Towards Arranging and Tightening Knots and Unknots With Fixtures


This paper presents a controlled tying approach for knots using fixtures and straightforward pulling motions applied to the ends of string. Each fixture is particular to a explicit knot; the paper offers a design process that allows a suitable fixture to be designed for an input knot. Knot tying is separated into two phases. In the primary section, a fixture is used to loosely arrange the string around a collection of rods, with the specified topology of the given knot. In the second section, the string is pulled taut around the tightening fixtures. Two tightening fixture designs are presented. The first style is a fixture with no moving elements; tilted rods whose cross-sections get nearer near the tips, guiding string in a very controlled fashion as string slides up the rods during tightening. The second design could be a collection of straight rods that may move passively along predefined paths during tightening. Successful tying is shown for three fascinating cases: a “cloverleaf knot” design, a “double coin” knot design, and therefore the high of a shoelace knot.

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