Large deflection stiffness analysis of parallel prismatic leaf-spring flexures

The support stiffness of a parallel leaf-spring flexure should ideally be high, but deteriorates with increasing displacement. This significant characteristic needs to be quantified precisely, because it limits the use of parallel leaf-spring flexures in precision mechanisms. We present new and refined analytic formulas for the stiffness in three dimensions taking into account shear compliance, constrained warping and limited parallel external drive stiffness. The formulas are supplemented by a finite element analysis using shell elements to include anticlastic curving effects. Several approximation equations are presented for determining the drive force precisely. Even at relatively large deflections the derived formulas are in good agreement with the finite element results.