Permutation Analysis of Track and Column Braiding

Introduction Trackandcolumnbraidingisanavailable3D braidingmethod1～3],whichperformsbraidingprocessbymovingbraidingcarriersalongroworcolumndirection alternatively.LiandDing4]examinethebraidingmethod andconcentratetheirstudyonthemovementofbraiding carriersonthebraidingplatform,onwhichthebraiding tracksarelocated.Accordingtothebraidingprinciple,a studyofbraidingprocessisactuallyastudyofthemovingpatternofyarnendsonthebraidingplatform.Intheiranotherpaper6],thepositionsofbraidingcarriersare r…

Permutation Analysis of Track and Column Braiding

The positions of braiding carrier in track and column braiding are represented by a diagrammatic braiding plan and a corresponding lattice-array is defined. A set is then formed so that the permutation analysis can be performed to represent the movement of carriers in a braiding process. The process of 4-step braiding is analyzed as an example to describe the application of the proposed method by expressing a braiding cycle as a product of disjoint cycles. As a result, a mapping relation between the disjoint cycles and the movement of carriers is deduced. Following the same analysis principles, a process of 8-step braiding and the corresponding initial state of the lattice-array is developed. A successful permutation analysis to the process manifests the general suitability of the proposed method.