Stiffness modeling of a 2-DoF over-constrained planar parallel mechanism

Stiffness model acquisition of over-constrained parallel mechanisms is relatively difficult since they have more than necessary kinematic loops. In this study, a stiffness modeling solution for over-constrained parallel mechanisms is proposed while considering the computational cost efficiency. Three contributions of the paper are: (1) Presenting the stiffness modeling procedure for serially connected closed-loop structures by using the Virtual Joint Method (2) Considering the effect of dynamic auxiliary forces and dynamic external forces on the mobile platform's deflection and achieving a direct solution by using superposition principle (3) A model fitting procedure for modifying the stiffness coefficients to comply with the experimental data. A 2 degrees-of-freedom over-constrained parallel mechanism is investigated as a case study. However, the proposed stiffness model is 6-DoF since compliant deflections occur in any direction. A finite element analysis and an experimental study verify the model's results.