This paper presents a controlled tying approach for knots using fixtures 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 suitable 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 around the tightening fixtures. Two tightening fixture designs are presented. The first design is a fixture with no moving parts; tilted rods whose cross-sections get closer near the tips, guiding string in a controlled fashion as string slides up the rods during tightening. The second design is a collection of straight rods that can move passively along predefined paths during tightening. Successful tying is shown for three interesting cases: a “cloverleaf knot” design, a “double coin” knot design, and the top of a shoelace knot.

Knot tying poses a challenge to robotic and human manipulation due to the need to regrasp a flexible string. Without sensing, it becomes nearly impossible to guess where the string is. However, by using a fixture, the string can be continually grasped during the entire tying process. We have developed fixtures for a simple overhand knot and a square knot, and have started developing a fixture for the two half hitches knot. We can tie knots in different types of wire and fishing line using these fixtures. In addition, we used a Cobra i600 SCARA arm to autonomously tie multiple overhand knots in sequence without sensing, using solder as the string-like material.