Characterization of dynamic behavior of flexure-based mechanisms for precision angular alignment

Angular alignment is a critical requirement in numerous precision motion control applications. Examples include beam-steering in optical communications and tool-sample alignment in imprint lithography. Flexural mechanisms are being widely used in such applications. The absence of non-linearities, including friction and backlash, makes flexural components ideal for achieving atomic-scale resolution. Closed-loop control implementations of flexural angle alignment mechanisms have been attempted in the literature in various cases. Performance limitations in closed-loop control implementations have been characterized traditionally considering effects of actuators, sensors, and control algorithms used. However, a critical limiting factor is imposed by the open-loop response of the plant, i.e. the natural frequencies of the flexural mechanism itself. In this paper, we assemble models for characterizing the dynamic behavior of flexural mechanisms for angular alignment. The performance trade-offs in terms of range, load-capacity, and control bandwidth are highlighted. A state-space formulation is proposed for mapping design performance variables, such as vertical deflection or angular acceleration. The effects on dynamic performance imposed by asymmetry resulting from manufacturing errors are studied.