  Parallel robots (PRs) have singular configurations where the robot gains at
least one degree of freedom and loses control. Theoretically, such singularity
occurs when the Forward Jacobian-matrix determinant becomes zero (Type II).
However, actual PRs could lose control owing to Type II singularities for
determinant values near zero, but not zero, because manufacturing tolerances
introduce errors that are complex to model due to their low repeatability.
  Thus, using an actual 3UPS+RPU PR, this paper presents three contributions:
i) a proximity detection index for Type II singularities based on the angle
between two Output Twist Screws. The index can identify which kinematic chains
contribute to the singularity. ii) an experimental benchmark to study Type II
singularities. iii) PR configurations where the proposed index is zero and the
Forward Jacobian determinant is not. In this last configuration, the findings
show that the actual robot is unable to handle external actions applied to the
PR.
