Recent research topics in bionics focus on the analysis and synthesis of
animal’s spatial perception of their environment by means of their
tactile sensory organs: vibrissae. The investigations lead to the task of
creating models and a stringent exploitation of these models in form of
analytical and numerical calculations to achieve a better understanding of
this sense. The sensing lever element vibrissa for the transmission of a
stimulus is frequently modeled as an Euler-Bernoulli-bending rod. But, most
of the literature is limited to reasearch on cylindrical and straight, or
cylindrical and pre-curved, or tapered and straight vibrissa-like rods. The
combination of a cylindrical and pre-curved shape is rarely analyzed. This
is the starting point of the bachelor thesis at hand. At first, an exact
theory for strongly pre-curved bending rods is derivated. Accordingly, a
series expansion of first order from the exact theory is made. A limit
value examination for weakly pre-curved rods leads to the well-known
Euler–Bernoulli bending theory. Afterwards, the so-called ``geometrical
stiffnesses'' are calculated for a circular and a rectangular cross-section
of the considered rod. Furthermore, error functions relating to the exact
theory and their series expansion are defined. This is followed by the use
of these three theories on a special application: a one-sided clamped
bending rod with constant force application direction, with varying system
parameters in simulations. Therefore, limits are sought among each theory
so that a defined error is none exceeded. Afterwards, an evaluation of the
error functions is given. Thus, a correlation between the number of order
of the series expansion and the increase of the discovered limits is
determined. Hereby, the error of some specific vibrissae relating to the
use of different theories is calculated. Finally, an examination of a
scanning process of an obstacle in using a tapered and pre-curved rod is
investigated. The focus is on a tensionless separation of the rod from the
obstacle. Various numerical simulations are done with respect to this
topic. In the end, linear functions of pre-curvature with integral average
of zero are examined relating to their advantages during the scanning
process.