Application of graph theory for detecting carriers’ collisions in braiding machines

Traditionally manufactured for ropes and fishing lines, braids are now found in structural composite parts used in the transportation industries and the medical sector. Braiding machines are increasing in size and complexity. However, engineers mostly rely on expertise and on trials and errors to select a collision-free carrier arrangement, which is inefficient in terms of both time and resources. In this paper, we propose a method, based on graph theory, to detect collisions between carriers for any braiding machine configuration and for any number of carriers. To do so, the braiding machine is modeled as a graph. Each horngear is represented by a face and each horngear slot is represented by a vertex. A collision detection algorithm is developed, which validates or invalidates the proposed carrier arrangement. Two case studies are carried out to demonstrate the algorithm. The first one is carried out on a traditional maypole braiding machine, while the second one is done on a T-shape braider. The T-shape braider has a more complex configuration with horngears having different number of slots and diameters. The developed solution is an efficient method to detect collisions based on any carrier arrangement.