Dimensionless design model for biaxial Cartwheel flexure hinges

Flexure hinges have been widely used in space-borne telescopes for mounting reflective optics with high surface figure requirements. To realize the three-point flexural mount of a Phi 750 mm primary mirror, a Cartwheel biaxial flexural hinge composed by filleted short beams is proposed and the dimensionless design graph method for the flexural hinge is presented. The finite element analysis is performed on the flexure model to validate the proposed method. We also demonstrate the feasibility of the proposed method experimentally. The maximum relative error of the rotational stiffness between analysis, testing result, and design value is 5.0%. The proposed dimensionless design graph can be used as a design tool to determine the optimal geometry of a spatial flexure hinge rapidly.