Dynamic modeling and damping-induced suppression of cross-coupling in an XY flexure-based stage

Compliant mechanisms are widely utilized in micro-nano motion applications. Cross-coupling in multi-axis motion is a significant source of errors in precision motion systems. Although the static and dynamic properties of flexure-based nanopositioning stages have been extensively studied, their unified parametric expressions for motion cross-coupling are still lacking, and the impact of damping on cross-coupling has not been thoroughly analyzed. In this paper, we further model the force–displacement relationship of compliant mechanisms and present an analytical framework for the dynamic cross-coupling of a precision motion stage based on the Beam Constraint Model (BCM). We predict the cross-coupling effect and analytically quantify cross-coupling errors in geometry. As a case study, this model is applied to the static and dynamic cross-coupling analysis of a flexure-based nanopositioning stage, examining the effective of damping on cross-coupling reduction. Experimental results show that the dynamic cross-coupling ratio decreased by 6.52% at low frequencies and 10.37% at the resonant frequency when the stage was equipped with passive damping. The nonlinear dynamic cross-coupling model effectively predicts cross-coupling behavior and the impact of damping, offering a simpler and clearer approach for forecasting the damping characteristics of cross-coupling. This model can be integrated into control systems for error compensation and the rejection of damping-induced cross-coupling, providing new insights into damping control in compliant mechanisms.