Programmable controllers in sophisticated precision winding systems are not the only way to wind material onto spools with tapered flanges. Rolling ring linear motion enables a mechanically controlled method for moving a traverse winder to spool material onto bi-conical reels. The linear speed and travel direction of the traversing unit are mechanically controlled -- independently of the drive motor speed. The movement of the traversing unit may be adjusted for precision without the use of an electronic control system. Reduced costs and ease of use are the result.