NON-GEODESIC WINDING EQUATION ON A TORUS

The non-geodesic Filament winding process is reproducible when the friction between the resin impreguated filament and bases (the core or other filament layer) is utilized in order to prevent any slippage of the reinforcing material.Based on normal and geodesic curvatures in Differential Geometry,this paper analyzed conditions of equilibrium of a non-geodesic winding:
K_g/K_n≤μ
where K_n is the normal curvature of the point on the point on the curve,K_g the geodesic curvatnte of the point on the curve,and μ the coefficient of friction between the resin impreguated filament and the bases.The calculation formulas of a non-geodesic winding on a torus are presented in this paper,which can be solved with the aid of a method of numerical mathematics (Runge-Kutta method) and can also be utilized for a geodesic winding on a torus.A non-geodesic turn-around of the winding on a torus free of slippage is easily realized and this can be a evidence for winding curved tube.