Abstract: Disclosed herein are various implementations of a fiber optic shape-sensing system comprising a plurality of optical fibers helically twisted and rigidly bonded to form a linearly-running shape-sensing bundle for measuring position, bend, and twist of the shape-sensing bundle, wherein each optical fiber from among the plurality of optical fibers comprises a single core. Several such implementations of the systems further comprise an array of Fiber Bragg Gratings (FBGs) disposed within the core of each single-core optical fiber from among the plurality of single-core optical fibers.