Method for winding textile yarns

A method for winding a textile yarn into a package is disclosed, and which is characterized by the ability to produce relatively large packages which are adapted to permit a high speed unwinding by withdrawal of the yarn over one end of the package. The method involves controlling the yarn traverse guide so as to include stroke modification cycles durin which the traverse stroke is progressively increased in length and then decreased, and such that a plot of the location of the stroke end points vs. time defines a parabola-like, arcuate curve. The exact shape of the curve is designed so as to produce a cylindrical wind in the end area, which is slightly greater in diameter than the diameter of the medial portion of the package. In addition, the traversing speed of the yarn guide and the circumferential speed of the package may be constantly accelerated and decelerated to avoid undesirable patterns, with the changes in speed being coordinated with the stroke modification cycles to provide a uniform yarn tension in the package.