Studies of the dynamics of fish locomotion show that most fishes use their caudal fin (i.e. the tail) as the primary motivator [Alexander1982]. According to Prince Prince81, there are three main types of caudal propulsion. In the first type, demonstrated by rigid-bodied and armored fish, the tail and a very small part of the adjacent body is used. In the second type, demonstrated by active swimmers such as herring, mackerel, salmon, etc., at least half the body is flexed. In the third type, demonstrated by eels, almost the entire body length is deformed in an undulating action.
We would like to develop the simplest biomechanical fish model whose
locomotion synthesizes the second kind of caudal swimming pattern. To
this end, we designed a mass-spring-damper model consisting of 23
nodal point masses and 91 spring-damper units illustrated in
Fig. 
. The units serve as uniaxial deformable elements
whose arrangement maintains the structural stability of the body while
allowing it to flex. The faces of the nodes are cross-strutted with
elements to resist twisting and shearing.
Twelve of the deformable units span the length of the body and serve
as simple muscles (the bold lines in Fig. ). These
muscles form three muscular segments, each with two pairs of muscles,
one on either side of the body. The posterior two segments which
cover half of the length of the fish body are used for swimming and
the anterior two segments are used for turning. This muscle
distribution and usage approximates that found in most natural fish
[Webb1984].
The shape of a fish directly affects the way it locomotes since the
hydrodynamic forces are shape-dependent (more details can be found in
Section ). Active natural fishes have evolved a
streamlined shape, where their greatest body diameter is just under
the midpoint of their bodies [Prince1981]. The streamlined shape
of the body reduces water turbulence that retards forward motion. The
large surface area of the mid-body induces relatively large
hydrodynamic forces on the sides which mitigate lateral
instability. Since we want the artificial fish to be able to locomote
realistically in simulated water, it is important that we design its
shape in accordance to the streamlined shape of natural fishes.
Fig. shows the top and the side view of the
physics-based fish model (without the cross-strut viscoelastic units).
Figure: The top and side view of the outline of the fish model at rest.
| Xiaoyuan Tu | January 1996 |
