Geometrical Models for Cardigan Structures Part I: Full Cardigan

Abstract

In this study a geometrical model for the full cardigan structure is given based on Kurbak’s plain-knitted loop model. In the model, loop and tuck heads were taken as ellipses in two dimensions, where the loop heads lean towards the thickness direction at an angle α1 and the tuck heads are in a vertical direction. The rest of the loops and tucks were taken as parabolic helices wrapped on circular cylinders. The parameters of the model were obtained by using a wash-relaxed wool fabric at medium tightness. Computer drawings of the model were created by using 3DSMax, which gave similar loop shapes to those observed in real fabrics. This full cardigan model will be used to obtain a model for a the half-cardigan structure in the following study as Part II.

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“…Peirce model [8] were universal accepted for woven structure, Zheng [9] proposed a revised algorithm based on progressive iteration of spring-slide model. As for the knitted fabrics and the braided fabrics, they have their special calculating model [10,11]. Whatever the type of the fabric, the positions of the central points and the shapes of the cross-section of all the control key points for a single yarn have to be determined, and the geometric structure of the yarn and then the fabric will be reconstructed and imitated by B-spline surface.…”

Geometrical model for a newly designed three-dimensional functional rib-knitted cord

“…There are geometrical models created for knitted fabrics by previous researchers. In this context, Chamberlain, 5 Pierce, 6 Leaf and Glaskin, 7 Leaf, 8 Munden, 9 Postle, 10 Smirfitt, 11 Natkanski, 12 Kurbak and Ekmen, 13 Kurbak and Soydan, 14 Kurbak, 15 Kurbak and Alpyıldız, 16 Kurbak and Soydan, 17 Kurbak and Amreeva, 18 Alpyıldız and Kurbak 19 and Kurbak and Alpyıldız 20–22 were given geometrical models for knitted fabrics.…”

“…The rest of the structure in Figure 8 is modeled by assuming the models of Kurbak and his colleagues 13–22 as the basic works. In particular, loop arms are modeled that are similarly to those in the 1 × 1 rib model given by Kurbak.…”

“…In Kurbak’s models, 13–22 yarn arms and also rib connecting parts are modeled by having imaginary elliptical cylinders (see Figure 10(a)) and wrapping the yarn axis around these cylinders using the equation where z is the wrapping length of the cylinder, S 1 is the elliptical arc length on the cross-section of the imaginary elliptical cylinders and a', b' and c' are constants.…”

Geometrical Models for Cardigan Structures Part II: Half Cardigan

“…Our interest here is to present a geometrical model for the half cardigan structure since no such models are described in the literature. The reason for such modeling studies has already been indicated in Part I of this series and the model is based on the full cardigan model given in Part I [1]. Previously created models for other knitting structures have been outlined in Part I [1], therefore they are not given again here.…”