Modeling of Stitches with Two-Ply Yarn

Knitted fabrics can be knitted with a single yarn or two-ply yarn. In the case of a two-ply yarn, two strands are twisted together in the opposite direction to their respective twists. The former twist is referred to as the final twist and the latter twist as the primary twist. The ratio between the final twist and primary twist is very important because a knitted fabric can be skewed if it is inappropriate. However, the relationship between such a ratio and the degree of skewing is not clear, and how much skewing occurs in a fabric is unknown until it is actually knitted. Therefore, this paper proposes a method to model a two-ply yarn discretely and derive the stitch shape knitted with a two-ply yarn. First, stitches with a single yarn are modeled. The yarn coordinate systems are set on individual discrete points on the central axis of the yarn. Their rotation is represented by the quaternions. The yarn is represented with extensional/contractional, rotational, and torsional springs. Then, its potential energy can be described by the use of normal strains and quaternions. Next, geometric constraints to form a plain-knitted stitch are formulated. Then, the stitch shape can be derived by minimizing the potential energy of the yarn under geometric constraints. This method can be applied to the modeling of stitches with a two-ply yarn. In the case of the two-ply yarn, its shape is represented by the quaternions and three additional parameters. Our proposed method is expected to predict the skew of stitches because it considers both the final twist and the primary twist.