Analytical representation of nanoscale parasitic motion in flexure-based one DOF translation mechanism

Flexure-based compliant mechanisms are capable of meeting the demanding requirements of the partially constrained ultraprecision motion systems. However, the geometric errors induced by manufacturing tolerances can cause parasitic motion along the constrained directions, limiting the precision capability. Understanding parasitic motion at the nano-scale necessitates a 3D model even for mechanisms that are designed to be planar. Analytical modeling of a flexurebased double compound rectilinear spring mechanism with one degree of freedom translation, for quantifying the nano-scale parasitic motion is presented here. A spatial kinematics based kinetostatic model, that systematically accounts for the geometric errors and enables estimation of the inherently spatial parasitic motion, is presented. A metric is defined to represent the intrinsic parasitic motion, and Monte Carlo simulation is used to estimate the standard deviation of the chosen metric. Further, the analytical model is used to investigate the influence of flexure joint compliance parameters on the parasitic motion of the mechanism. The simulation results indicate greater than 50% improvement in the precision capability of the mechanism by improved design of flexure joints, without changing the manufacturing tolerance limits.