Principles of the Swimming Fish Robot|
February 6, 2001 by Koichi Hirata
We can say that fish swim with pushing water away behind them, though fish swim by various methods. As the well-known categories for the swimming fish, a zoologist, C.M. Breder classified into the following three general categories based on length of a tail fin and strength of its oscillation (see the figure to the right).
(a) Anguilliform: Propulsion by a muscle wave in the body of the animal which progresses from head to tail like the Eel.
On the other hand, several analytical methods for the swimming fish, such as a changing wave propulsion, a slender body theory and an oscillating wing theory, were published by researchers.
In this report, we discuss the following four general categories in the viewpoint of the mechanical design of a fish robot, based on the above classification and analytical methods.
(a) Changing Wave
Fish using this method are propelled by a muscle wave in the body of the animal which progresses from head to tail. This causes the fish to be propelled by the action of its body upon the water. In order to get propulsive force, it is needed that velocity of the wave is faster than forward speed of the fish, and amplitude of the tail part is bigger than that of the head part. We find that most of these fish can reverse this wave motion, thereby enabling them to swim backwards in a similar fashion. Normally, these fish have a long body or a long fin like a ribbon.
A fish robot using this method needs smooth motion of the whole body with many hinge joints and so much complex control system for the joints. However the fish robot can realize delicate motion, and work well in narrow water area like a coral reef, when a high quality control system is completed.
(b) Body Foil
Trout and Salmon are fish typical of those using this swimming method. These fish push water away behind them with using both oscillation of a tail fin and motion of a body. (a) of the figure to the right shows pressure distribution by the motion of body conceptually. There are positive and negative pressure gradients, or we may have to say them action -reaction force, their total force then becomes propulsive force.
We can consider the characteristics of this propulsive method with aspect ratio which is often used to estimate the performance of a wing, defined the ratio of span of a wing, c and chord of a wing, b. When we consider the body to be a wing as shown in (b) of the figure boldly and extremely, the wing has low aspect ratio. Low aspect ratios are often associated with high lift devices, jumbo jet wing flaps, multi-purpose aircraft wings (utility, trainer), towing propellers, and multi-purpose boat propellers. Because it performs well at low and medium speeds and wide range of the attack angle, it is used to multi-purpose. It can travel far but needs a bit more fuel to go great distances. Also a wing with low aspect ratio is not suitable for high speed and high propulsive efficiency, because it has large drag for a surface area of the wing. However the wing is expected to get huge propulsive force, because the wing has large surface area remarkably for a size of the fish robot. As the result, it is considered that the fish robot with the low aspect ratio can accelerate well from stationary position. As the other excellent characteristics, it is expected to have good turning performance with changing the direction of the propulsive force, and it has no concentrated force at hinge joints with dispersing of the driving power to the whole body.
On the other hand, fish using this method such as Trout and Salmon have a triangular tail fin generally. The fish propel by the oscillation of the tail fin with the same principle of the Oscillating Wing described below. It is very interesting from the viewpoint of hydrodynamics that the triangular tail fin has lower aspect ratio than that of the Oscillating Wing.
(c) Oscillating Wing
Fish using this method derive nearly all of its propulsive force from an oscillating wing-shaped tail fin. The motion of the oscillating wing is combined heaving motion and feathering motion of the tail fin, and has about 90 degrees of phase angle between the heaving and the feathering of the tail fin. Tuna and Bonito use this method. Cetaceans also use this method, although they wave their tails up and down, not left and right. These fish has a crescent and wing-shaped tail fin. As its span is long and its chord is short, the tail fin has high aspect ratio. High aspect ratios are associated with very high lift performance in wings, propellers, helicopter rotors, high-speed motorboat propellers and hydrofoils. A wing with high aspect ratio has the great characteristics such as low drag and strong lift for a surface area of the wing. Thus, the Oscillating Wing gets the great performance, when a high performance tail fin in hydrodynamics, a streamlined body and a slim peduncle are combined. The body with few drag and strong propulsive force by the tail fin obtain high-speed swimming. The energy for driving the tail fin is a few, because the surface area of the wing is small for a size of the fish robot. Then the oscillating wing propulsion can get high propulsive efficiency. But the fish robot with this method does not expect to get good accelerating performance from stationary position, because the propulsive force is somewhat small for the size of the fish robot. It also is important that we should design the joint at the tail fin in careful, because the strong force is concentrated at the joint.
(d) Oscillating Plate
Fish using this method oscillate only a tail fin alike a plate without moving the body. The direction of water pushed by the Oscillation Plate may disperse to left or right, not behind the fish. As the result, this propulsive method has weak points at swimming speed and propulsive efficiency. But the method is expected high mechanical efficiency, because it has a few hinge joint with small mechanical loss. Also from the simple structure of the mechanism, it is considered that the method is the most suitable for a small-size fish robot. In addition, it is considered the elastic tail fin of this method obtains somewhat stronger propulsive force, because the direction of the pushed water may become to behind similarly.
Above four propulsive methods are classified in the viewpoint of the mechanical design for a fish robot. Thus they may not correspond to the swimming nature fish and rigorous hydrodynamics. However we can discuss design points in detail with the consideration of the classification.
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