Fiber Bragg grating (FBG) sensors are a promising tool for real-time shape reconstruction of dexterous continuum manipulators (DCM). We have recently developed a novel FBG-based shape sensor which is capable of detecting a radius of curvature of 15 mm for a 35 mm length DCM. This paper aims to further evaluate the accuracy of this shape sensor during motion of the DCM. Different experiments were performed including free bending, bending in the presence of an obstacle, and bending with a tool inserted in the lumen of the DCM. Results indicate that this sensor can track the tip position with an average error of 0.81 mm for free bending, 2.73 mm for bending with an obstacle, and 0.93 mm for bending with a tool.