Splines in the parameter domain of surfaces and their application in filament winding

For non-axisymmetric filament winding in the composite industry, it is difficult to automatically design fiber paths with uniform distribution, full coverage, and non-slippage. Geodesics and semi-geodesics are commonly used as non-slippage trajectories in the fiber path design. However, the uniqueness of these curves from the initial conditions severely restricts the freedom of design, which plays an important role in producing high performance parts. This paper presents a new class of trajectories with more freedom by generalizing splines, and gives the conditions to make these splines on cylinders and cones stable. The proposed trajectory has been applied to filament winding on elbows. Practical results show that the fiber distribution is excellent, and the finished product has extremely uniform thickness.