Abstract
In this paper, a modeling method of knitted loops in a plain stitch fabric, which can simulate its curling and wale skew, is proposed. First, a yarn is modeled as an elastic linear object whose cross-section is circular and does not change during deformation. Then, the shape of the yarn and its potential energy can be described by use of Euler angles based on the differential geometry and its stable shape can be derived by minimizing its potential energy under geometric constraints imposed on it. Applying this model, the shape of a knitted structure can be determined when only properties of a yarn such as the radius, flexural rigidity, and torsional rigidity and parameters for knitting such as the length of one loop, wale width, and course width are input. Curling/wale skew is phenomenon caused by decrease of the potential energy of a knit with an asymmetric structure/twisted yarns. Therefore, such phenomena also can be simulated with our proposed method in which the shape of a knit is determined by minimizing its potential energy. Computational results show the qualitative validity of our proposed method.
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