Design and analysis of a tip–tilt guide mechanism for the fast steering of a large-scale mirror

A devised tip–tilt guide mechanism (TTGM) for the fast steering of a large-scale mirror is presented. The TTGM uses a parallel structure with four struts, in which a double right-circular notch and a leaf spring are serially connected via a nondeformable rectangular linkage in aid of an axial flexure at the center of the payload. The benefits provided by the TTGM include pure rotation in the desired directions, an adaptable mechanism for a large and heavy mirror, and an adjustable virtual pivot of the moving body allowed by the configuration design. Closed-form stiffness equations of the individual flexure hinges are derived, and the equations of motion of the TTGM are mathematically formulated to predict the behaviors of the mechanism. To validate the performance of the TTGM, a design is presented and optimization of the geometric parameters of the TTGM is carried out. The model prediction accuracy for the resonant frequency relative to experimental results is found to be satisfactory, with errors of less than $11.4%$. It is proven that the devised TTGM is an appropriate structure as a two-axis guide mechanism in three-dimensional space for the 160-mm diameter mirror with an angular travel range of 1 mrad.