Design and analysis of a bi-axial centralized butterfly flexure hinge for fast steering mirrors

A bi-axial centralized butterfly flexure hinge for a fast steering mirror (FSM) was presented to adapt highly stabile accuracy of beam-pointing control performance in space laser communication. According to the requirements of two-dimensional reciprocating movements and high bandwidth provided for the FSM, the solid model of the bi-axial centralized butterfly flexure hinge was designed. By applying Castigliano's displacement theorem, the numerical model was simplified and deduced. Furthermore, to quantify the numerical model, natural frequencies of the finite-element analysis (FEA) and experiments were carried out the results of which were compared with the analytic solutions. The experimental results show that the in-plane natural frequencies are 66.37 and 112.2 Hz, respectively. The comparison shows that the errors between numerical analytic and experimentation are 3.0% and 1.4%, respectively, and errors between FEA and experimentation are 1.7% and 2.4%, respectively. It is proven that the bi-axial centralized butterfly flexure hinge we built is an appropriate structure as a two-axis guide mechanism in two-dimensions for an FSM system with a large bandwidth of 225 Hz.