A method of producing a coil for a flexible drive shaft includes: winding a roving into at least one helical groove of a mandrel; coating the roving with an uncured material; heating the coated roving to a curing temperature in the at least one helical groove of the mandrel to cure the uncured material and form a composite roving; and stripping the composite roving from the mandrel. A method of forming a flexible driveshaft for a surgical instrument is also provided and includes: feeding a plurality of flexible coils into a feeder such that each of the plurality of flexible coils are spaced from one another about a rod; rotating the rod to wind the plurality of flexible coils about the rod; and binding the wound plurality of flexible coils and rod together.