Practical range of applicability of a linear stiffness model of an elliptical flexure hinge

Insights into Bending Stiffness Modeling of Elementary Flexure Hinges

“…The flexure hinge is considered in the most stressed condition, namely when α Q = 0 and α M = 1, whereas the values of ρ and β y are chosen respectively equal to 15 and 0.1. The resulting values of θ f are collected in Table 1, where the superscript + indicates the choice of the positive sign in Equation (42). Entirely similar results but mirrored in the signs, in agreement with the absence of the transversal force Q, are obtained for negative rotations, in the following indicated by the superscript −.…”

“…Regarding parameter ∆M, it is easy to verify that when it is null, the classical linear relation between M f and θ f is obtained, namely: M f = Kθ f . Moreover, by looking at the second expression in Equation ( 45), the right side of the equation represents the first addendum in Equation (42). With reference to the results presented in Equations ( 42) and (44) and remembering the definition of µ Q , the following expressions of M f and Q can be imposed introducing the two coefficients α Q and α M : (46) where α M ∈ [0; 1] and α Q ∈ [−1; 1].…”

“…FE analyses were performed on a three-dimensional elliptical flexure with depth derived from Equation (54) when the equal sign is taken. They are provided in more detail in a previous work of the same authors [42]. Still, some information can be recalled here: the model of the flexure hinge was divided into three parts in order to refine the mesh in the thinnest central area.…”

“…The results are proposed in the form of maps and tables to appreciate the effect of varying different parameters on the accuracy of the stiffness model chosen for the flexure joint of interest. An example of how to use the information reported in this paper is shown in [42], where a case study is proposed to provide instructions for designing a flexure hinge with given specifications. The undeformed state of the beam represents the reference condition, with points A and B being its two ends.…”