This article presents the theoretical background for the arrangement of horn gears in maypole braiding machines in order to act as equivalent larger gears. The theoretical analysis is verified with numerical simulation and experiments. After review about the state of the art, an analysis of the process for one specific configuration of horn gears is given. This analysis demonstrates how a set of horn gears can be arranged to work as an equivalent to a larger one horn gear. The braiding equation is checked as remaining valid for such extended configurations, too. The theoretical result is verified using numerical simulation for all cases and practical validation for several variants. The theoretical rules give a clear extension of the current braiding knowledge and make the design of complex configurations of braiding machines more systematic and clear.

The pattern changes on the 3D rotary braiding machines (maypole principle with horn gears with full and empty slots) require complex planning of the carrier positions and timing and allow for production of bifurcated and other complex braids with variable cross sections for medical and technical applications. Another common application of pattern changes is to make a visually different pattern for marking of the remaining length of rope when used in a climbing context or for generally lengthened pieces for medical sutures. The development of such samples has previously been done using the trial-and-error method. This paper presents one rule for supporting a more systematic and purposeful trial, which significantly speeds up the development process. After a short review of the related literature, the main theoretical background is given and two practical cases for pattern change are demonstrated. The patterns were developed using numerical simulation before being tested on a real braiding machine. With this paper the authors hope to give some motivation for the remaining braiders in the world to continue working on the development of systematic rules for this complex process.

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