A geometrical model for widthwise curlings in plain knitted structures is suggested here based on the plain knitted fabric model of Kurbak (1998). The main aim is to create models of m × n rib fabrics and also to model small diameter tubular fabrics. The model obtained is drawn to scale using the 3DS-MAX computer graphics program. With this model, the changes in radius of curvature at each part of the loop are shown.

Geometrical modelings of the fabric structures are needed to understand the dimensional behavior of knitted fabrics, to be able to define the surface properties and to prepare the basic work for creating physical models. Our main aim here is to prepare basic work for creating physical models for complex knitted structures. Firstly, we wish to discuss the dimensional properties of the whole basic weft knitted structures first, and after obtaining the whole picture, we will study the physical models. Thus, any physical parameter is not discussed here.Many researchers have studied the dimensional properties of weft knitted fabrics. Among these researchers, some [5,6,9,11,18,36,41,[46][47][48]53, 60] studied the mechanical modeling of weft knitted structures, some [8,27,29,37,38,41,45,49,52] suggested geometrical models to fit the plain-knitted loop shape, and some [22,27,42,49,55,64] suggested geometrical models for 1 × 1 rib fabric. However, the models given for 1 × 1 ribs were not general models to explain the whole phenomena observed in practice.A physical model of 1 × 1 rib fabric was given by Hepworth [17], but it is too difficult to apply the model to all relaxed fabric simulations.There are studies [1, 10, 15, 19-21, 23, 51, 58, 65, 66] which have defined the weft knitted textile material behavior in technical textile applications. In these studies, mostly basic knitted structures (plain, rib, milano and interlock) were used to manufacture the technical textiles.For further analysis, for example with finite element method, there is the need for proper geometrical definition of the structures to be considered as the initial state and also to make some assumptions in creating physical models. In the first part of this study, geometrical model for the 1 × 1 rib knitted fabric is developed because this fabric is commercially very popular as classical textiles and it is also very popular for technical applications nowadays. Application of the model to conventionally knitted fabrics (fabrics knitted using conventional take down tension) is also given in part I of this series. Part II will deal with the applications of 1 × 1 rib model to the structures as interlock, half milano and presser-foot knitted 1 × 1 rib. Part III will deal with the geometrical models of 2 × 2, 3 × 3, 4 × 4 and 5 × 5 rib fabrics, in which a modified version of the present 1 × 1 rib model will be used. 1Abstract The 1 × 1 rib knitted fabric is mostly used for collar, cuff, waistband, etc. of outerwear knitted garments and it is also very popular nowadays for using as preforms of knitted composite structures. A geometrical model to predict the dimensional properties of conventionally knitted 1 × 1 rib fabric is created and given in part I of this series of papers. With the 1 × 1 rib model, relaxation mechanism and the effect of tightness on conventionally knitted 1 × 1 rib fabrics of wool are attempted to be explained (as an example of application of the model).

A geometrical model for milano rib fabric at a normal tightness condition, based on Kurbak's (1998) plain-knitted loop model, was created. The model showed that small yarn compressions at the interlocking points and 50% yarn swellings away from the interlocking points might have occurred in the experimental sample used for comparison. Drawing of the model using the 3DS MAX computer graphic program gave a similar shape to that obtained experimentally with the real fabrics.

In this work, the dimensional properties of milano rib and half milano rib knitted fabrics were investigated experimentally using five different take-down tension values, five different tightness values, and three different yarn types. Dry, wet, and wash relaxations were applied to the samples, and after each relaxation, course-spacings ( c) and wale-spacings ( w) were measured. Loop lengths (ℓ) were also measured only after dry relaxation. Linear regression analysis was applied to the relations between c and ℓ and between w and ℓ. High correlation coefficients were found and the intercepts Ac and Aw of these linear regression equations were statistically important. Yet another regression equation between the intercepts Ac and the inclinations 1/ Kc and also between Aw and 1/ Kw could be applied with high correlation coefficients. The results showed that Kurbak's empirical equations were also applied to milano rib fabrics and the coefficients of the equations were given together with the most popular weft knitted fabrics.

A new double-face knitted structure has been developed which is composed of tuck stitches and has the same back and front faces. The newly derived structure, manufactured from p-aramid fibers with and without inlay yarns, has been compared with jersey and plush structures of these same fibers in terms of cut and stab performances. Not only have new structures been proposed, but the effect of the inlay yarns has been investigated also. In order to manufacture the plush structure on a V-bed Flat Knitting Machine instead of a traditional circular knitting machine a new design has been developed. The results show that the newly derived structure with inlay yarns has the best cut and stab performances when a comparison is made between samples of different structures with the same mass per unit area and thickness values.