Abstract:

Objective From the manufacturing of single component to one-piece products, the full forming computerized flat knitting machines are now capable of rapidly producing knitted products. However, the structure of knitted three-dimensional products is complex, and the forming process needs to be further improved. On the basis of the existing process design methods, the full forming process design of knitted three-dimensional products with more complex structure was carried out, and the process algorithm in the forming process was discussed, so as to facilitate the full formation of three-dimensional knitted fabrics.

Method According to different appearance contours, three-dimensional knitted products was classified and the cylindrical structure, cubic structure and spherical structure were analyzed based on the full forming process, before selecting truncated cone, frustum of a pyramid and sphere with general characteristics for algorithm model construction. After transforming into the full forming paper pattern, the mathematical relationship between the number of knitting rows, the number of narrowing and widening needles and the inclination angle was explored. Finally, the curved lamp shade was knitted on the four-needle-bed flat knitting machine to verify the feasibility.

Results From the perspective of appearance and contour modeling, knitted three-dimensional products can be divided into cylinder structure, cubic structure, spherical structure and special-shaped structure, which were utilized to produce clothing, bags, lighting, seats and other categories of knitted products. The truncated cone obtained a full forming paper pattern by cutting and expanding, and a trigonometric function relationship was formed between the number of knitting rows, the number of narrowing and widening needles and the inclination angle, and hence the trigonometric transformation method was proposed. The side shape of the truncated cone was achieved by entering the number of knitting rows and the number of narrowing and widening needles (Fig.6). The frustum of a pyramid was converted into a two-dimensional paper pattern after flattening along the diagonal line of the bottom face, and the upper and lower cover surfaces were converted into parallelograms corresponding to the sides, so as to propose a parallelogram transformation method to simplify the connection process between the sides and the upper and lower bottom surfaces. Similarly, there was a trigonometric relationship between the number of knitting rows, the number of hanging needles and the tilt angle, and the three-dimensional shape was achieved with the help of parallelogram transformation method and triangular transformation method (Fig.8). The sphere was cut and stretched to obtain the full forming paper pattern, and the arc profile was converted into several successively connected moment blocks, so as to propose the inverse fitting method. The edge moment block was adopted to create the arc shape (Fig.10). The example of the arc lamp shade was knitted with obvious arc contour of the lamp shade using the reverse fitting method, and the size parameters met the design requirements (Fig.14).

Conclusion In the transformation process form a three-dimensional structure to the two-dimensional paper pattern and then to the full forming paper pattern, a corresponding mathematical transformation relationship was established, based on which triangular conversion method is adopted to construct the edge straight contour for the cylindrical products, the parallelogram transformation method is employed to facilitate the three-dimensional structure of the upper and lower cover surfaces for the cube products, and the inverse fitting method is applied to achieve arc appearance modeling for the spherical configurations. The knitted three-dimensional products after structural transformation are knitted on the computerized flat knitting machine, forming one-piece fabrics by the transformation of the full forming process, supported by the process models and algorithms.

Key words: three-dimensional configuration, full forming knitting, process modeling, paper pattern transformation, computerized flat knitting machine, two-dimensional pattern