This paper handles a model of a tactile sensor which allows to
reconstruct objects with a strictly convex, continuously differentiable
contour function by a procedure called rotatory scanning. The sensor is
inspired by vibrissae which a lot of mammals posess. The vibrissa is
modeled as a long, slim bending rod with circular cross section, constant
second moment of area and constant Young's modulus which is pivoted by a
bearing. The rotatory scanning is regulated by a moment and is operated
quasi-statically. At first, the set of autonomous differential equations,
which describes the deformation of the rod, is derived and all parameters
are dimensioned. After that assertions about existence and uniqueness of
initial-value problems and boundary-value problems are presented. There are
two possible methods for solving the set of autonomous differential
equations: method 1 uses the shooting method to get three unknown
parameters, in method 2 the number of unknown parameters is reduced in
advance by analytical transformations so that only one unknown parameter
has to be determined by the shooting method. During the rotatory scanning a
distinction between tip contact (phase A) and tangential contact (phase B)
of the rod with the object is made. In case of tip contact, formulas for
$x(\varphi)$, $y(\varphi)$ and force $F$ are derived, in case of tangential
contact, formulas for $x(s)$, $y(s)$, $F$ and arc length $s_1$ where the
contact occurs are derived. During derivation elliptic integrals arise and
are transformed into combinations of standard elliptic integrals of the
first and second kind. With these formulas, the contact point can be
determined for both phases. For the reconstruction of the object by means
of the boundary conditions to the support and the bearing reactions, that
means, with the parameters which would be available for such an animal with
vibrissae during the procedure of sensing, a formula to decide whether the
rod happens to be in phase A or phase B is derived. During the quasi-static
rotation of the rod, a sequence of contact points can be determined which
enables to approximate the contour function of the object. Finally, some
simulations with a Matlab program which is able to reconstruct various
contour functions are conducted.