Development of a Fish-Like Propulsive Mechanism€¦ · Development of a Fish-Like Propulsive...

Development of a Fish-Like Propulsive Mechanism Hamed lashkari, Aghil Yousefi-Koma, Peyman Karimi Eskandary, Donya Mohammadshahi,

Alireza Kashaninia Center for Advanced Vehicles (CAV), School of Mechanical Engineering

College of Engineering, University of Tehran Tehran, Iran

[email protected], [email protected], [email protected], [email protected], [email protected]

Abstract: This paper presents the design process of a fish-like propulsive mechanism for robotic tuna fish, ARTEMIS, fabricated at the Center for Advanced Vehicles (CAV), University of Tehran. The mechanical design enables efficient sinusoidal motions, for dominant thrust and motion in water. More importantly, maneuverability of the robot fish will enhanced by varying oscillatory characteristics. The desired characteristics are met by implementing predefined kinematics.Experimental results are presented to show the feasibility and performance of the fabricated mechanism. Key-Words: Robot Fish, Bio-Inspired Mechanism, Scotch Yoke, Mechanical Design 1 Introduction Biomimetic robots such as robot fishes act an important role within the underwater robotics community, which provide innovative solutions to underwater propulsion and maneuvering. Compared to propeller-type underwater vehicles, this kind of biomimetic propulsion mechanism is less noisy, more effective, can cruise greater distances at a significant speed, maneuver in tight spaces, accelerate and decelerate more quickly, and even jump to remarkable height with the same integrated propulsion and steering system. Therefore researchers have focused on the development of novel robot fishes. Building various types of robot fishes would be applied to underwater transportation, anti-terrorism, seabed exploration, search and rescue, military missions, and so forth. In 1994, the first robot fish named robotuna was developed by MIT [1]. In 1998, the Draper Lab realized Vorticity Control Unmanned Undersea Vehicle (VCUUV) [2] on the base of robotuna. VCUUV could avoid obstacle and realize the up-down motion. It is the most widely known robotic fish developed up to now. After that, many researchers put forward several kinds of robot fish. The Northwestern University applied Shape Memory Alloy (SMA) on the robotic lamprey [3] which make aim to realize mine countermeasures. In Japan, Nagoya University developed a kind of micro robotic fish using ICPF Actuator [4] and Tokai University realized a robotic Blackbass [5] to research the propulsion of pectoral fins. National Maritime Research Institute of Japan developed many kinds of robotic fish prototypes from PF300 to PPF- 09 [6] to exploit the up-down method and effective swimming. In

China, the Beihang University (BUAA) developed three kinds of robotic fish [7] and the Institute of Automation Chinese Academy of Sciences (CASIA) [8] also made some progress on four-joint robotic fish. It is well known that the tuna swims with high speed and high efficiency. Such astonishing swimming ability inspired us to choose the Tuna as the model of our robot fish. The objective of this paper is developing an improved propulsive mechanism for generating an undulating motion with best approximation of kinematical swimming function of a real prototype tuna fish. The propulsive mechanism is implanted in ARTEMIS, the 1m long robotic Tuna fish that is shown in Fig. 1 .This mechanism actuated by one DC motor as the primary propulsive mechanism. Two different mechanisms are proposed Compared to previous version of robot fish's propulsive mechanism that used Scotch yoke[9], ARTEMIS propulsive mechanism motivates the three-stage fish tail set with the purpose of mimicking the locomotion of natural Tuna fish.

Fig. 1 The designed robot fish

More importantly, this device should possess compact

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ISSN: 1792-4294 389 ISBN: 978-960-474-203-5

construction suitable for developing large-scale integrations via available engineering means, so the proposed mechanism, have designed for the full scale of tuna fish in the nature. Generally, ARTEMIS can be divided into several modular units as shown in Fig. 2 : (1) a main body or head box that providing enough interior capacity for electrical and mechanical parts, accessories and to enable further modifications. The three-stage tail set is attached to this part; (2) a set of three-stage tail consisting of three parts capable of approximating the traveling wave function of tuna fish; (c) a propulsive mechanism consisting of Scotch yoke, two pair of rack and pinion and four bar linkage to provide movement and maneuver of three-stage tail set.

