Mathematical Characterization of Twisted Yarn

Twist leads to yarn torsion,which influences the physical and mechanical properties of yarn or fabric directly.In this paper,according to the basic principle of space geometry,the space geometric model of yarn was established,then the linking number,twisting number,and writhing number of elastic rod model were defined.The reason of yarn snarling was analyzed based on the energy,and the relation between yarn snarling and yarn torsion was studied according to White formula.The results show when tow ends of yarn are fixed,the linking number is constant,which means the sum of twisting number and writhing number for yarn torsion deformation and bend deformation is constant.