Generation and characteristics analysis of the overhand knot using co-screw as gene

Aiming to generate the overhand knot and analyze its characteristics, a model of co-screw is established and a method is proposed by twisting and connecting two distinct rope segments. The results demonstrate that the co-screw has the feature of winding transfer, while the total angle of co-screw remains constant at 360°. The co-screw provides the overhand knot with one-direction interlocking function. The analysis and comparison of the connection types of co-screw endpoints demonstrates that, the co-screw is a common gene among the overhand knot, the Hopf link and the trefoil knot. The research on the characteristics of overhand knot shows that the upper-lower and the inner-outer relationships of the overhand knot have AB rhythms feature. The proposed approach provides a foundation for the development of overhand knot tying equipment.