  The first analytical evaluation of free-hinged-hinged-hinged-free beam,
proposed to be used as a primary sensing element for gravity gradiometry, is
presented. The results of the evaluation, obtained in quadratures, are applied
to the beam's structure such as the locations of hinges that form the beam's
boundary conditions allowing only free rotations around the nodal axes. The
latter are purposely chosen to minimize the beam's symmetric free ends
deflection under the uniform force of gravity while simultaneously permitting
the beam's maximum possible mirror-symmetric free ends deflection due to a
gravity gradient along its length. The flexible triple hinged beam's deflection
from its unperturbed position is internally entangled at all locations
including free ends and this allows for synchronized mechanical displacements
measurements at any beam's deflection point. Some methods of manufacturing such
sensing element and the corresponding error factors are also discussed for the
first time.
