Empirical compliance equations for conventional single-axis flexure hinges

In consideration of the stress concentration, unified compliance equations for conventional single-axis hinges are presented. The relationship between the stress concentration and the compliance of corner-filleted flexure hinges is first analyzed. Considering the stress concentration, coupled with a wide range of geometrical parameters, empirical compliance equations for conventional flexure hinges, are then obtained by using the exponential model. Subsequently, the proposed equations are unified. To verify the validity and accuracy of these equations, the characteristics of a bridge-type flexure-based mechanism are then analyzed by the proposed equations and finite element analysis, respectively. The results of compliances and displacement amplification ratios obtained by these two methods are in good agreement. It demonstrates that the empirical compliance equations could be obtained by exponential model, and these equations can be unified.