Design and Dynamic Modeling of a 2-DOF Decoupled Flexure-Based Mechanism

Flexure mechanisms with decoupled characteristics have been widely utilized in precision positioning applications. However, these mechanisms suffer from either slow response or low load capability. Furthermore, asymmetric design always leads to thermal error. In order to solve these issues, a novel 2-DOF decoupled mechanism is developed by monolithically manufacturing sets of statically indeterminate symmetric (SIS) flexure structures in parallel. Symmetric design helps to eliminate the thermal error and Finite Element Analysis (FEA) results show that the maximum coupling ratio between X and Y axes is below 0.25% when a maximum pretension force of 200 N is applied. By ignoring the mass effect, all the SIS flexure structures are simplified to "spring-damper" components, from which the static and dynamics model are derived. The relation between the first resonant frequency of the mechanism and the load is investigated by incorporating the load mass into the proposed dynamics model. Analytical results show that even with a load of 0.5 kg, the first resonant frequency is still higher than 300 Hz, indicating a high load capability. The mechanism's static and dynamic performances are experimentally examined. The linear stiffnesses of the mechanism at the working platform and at the driving point are measured to be 3.563 0 N.mu m(-1) and 3.362 1 N.mu m(-1), respectively. The corresponding estimation values from analytical models are 3.405 7 N.mu m(-1) and 3.381 7 N.mu m(-1), which correspond to estimation errors of -4.41% and 0.6%, respectively. With an additional load of 0.16 kg, the measured and estimated first resonant frequencies are 362 Hz and 365 Hz, respectively. The estimation error is only 0.55%. The analytical and experimental results show that the developed mechanism has good performances in both decoupling ability and load capability; its static and dynamic performance can be precisely estimated from corresponding analytical models. The proposed mechanism has wide potentials in precision positioning applications.