A fast and precise filament winding path planning method based on discrete non-iterative semi-geodesic algorithm for all applicable mandrel

Obtaining reliable and stable winding paths for complex shapes with current filament winding technologies is still a challenge. Aiming at a practical design of the filament winding process, a novel discrete non-iterative semi-geodesic (NIS) algorithm is proposed, in which a first-order ordinary different equation (ODE) of the tangent vector is directly solved over triangle meshes and then the tangent vector is parallel transported along a geodesic path. Compared to the existing discrete iterative semi-geodesic algorithm, the NIS algorithm does not require trial-and-error to determine the next path point and the time complexity of the NIS algorithm to generate a semi-geodesic path is O(n). The relative error of the NIS algorithm compared with analytical method is less than 1% in terms of mandrel’s rotation angle and winding angle. Then, a complete discrete winding path planning method based on the NIS algorithm is presented, including constant-wall-thickness winding paths at regular winding region, semi-geodesic winding paths at return regions and certain winding pattern construction. This winding path planning method does not require knowledge of the parametric equations of mandrel and is particularly useful for designing winding path for all applicable mandrels, such as vessel, rocket motor and so on.