Knitting Machine State Representation Using the Artin Braid Group

Industrial knitting machines are are incredibly powerful, flexible machines that are capable of creating a wide variety of shapes and structures using just a few basic operations. However, effectively using these operations to take full advantage of the machine’s capabilities is nontrivial; when creating a machine knitting pattern, the designer must decide how to move loops of yarn around the machine’s hundreds of needles, all while tracking interloop connections and tangles. Furthermore, they should do so in a way that minimizes construction time and error rate. To enable the computation of optimal machine knitting patterns, we developed an abstraction of the knitting machine state that uses the Artin braid group when describing interstitch relationships. We provide a formulation for each machine operation’s effect on this abstract representation. In addition, we leverage key properties of the braid group when considering the distance between any two machine states. These insights make searching the knitting machine state space for efficient patterns more computationally tractable, and we show several computationally planned patterns.