Fig. 2 The prototype of ARTEMIS

This paper focused on the improved mechanical design enabling efficient traveling wave, for dominant thrust and motion in water and will be detailed. More importantly, maneuverability of the robot will enhance by varying oscillatory characteristics. The desired characteristics meet by implementing predefined kinematics. The rest of the paper is organized as follows. The design scheme and procedure for the propulsive mechanism is described in Section 2. Experimental results that showing the feasibility and good performance of proposed mechanism are provided in Section3. 2 Designing Fish-Like Propulsive Mechanism The thunniform locomotion is an autapomorphy of the tuna fish that is considered as a high-speed long-distance swimmer. Our basic idea is designing a three-stage robot fish tail mechanism to generate an undulating motion by approximating the kinematical swimming function of a real tuna fish.

There is a traveling wave pass among the tail in the thunniform locomotion, and the amplitude of the traveling wave increased at the end of the tail fish [10]. According to the research of zoologists, the form of a traveling wave given by (1) [11]:

axismain alongnt Displaceme:x

number body wave: 2=k

(Radian body wave ofFrequency :f2=envelope. amplitude waveQuadratic:C

envelope amplitude eLinear wav:C

body ofnt displaceme Transverse=t)(x, Y

)1(t)]+][sin(kx xC+x[C=t)(x, Y

2

1

body

221body

λππω

ω

The schematic of the traveling wave function of thunniform locomotion is shown in Fig. 3 with dash line besides the three-stage of the tail fish with solid lines. As it is obvious in Fig. 3 the schematic of the tail stages is a piecewise linear approximation of the traveling wave function.

Fig. 3 ideal wave of thunniform swimming function

c1=0.05 c2=0.08 k=0.5 It is obvious that the motion of tail is sinusoid, so the three-stage tail set and the propulsive mechanism that actuate the tail set will be designed in a manner that they approximate Eq. 1. The optimal ratio of lengths of these three links ( 3:2:1 lll ) are set to (1:0.72:0.65) based on [12]. This tail set is actuated by Scotch yoke and DC motor as the primary propulsive mechanism to generate sinusoidal motion as it shown in Eq. 1. A conventional Scotch yoke, as outlined in Fig. 4, is designed for converting rotational motion of motor to reciprocating sinusoidal motion of a slider or vice versa. The reciprocating part is directly coupled to a sliding yoke with a slot that engages a pin on the rotating part which performs the same function as a simple crank, while the linear output motion is a sinusoid and more smoother.


ISSN: 1792-4294 390 ISBN: 978-960-474-203-5

Fig. 4 schematic of the scotch yoke mechanism

the slotted T-shaped body, L2, it is connected to free end of the crank L1 by means of the pin P. Xp and YP are the X and Y coordinates of the point P, respectively.

⎩⎨⎧

==

θθ

SinLCosL

.Y.X

1P

1P (2)

The velocity vector VP perpendicular to L1 can be obtained by differentiating Eq. (2) with respect to time. Such differentiation yields to Eq. (3).

⎩⎨⎧

=−=

θωθω

CosLSinL

..V..V

1PY

1Px (3)

where VP is separated into components VPx in the X direction and VPy in the Y direction, and ω1 is the angular velocity of L1. Furthermore, it may be seen that Y coordinate of the point Q on the output-slide link in Fig. 4. is determined by Eq. (4).

⎪⎩

⎪⎨

⎧

−=

+=

+=

12Qmin

2Qmax

12Q

X)4(X

X

LLLLCosLL θ

It can easily be derived that as θ varies continuously from 0° to 180°, the position of point Q varies between XQmax=L2+L1 and XQmin=L2-L1 for a total travel of 2L1. Note that it is necessary to choose a crank that has a length equal to one half of the desired travel when designing a Scotch yoke. The velocity VQ and the acceleration AQ can be obtained by differentiating Eq. (4) with respect to time as shown in Eq. (5).

⎪⎩

⎪⎨⎧

−=−=

−=−=

)(...A

)(....V

.1

21

2Q

11Q

tCosLCosL

tSinLSinL

ωωθω

ωωθω (5)

In this case, it will be feasible to adjust the amplitude of the sinusoidal motions by changing the length L1 . The shape of the motion of point Q is a pure sinusoidal wave with respect to time at a given rotational speed that reciprocates along a line. Two methods are proposed for converting motion of point Q to desired sinusoidal rotational motion. In the first method, the Scotch Yoke is combined with two linkages as it shown in Fig. 5. In the second method, Scotch yoke come along with a rack and pinion as it shown in Fig. 9.

