A Closed-Form Model for the Support Stiffness of Spatial Flexure Strips With Limited Twist

The stiffness characteristics of flexure strips in the constrained directions are an important attribute of their behavior when serving as a constituent of flexure mechanisms. The decrease in support stiffness that accompanies movement in the intended degrees of freedom limits the performance of mechanisms comprised of such strips. This paper presents a closed-form nonlinear model that describes the support stiffness in 3-D under arbitrary end-load for the elementary flexure strip. The formulation takes into account geometrical nonlinearities by means of finite strain relations and deformed-configuration equilibrium equations. By distinguishing the low-stiffness large-deflection motion (the degrees of freedom) from the high-stiffness small-deflection motion (the constrained motion) with the appropriate simplification of limited twist, a closed-form stiffness model is obtained for dimension and load ranges of practical interest.