  It is well-known that parallel manipulators are prone to singularities.
However, there is still a lack of distance evaluation functions, referred to as
metrics, for computing the distance between two 3-RPR configurations. The
proposed extrinsic metrics take the combinatorial structure of the manipulator
into account as well as different design options. Utilizing these extrinsic
metrics, we formulate constrained optimization problems. These problems are
aimed at identifying the closest singular configurations for a given
non-singular configuration. The solution to the associated system of polynomial
equations relies on algorithms from numerical algebraic geometry implemented in
the software package \texttt{Bertini}. Furthermore, we have developed a
computational pipeline for determining the distance to singularity during a
one-parametric motion of the manipulator. To facilitate these computations for
the user, an open-source interface is developed between software packages
\texttt{Maple}, \texttt{Bertini}, and \texttt{Paramotopy}. The effectiveness of
the presented approach is demonstrated based on numerical examples and compared
with existing indices evaluating the singularity closeness.
