As a connecting component of tubes, the elbow is indispensable to pipe-fitting in composite products. Previous studies have addressed methods for generating winding paths based on parametric equations on the elbow. However, these methods are unsuitable for elbows whose surfaces are difficult to describe using mathematical expressions. In this study, a geometric method was proposed for generating winding patterns for various elbow types. With this method, the mandrel surface is first converted into uniform and high-quality quadrilateral elements; an algorithm is then provided for calculating the minimum winding angle for bridging-free. Next, an angle for non-bridging was defined as the design-winding angle to generate the uniform and slippage-free basic winding paths on the quadrilateral elements in non-geodesic directions. Finally, after a series of uniform points were calculated on the selected vertical edge according to the elbow type, the pattern paths were generated with the uniform points and basic paths. The proposed method is advantageously not limited to the elbow’s shape.

High-strength, continuous and uniform filament winding patterns remain challenging to find for non-axisymmetric models under various loading conditions. In this study, various loading conditions are considered in the development of an algorithm for generating uniform winding patterns for axisymmetric and non-axisymmetric mandrel models with flexible rotation at the ends of the mandrel. First, the mandrel surface is divided into sections by uniform quadrilateral elements and the ideal winding angle at each boundary is calculated based on the stress field. Then, stability analysis is used to calculate suitable winding angles as close as possible to the ideal winding angle for each boundary. These suitable winding angles can be used to generate the uniform winding pattern maintaining non-slippage and non-bridging while realizing flexible rotation at both ends of the mandrel. Finally, uniform patterns for various mandrel models are generated based on their respective suitable winding angles. Stress analysis result demonstrates that the wound mandrel generated by the proposed method can have better carrying capacity.

Roll-on and roll-off (Ro-Ro) ships are economical transportation vessels that are very useful for transporting large freights, such as plant equipment and aircraft bodies. To load a large freight on a Ro-Ro ship, a tractor is generally used to pull a trailer on which the cargo is secured via a ramp from the port berth to the ship deck. In the case of a long cargo, the trajectory of the trailer is not the same as that of the tractor, which can cause a collision with the ramp or the gate or obstacles on the deck. Also, if the freight is too high, it may overturn when the trailer is tilted due to the ramp slope. This research proposes a method for calculating the best and safest trajectories for large freights to be loaded on Ro-Ro ships without the occurrence of any collisions or overturns. By reasonably assuming a low speed of the tractor, the proposed method generates all the possible tractor paths based on the Bezier curve and also calculates the trajectories of trailers when moving on inclined ramps; thus, it is the first method to calculate 3D trajectories for trailers when the tractor and trailer move on different planes. Besides, it searches for the best paths without any collisions or overturns and with the minimum shipping time possible. Since the proposed method calculates the paths by taking the ramp angle as a variable input, the trajectories can be automatically generated based on the change in the waterline of the ship according to the loading of the cargoes. Overall, the proposed method can be useful for transportation companies when planning the shipping of large freights, and it can also be beneficial for future autonomous driving systems.

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