A characterization of singularities for a six-wire parallel architecture is presented as a result of numerical and experimental analyses. Numerical analysis has been developed through geometrical and analytical considerations. The study is based on a classification that has been derived on the basis of the geometry of tetrahedra, and singular configurations have been classified as a function of the tetrahedron volume. Experimental characterization has been carried out by considering the wire parallel architecture Cassino tracking system (CATRASYS). Experimental results are reported to characterize the performance of the CATRASYS chain in different operating conditions as an illustrative practical example.