2.1 Scotch Yoke with two linkage mechanism In Scotch Yoke with two linkage mechanism (Fig. 5), the rotating link is PS, the first stage of tail set. As motor runs it forces the point Q to move as the output of Scotch Yoke. Point Q joints to link PS via the middle link SQ. Then it will push the link PS to turn right or left at angle θ to new position P'S' and P''S''. Also the counterclockwise turning will make the link PS to turn left at angle θ.

Fig. 5 Schematic structure of the Scotch Yoke with two linkage

PS: the first stage of tail set QS: The middle linkage

Table 1 gives the definitions of symbols:

THE SYMBOL OF FIG. 5 TABLE 1

Symbol Parametric valueQR h

QS,Q'S',Q''S'' k QQ',QQ'' 1L

QP l PS,P'S',P''S'' R

Initially β is assumed to be 90degree, so PS has a symmetrical motion. The relationships between parameters are described in the Eq. (5), (6) and (7).

)5(11L

SinR

θ=

The height of Q is the average height of S and S', Eq. (6).

)6(2

12

12 1L

SinCosRCosRCosRh

θθθθ +

=+

=+

=

The length of QS is calculated when PS is in vertical position. Thereby according to Pythagoras's Law, k is obtained from Eq. (7).

)7()2

1()( 21

2222 LSinCoslhRlkθθ−

+=−+=


ISSN: 1792-4294 391 ISBN: 978-960-474-203-5

Table 2 gives the value of R and h for some desired amplitudes of θ:

THE PARAMETRIC VALUE OF FIG. 5

TABLE 2 3025 20 15 θ

2 1L 2.37 1L 2.92 1L 3.86 1L R 1.87 1L2.26 1L 2.83 1L 3.79 1L h

The displacement, velocity and acceleration of link PS with respect to time are shown in Fig. 6, Fig. 7 and Fig. 8 respectively.

Fig. 6 displacement of link PS with respect to time

Fig. 7 Velocity of link PS with respect to time

Fig. 8 Acceleration of link PS with respect to time

As it is seen, the position and velocity of link PS are pure sinusoid curves, but the acceleration is a semi-sinusoidal. 2.2 Scotch Yoke with rack and pinion In Scotch Yoke with a rack and pinion mechanism, the sinusoidal linear motion is transferred to two parallel

racks that have the same motion. These racks transmit their motion to two concentric pinions A and B (Fig. 9 and Fig. 10) .Pinion A with larger pitch diameter is used to move the first section of tail specified by PS; pinion B with the smaller pitch diameter provides motion for the second part specified by SM in Fig. 9. Pinions A and B don’t have the same radiuses; by the way their circular displacements are equal, in that both of them are connected to the rack; consequently the angular displacement of this two pinions are different and proportional to their radius.

Fig. 9 Schematic structure of the Scotch Yoke with rack and

pinion As it shown in Fig (9), the first section of tail set, PS, is directly welded to the bigger pinion A. To transmit motion from the smaller pinion B to second section of tail set, SM, a four-bar linkage OABC is also designed. The link OA is attached to pinion B. The link CB is attached perpendicularly to SM. At first the link OA and CB are chosen to have same length to form a parallelogram four bar linkage. The main feature of this linkage is that the link CB will duplicate the motion of link OA. This way the sinusoidal motion of racks is transferred to the second section with same frequency with larger angular displacement. For further experiment, it is possible to adjust the length OA and CB, and the radius of pinion A and B which results in creating different semi-sinusoidal motions. The flexible tail fin MN attached at the end of the tail set as the third part. Due to the interaction between the flexible body and the surrounding water, the shape of the tail fin MN changes to the M'N' to forms the correct form of undulation motion. [13]


ISSN: 1792-4294 392 ISBN: 978-960-474-203-5

As it shown in Fig. 9, the ARTEMIS's three-stage tail mechanism generates approximation form of the traveling wave function as the racks move. Table 3 gives the definitions of symbols in Fig. 9:

