Page 468 - Handbook of Biomechatronics

462 Ahmet Fatih Tabak

numerical investigations (especially after powerful numerical tools have
emerged), conceptual work on swimming micro-robots, experiments on
artificial micro-swimmers, experiments with cybernetic micro-robots, con-
trol studies, robotic swarm studies, and conceptual demonstrations.

2.1 Observations of Bacteria and Spermatozoa

At this juncture, it should be sufficient to briefly present key elements to this
context gathered from observation. The first example is the sea-urchin
spermatozoa which possess a single slender tail known as a flagellum. The
flagellum is actuated locally by sliding protein chains embedded within.
Thus, planar wave propagation is induced from the base of the flagellum,
where the tail and head are connected with a flexible joint, toward the
end trailing freely (Gray and Hancock, 1955; Brennen and Winet, 1977).
On the other hand, bacterium species utilize helical-wave propagation along
their flagellum or bundle of flagella. The flagellum, in this case, is attached to
the cell membrane with nanoscale machines called bacterial motor. Surpris-
ingly, this structure has a bearing feature similar to an electric motor that
allows it to rotate at the base canceling motion on the other axes, thus rotat-
ing the flagellum. The elastic flagellum takes a helical shape due to this rota-
tion. As for the bacterium species with bundles, such as Salmonella abortus
equi, the wave propagation is more of a combination of rotation and active
deformation along the intertwined flagella group (Brennen and Winet,
1977; Flores et al., 2005; Berg and Anderson, 1973).
It is also important to note that geometry of waves is not constant under
all conditions. Given that the structural deformation occurs as a result of
force balance between internal and external stress, the distinctive wave
parameters such as wavelength, λ, wave amplitude, A, and angular frequency
of the wave, ω, are subject to change under different viscosities (Brokaw,
1966). A very interesting observation made over the years is that some sperm
cells can induce helical-wave deformation along their flagellum. It is now
understood that certain spermatozoa cells, such as of the Echinus esculentus,
are capable of switching to helical-wave propagation when the viscosity
of the liquid they are immersed in is lower than certain values (Woolley
and Vernon, 2001). It is safe to say that this behavior is to optimize the
efficiency of swimming performance thanks to the overall survival strategy.
The reader will later be introduced to the possible mathematical definitions
efficiency, η, followed by informative discussions on its importance and
implications within the contexts of geometric and structural design, motion
control, and maneuvering of swimming micro-robots, as a key issue.