Discrete simulation of maypole braiding machines to create collision-free braiding programmes

We present a novel approach to the discrete modelling and simulation of maypole braiding machines with continuously rotating horn gears and controllable switches. Previously published models are not generally applicable because they are limited to specific machine geometries. We model maypole braiding machines with continuously rotating horn gears as 1-regular cyclic directed graphs with vertices at fixed positions on the machine bed. We will show how to efficiently represent machine state changes such as switch or domain operations, as well as carrier movement and collision checking by means of matrix operations. Our approach allows us to approximate the carrier motion of arbitrary maypole braiding machines by jumps between the fixed equidistant points. It allows effective calculation of carrier motion and collision checking. This provides interactive assistance to braiding machine programmers. During interactive programming, it is possible to calculate the number of steps in which a carrier is expected to collide, or whether the programme is verified to be collision free.