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.

翻译：并联机器人存在奇异构型，此时机器人至少获得一个自由度并失去控制。理论上，当前向雅可比矩阵行列式为零时会发生此类奇异点（II型）。然而，由于制造公差引入的低重复性误差难以建模，实际并联机器人在行列式接近零但非零时也可能因II型奇异点而失控。本文以实际3UPS+RPU并联机器人为研究对象，提出三项贡献：i) 基于两个输出扭转螺旋夹角的II型奇异点接近度检测指标，该指标可识别导致奇异点的运动链；ii) 用于研究II型奇异点的实验基准；iii) 提出指标为零但前向雅可比行列式非零的机器人构型。在最后一种构型中，实验结果表明实际机器人无法应对外部作用力。