Kinematical properties and optimal design of 3-DOF precision positioning stage

To achieve the precise motion of a 3-RRR compliant parallel precision positioning stage,a closed-form exact motion model was established and the optimized design of structure parameters was investigated.The Castigliano's second theorem was applied to establishment of the closed-form compliance model for the precision positioning stage.According to the structural characteristics of compliant parallel mechanisms,the system was divided into three symmetrical motion sub-chains.Combining the compliance equations of flexure hinge with the force transmission relations of mechanisms,the stiffness model of each sub-chain was obtained,and the stiffness of the entire system was calculated by summing the stiffness of three sub-chains in the same coordinate system.The proposed stiffness model took the hinge flexibility as the independent variables in the closed form.According to the flexibility matrix,the Jacobian matrix to reflect the relationship between input displacement and output one could be derived.By comparing the kineamatic model between theoretical analysis and FEA,the results show that the errors are within 1.0%~9.5%,which illurastrates that the proposed kinematic model is correct and precise.According to the closed-form Jacobian matrix,its sensitivity to structureal parameters was analyzed,then the design variables with greater impact on the kinematic properties were chosen.By taking the maxmium workspace as a target and the hinge strength,maxmium input forces,geometric dimensions and input coupling as the constrains,an optimal model was proposed.The results show that the optimized structural parameters can obtain more output displacements,and the proposed model can meet the design requirement.