THE SYMBOL OF FIG. 9 TABLE 3

θ Angular displacement of pinion A that equals to angular displacement

of the first stage of tail set

β Angular displacement of pinion B

that equals to angular displacement of the second stage of tail set

PS, P'S' Primary and secondary location of the first stage of tail set

SM, S'M' Primary and secondary location of the second stage of tail set

MN, M'N' Primary and secondary location of

the third stage of tail set (flexible stage)

OABC,O'A'B'C' Primary and secondary location of the Four-bar linkage mechanism

The limit oscillating amplitude of stage 1 and 2 of tail set depends on pitch diameter of pinion A and B respectively. These amplitudes are able to vary from π/12 to π/5. The velocity and acceleration of second stage of tail are shown in Fig. 11 and Fig. 12 respectively.

Fig. 11 Angular Velocity of second stage of tail structure with

respect to time

Fig. 12 Angular Acceleration of second stage of tail structure

with respect to time

The results demonstrate the sinusoidal motion of the

second stage.

2.3 The fabricated fish-like propulsive mechanism Comparing the two presented methods by analytical and fabrication aspects, we decide to use rack and pinion for translating the scotch yoke motion to first part of tail. The Scotch yoke mechanism, as illustrated in Fig. 10, equipped with two linear guides, one of them is fixed and is used as slider, another linear guide is attached to first linear guide's block perpendicularly, be capable of fast sliding along the guide rail. Notice that to avoid unwanted wear of the slot in the yoke caused by sliding friction; this design is employed so that the undergone friction is converted into rolling friction.

Fig. 10 Propulsive mechanism of ARTEMIS

The main shaft 1L driven by a high torque DC motor (referred to as the master motor) moves the sliding yoke. The reciprocating amplitude of tail set and speed cruising of the robot fish is determined by the length of

1L and DC motor's speed respectively. The DC motor speed determines the oscillation frequency of tail. The Position controlling of the crank 1L by DC motor steers the robot fish to left and right. Pinion A with the pitch diameter of 100mm and pinion B with the pitch diameter of 70mm, with the same module of 2 is used. Fig. 13 presents data transferring module in ARTIMIS to observe the operation of propulsive mechanism in water.


ISSN: 1792-4294 393 ISBN: 978-960-474-203-5

Fig. 13 The logical connection between

components of data transferring module

3 Test Result and Analysis In this paper the experimental results are presented to prove the feasibility of the designed mechanical structure. The dimensions of the experimental pool are 3m x 5m x 1m. Table 4 gives the technical characteristics of ARTEMIS:

THE TECHNICAL CHARACTERISTICS OF ARTEMIS

TABLE 4 Size (L x W x H) ~1200x20x 30

Weight 30 Kg Working voltage 12 Volt

Max oscillation frequency 1.2 Hz maximum speed 2 m/s

No-load power (out of water) 18 Watt Maximum power 60 Watt

Derivation of equation of motion of the tail structure proves that the tail oscillates sinusoidal with respect to time. The tail oscillating rate remains constant assuming that the power of the driver DC motor is infinitive, even in the highest resistant of water; the tail speed is affected by the drag force of water since the speed of the motor varies versus its torque in constant voltage. The Fig. 14 shows the angular position of the tail with respect to time (the time sampling is set to 0.01sec) for two cases; 1st: there is no load on tail; 2nd: there is drag force of water on the tail. The drag force is proportional to the second power of speed, so the maximum water drag force resists at the midpoint of its movement where the tail has its maximum rotational velocity. The tail doesn’t deviate from sinusoidal pattern at the endpoints of its movement because the tail rotational speed decreases to its minimum value (zero deg/sec at the endpoint) and the torque of tail increases to its maximum value at the endpoints. Also deviation from sinusoidal pattern increases to maximum value at the midpoint of tail's movement.

Fig. 14 validation of the sinusoidal pattern of tail structure

Due to constant time sampling intervals and the reduction of speed due to water drag force, the angular displacement intervals are reduced. For modelling the positional response of system with respect to time, it is supposed that the angular displacement step θd is constant. When the rotational velocity decreases, the time step

dt will expand. The

relation between the new expanded EXPdt that varies with angular velocity and the time step dt that used in data sampling ( sdt 01.0= ) is given by Eq. (8).

