Basic Studies for Modeling Complex Weft Knitted Fabric Structures Part II: A Geometrical Model for Plain Knitted Fabric Spirality

A model for the spirality of plain knitted fabrics with compressible yarns is given here by modifying Kurbak's (1998) plain knitted loop model. The proposed model is thought to be applicable not only to the spirality of classical textiles, but also to modeling small diameter tubular technical textile fabrics. In the present study, it is suggested that because of the three-dimensional nature of the plain loop, the yarn part at the left arm of the loop and the yarn part at the right arm of the loop have torsions in opposite directions, so that if the yarn used is already twist lively, this potential twist applies in the same direction for both of the arms. Therefore, the total twist decreases in one arm and increases in the other. To equalize their total twists, the curves of the yarn axis in the arms differ from each other (the elliptical cylinders on which the yarn arms wrapped differ in length and in radius). The upper and lower parts of the loop adjust themselves by transforming into parametric elliptical shapes from their original elliptical shapes. There is another method of twist redistribution in the fabrics, which is to differentiate the wrapping angles of the helices on two arms of a loop. This is defined as “the second kind of spirality” and is mainly seen in m × n rib structures as well as in some of the technical textile plain knitted fabrics. This second kind of spirality is not considered during the creation of the model, but a discussion is given on this subject at the end of the work.