The Mechanics of Bent Yarns

This paper analyzes the idealized geometry of a bent yarn. Expressions are derived for the cal culation of local fiber tensile strain, average strain in the helix half loop, motion of the fibers during bending of the yarn, changes in local helix angles, and fiber curvatures at the bend. The relationships between the geometric quantities of a bent yarn are presented graphically in dimen sionless parameters, and conversions to the usual textile terms are provided. Attention is given to the practical applications of this analytical approach to textile problems.