Flexible Helicoids, Atomic Force Microscopy (AFM) Cantilevers in High Mode Vibration, and Concave Notch Hinges in Precision Measurements and Research

Abstract: Flexible structures are the main components in many precision measuring and research systems. They provide miniaturization, repeatability, minimal damping, low measuring forces, and very high resolution. This article focuses on the modeling, development, and comparison of three typical flexible micro- nano-structures: flexible helicoids, atomic force microscopy (AFM) cantilevers, and concave notch hinges. Our theory yields results which allow us to increase the accuracy and functionality of these structures in new fields of application such as the modeling of helicoidal DNA molecules’ mechanics, the definition of instantaneous center of rotation in concave flexure notch hinges, and the estimation of the increase of spring constants and resolution at higher mode vibration in AFM cantilevers with an additional concentrated and end extended mass. We developed the original kinetostatic, reverse conformal mapping of approximating contours, and non-linear thermomechanical fluctuation methods for calculation, comparison, and research of the micromechanical structures. These methods simplify complicated solutions in micro elasticity but provide them with necessary accuracy. All our calculation results in this article and in all corresponding referenced author’s publications are in a good agreement with experimental and finite element modeling data within 10% or less.