Workspace of parallel kinematics machines with minimum stiffness limits: Collinear stiffness value based approach

Stiffness features of the parallel kinematics machines (PKM) are considered. To overcome the difficulties caused by heterogeneous units of measurement of the Cartesian stiffness matrix entries, a new performance index – the collinear stiffness value (CSV) – is applied. The CSV gives natural stiffness evaluation in both regular and singular configurations. Effective computation procedures for a search for the minimum–maximum CSV are developed. The minimum CSV is applied to construct a PKM workspace satisfying preliminary given stiffness limits and compute a virtual protective barrier, keeping the PKM mechanism from approaching the vicinity of singular configurations. As an application example, the CSV-based local and global stiffness features of the Gough–Stewart platform mechanism are simulated, investigated, and visualized.