Kinetostatic modelling of a 3-PRR planar compliant parallel manipulator with flexure pivots

Flexure pivots are widely used in long stroke complaint parallel manipulators (CPMs) for their large deformation capacity. However the parasitic motion caused by the flexure pivots cannot be neglected as the rotation angle gets large, which will finally affect the absolute positioning accuracy of the manipulators. In this paper, a modelling approach to calculate the nonlinear kinetostatics of a long stroke planar CPM with flexure pivots is proposed, in which the parasitic motion of the flexure joints are taken into account. The displacement constraint equations and the static equilibrium equations of the CPM are established under the deformed configuration. Finite element analysis (FEA) shows the accuracy and efficiency of the nonlinear kinematic model (NLKM) for both the inverse and forward kinematic analysis. Moreover, the prediction accuracy of the CPM's kinematic behavior has been improved more than 20 times by employing the NLKM compared with the conventional kinematic model (CKM).