A novel method for listing all collision-free carrier arrangements of maypole braiding machines

This paper presents a multi-threaded approach for the distributed calculation of all collision-free, unique switch states and carrier arrangements for maypole braiding machines with rectangular horn gear configurations, taking into account reflection and rotation. The algorithm is based on a sequential four-stage approach. In this approach, the configuration of horn gears, switch states, track layouts and carrier arrangements are enumerated in consecutive order, building on each other. The individual stages consistently employ rotational and mirror-symmetrical simplifications. The calculation of switch states, track layouts and carrier arrangements is performed in parallel on a single CPU with multiple threads and synchronised by a main thread, thus enabling calculation on commodity hardware. Using the novel algorithm presented here, all collision-free carrier arrangements can be enumerated. Based on this, an initial quantitative evaluation was conducted of the braids that can be produced on Maypole braiding machines with 4 × 4 horngears. The comprehensive description of all collision-free carrier arrangements is the basis for a mathematical and data-driven analysis of modern Maypole braiding machines.