The importance of imperfections in leaf-spring flexures for the support stiffness

In the design of mechanisms with elastic joints, leaf-springs are often used. These have a large in-plane stiffness and a relatively small out-of-plane stiffness, which allows the design of elastic joints with a large stiffness in some directions, called the support stiffness, and a small stiffness in the complementary directions in which motion is desired, called the drive stiffness. Examples are a parallel leaf-spring guidance as an approximation for a prismatic joint and a cross-spring pivot as an approximation for a revolute joint. The support stiffness decreases when a joint is deflected from its central position. Also imperfections in the leaf-springs due to lack of flatness or assembly misalignments can have this effect. Residual stresses mainly influence the torsional rigidity of leaf-springs, whereas the influence on the flexural rigidity is non-linear and becomes important near the stability limit. Initial deflections of the order of the thickness of the leaf-springs can already have a significant influence on the support stiffness in the central position.