Based on the differential lever principle, a multi?stage compliant magnifying hinge was designed, and a micro?positioning platform with three translational degrees of freedom was assembled in an orthogonal way, and the symmetrical closed?loop structure formed has the characteristics of shock resistance, no cumulative error and better isotropy. The material is 7075 aluminum, and the stacked piezoelectric ceramics were used as the driving device to provide input displacement. Combined with the path search method and the static matrix method, the static balance equation and geometric deformation equation of the mechanism were obtained; the sensitivity analysis of the structural parameters was carried out, and the parameters with higher sensitivity in the mechanism are optimized with the displacement amplification ratio as the goal; a finite element analysis was performed on the assembly. The results shows that the stroke can reach 391.42 μm and the magnification is 13.05, and the platform has a high displacement magnification ratio and good positioning accuracy.