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