Design and stiffness modeling of a four-degree-of-freedom nanopositioning stage based on six-branched-chain compliant parallel mechanisms

Multi-degree-of-freedom (multi-DOF) nanopositioning stages (NPSs) have rapidly growing applications in the spatial micro-/nano-machining and manipulation. Compliant parallel mechanisms (CPMs) demonstrate advantages to achieve a large output stiffness and high payload. A four-DOF NPS based on six-branched-chain CPMs is proposed in this paper. First, a mechanism design approach is introduced. One primary vertical DOF is generated using three parallel-kinematic lever amplifiers. A three-revolute-revolute-revolute mechanism acts as the kinematic configuration to produce three secondary planar DOFs. Three types of single-axis and one type of double-axis notch flexure hinges (NFHs) are employed to realize the nanoscale displacement/movement guiding, transferring, and decoupling. Second, a stiffness modeling approach is derived. Combined with exact compliance matrices of 54 NFHs and 95 flexible beams, a four-DOF high-efficiency stiffness model of the six-branched-chain CPM is built. The calculation procedure of the whole input/output stiffnesses and coupling ratios takes 12.06 ms. Simulation and prototype test results validate the calculation accuracy. For example, the maximum calculation deviation of input stiffnesses is verified to be 4.52% and 8.18%, respectively. The two proposed approaches contribute to the statics parameter optimization of spatial multi-DOF NPSs.