This paper presents the development of a 3-D displacement sensor based on one fiber Bragg grating (FBG). In order to obtain higher sensitivity and dynamic range, the FBG is inscribed in low-loss, multimode, cyclic transparent amorphous
fluoropolymers (CYTOP) using the direct-write, plane-by-plane femtosecond laser inscription method. The proposed sensor is
based on the influence of each displacement condition, namely
axial strain, torsion and bending on the FBG reflection spectrum.
Such influence is analyzed with respect to the FBG wavelength
shift, reflectivity and full width half maximum (FWHM). The operation principle and theoretical background of the proposed approach is numerically analyzed by means of finite element analysis for the strain along the grating length and coupled-mode theory with a modified transfer matrix formulation for the FBG
spectrum. The sensor is experimentally characterized and validated in which the results show good agreement between the
applied axial strain, bending and torsion with relative errors
below 5.5%. Thus, the proposed sensor is an interesting alternative for measuring displacements in 3-D applications such
as movement analysis and the instrumentation of novel soft robots.