Towards arranging and tightening knots and unknots with fixtures

Abstract. This paper presents a controlled tying approach for knots using fix-tures and simple pulling motions applied to the ends of string. Each fixture is specific to a particular knot; the paper gives a design process that allows a suit-able fixture to be designed for an input knot. Knot tying is separated into two phases. In the first phase, a fixture is used to loosely arrange the string around a set of rods, with the required topology of the given knot. In the second phase, the string is pulled taut and slid along the rods (the tightening fixture) in a direction such that the cross-sections of the rods get closer together, allowing controlled tightening. Successful tying is shown for two interesting cases: a “double coin” knot design, and the top of a shoelace knot.