Abstract:

Objective The loop-transfer cable stitch is the main structure that forms the surface texture effect of the flat knitted sweater product, and its application is very extensive. Achieving the rapid design and three-dimensional structure simulation of the cable fabrics to facilitate quick prediction of the fabric effect of the cabled fabrics is of great significance to reduce the design and development cost of cable-knitted sweater fabrics.
Method Based on the knitting principle and knitting method of the cable stitch, the knitting action was parameterized, and the mathematical models for the pattern and for the knitting structure diagram were proposed. Combined with the structural characteristics of each loop of the cable fabrics, an ideal loop model was established, and the trajectory of the value point for the transfer loop was analyzed. Finally, C# and WebGL were used to program the three-dimensional structure simulation of the flat knitted cable fabric.
Results The pattern matrix model and the minimum structure unit matrix were established by the minimum pattern cycle of the cable fabric, and the block matrix F_A of the expanded pattern was established according to the color value of the pattern matrix. Then the relationship between the block matrix F_A and the structure diagram matrix in the pattern diagram matrix was obtained in combination with Equation 4, and the process knitting diagram matrix model of cable fabric was obtained by replacing the matrix elements, see Equation 5. The loop of transferred was based on the normal flat needle loop knitting, and the needle was transferred through the needle bed traversing to transfer the needle arc to form the loop tilt effect. A loop geometry model based on the normal flat needle loop geometry model showed that transfers one needle to the right, based on the establishment of the loop type value point and the loop root junction point (Fig. 4). The coordinates of the 4 type value points near the root junction point of the transfer loop remain basically unchanged, and the coordinates of the 4 type value points near the needle arc were related to the ratio between the number of needles transferred by the loop and the loop distance (g_w) and loop height (g_h). For the transfer loop with different needle transfer directions, needle transfer rows and needle transfer needle numbers showed the change law of the type value point of the transfer loop (Fig. 5). It can be seen that the coordinate values of the four type value points near the root junction point of the transfer loop are determined by the loop root junction point O₀ before the transfer loop, and the coordinate values of the four type value points near the needle arc of the transfer loop are determined by the loop root junction point O₁ at the next position of the transfer loop. Such change was reflected in Equations 7 and 8. Based on the above theory and model, the three-dimensional structure simulation diagram of the cable fabric was finally obtained, and the loop structure of the cable fabric in several weaving states was clearly presented (Fig. 6).
Conclusion Through the conversion between the pattern model and the knitting structure diagram model of the cable fabric, and based on the establishment of the fabric loop geometry model under the ideal state, the rapid design and three-dimensional simulation of the sweater cable fabric can be realized. Although the three-dimensional simulation of the fabric based on the geometric models can clearly represent the string relationship of the fabric, the realization of the cable fabric simulation requires the next step of research on the physical and mechanical model.

Key words: cable fabric, pattern design, loop structure model, three-dimensional simulation, sweater