Model of cord winding on the elbow mandrel

A winding mode on the elbow mandrel was designed. The differential equation of the cord thread winding locus on the elbow mandrel was derived and solved numerically by means of fourth-order Runge-Kutta numerical procedure with the self-adapting step length. The theoretical and experimental results indicate that the winding angle of the cord on the straight part of the elbow mandrel is constant if the axis of mandrel coincides with the rotating center of the yarn tray. If the axis of mandrel departs from the rotating center of the yarn tray，the winding angle is variable. When the cord thread winds on the curved part of the elbow mandrel，the winding angle is always variable and reaches its extreme value on its both sides，which is consistent with experimental results.