)8())]4(1(1[))]2((1[ 2 ftCosdtftSindtdtEXP παπα ++=+= α is environmental effectiveness that affects the power consumption of oscillating tail . Performing the integration of EXPdt yields to Eq. (9):

)9()()])4(41[(

0

tGftSinf

ttdttt

EXPEXP =−+== ∫ ππ

α

Et is function of time. Using Eq. (5) and Eq. (9):

)11())t(.2(.)2(.)t( EXP1

EXP−−=−= GftCosKftCosK ππθ

))(.2(.t)( 1Drag tGftCosK −−= πθ

As shown in Fig. 14 and Fig. 15, when loads and environmental effectiveness α change, the extremums of tail position graphs don’t change and the velocity change more in zero angular position of tail. The effect of α on the sinusoidal oscillation of tail is shown in Fig. 15.

Fig. 15 The effect of α on the sinusoidal oscillation of tail


ISSN: 1792-4294 394 ISBN: 978-960-474-203-5

4 Conclusion The paper developed two improved propulsive mechanism of the robotic tuna fish, (ARTEMIS) that fabricated at Center for Advanced Vehicles (CAV) at University of Tehran. 1st: The Scotch yoke with multi-linkage mechanism. 2nd: The Scotch yoke with rack and pinion mechanism. The second mechanism is selected to motivate a three-stage tail set mimicking the locomotion of natural Tuna fish's tail. The considerable advantage of this mechanism is its simplicity and durability. The three-stage tail set of ARTEMIS has just one degree of freedom controlled by DC motor to produces thunniform traveling wave. The cruising speed of ARTEMIS and its steering to left and right all is controlled by the same DC motor. References: [1] K. Streitlien, G. S. Triantafyllou, and M. S. Triantafyllou, “Efficient foil propulsion through vortex control” AIAA J., vol. 34, pp. 2315–2319, 1996. [2] J.M.Anderson, “Vorticity control for efficient propulsion” Ph.D. dissertation, Massachusetts Inst. Technol./Woods Hole Oceanographic Inst. Joint Program, Woods Hole, MA, 1996. [3] http://www.dac.neu.edu/msc/burp.html [4] S. Guo, T. Fukuda, Norihiko KATO, Keisuke OGURO. “Development of Underwater Microrobot Using ICPF Actuator”. Proceedings of the 1998 IEEE International Conference on Robotics & Automation. pp1829-1834. [5] N. Kato. “Control performance in the horizontal plane of a fish robot with mechanical pectoral fins”. IEEE Journal of Oceanic Engineering 25 1 2000 IEEE p 121-129 0364-9059 [6] http://www.nmri.go.jp/eng/khirata/fish [7] J. Liang, etc. “Researchful Development of Underwater Robofish II- Development of a Small Experimental Robofish”. Robot .2002, 24(3) [8] J.Z. Yu, E.K. Chen, S. Wang, M. TAN, “Research Evolution and Analysis of Biomimetic Robot Fish”. Control Theory and Application. Accepted in Chinese.2002 [9] Yu, J., Wang, L., Hu, Y., and Huo, J., 2008, “Dolphin-like Propulsive Mechanism Based on an Adjustable Scotch Yoke,” Elsevier, No. 37791-HL. [10] Wang, S., Zhang, Z., and Sang, H., 2004, “Analysis of Velocity Control Algorithm for Biomimetic Robot Fish,” Proc. IEEE international conference on Robotics and Biomimetics, Shenyang, China, pp. 972–975. [11] D. Barrett, M. Grosenbaugh, M. Triantafyllou, “The Optimal Control of a Flexible Hull Robotic Undersea Vehicle Propelled By An Oscillating Foil”. Symposium on Autonomous Underwater Vehicle Technology,

Proceedings of the 1996 AUV. New York: IEEE Press, 1996, P1-9. [12] Yu, J., Wang, L., Zhao, W., and Tan, M., 2008, “Optimal Design and Control of Biomimetic Robot Fish,” Science in China Press, Springer, PVP-Vol. 51, pp. 534-549. [13] Liu, J., Dukes, I., and Hu, H., 2008, “Novel Mechatronics Design for a Robot Fish,” IEEE Explore, No. 711-PK-48.


ISSN: 1792-4294 395 ISBN: 978-960-474-203-5

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