A tool for forming a sensor coil that may be employed, for example, in a fiber optic gyroscope with reduced Shupe effect-induced bias. The tool includes a takeup reel having a cylindrical mandrel with inner flanges fixed to its opposed ends sandwiched between two outer flanges. Each of the inner flanges includes a pair of radially-directed apertures that form a radially-directed wedge therebetween. A recess in the planar portion of each of the outer flanges that contacts an inner flange is aligned with the apertures. This permits the winding of the sensor coil to form climbing turns at the ends of wound layers that lie outside an encapsulated fiber pack. Such turns, which join layers with overlying layers, avoid crossovers and the resultant stress that contributes significantly to Shupe effect-induced bias. A sensor coil having reduced internal stress is thus also provided.