Torsional Models of Two - ply Yarn

In this paper, the vector equation of a generalised doubly wound helix was derived. Treloar's[1] plied yarn geometry could be obtained as a special case of the generalised doubly wound helix. The shortest fibre length around the surface of a helical tube (formed by fibre helices) was determined by applying variational principles. The fibre length as calculated by using Treloar's geometry was compared indirectly with the shortest possible fibre length at different levels of yarn deformation when some of Treloar's rigid geometrical constraints were relaxed. A new idea based on non - concentric circles was introduced to approximate the fibre helix movement in a two - ply yarn. A torsional model of two - ply yarn was developed and the theoretical predictions were compared with some preliminary experimental results.