Computer-aided modeling of braided structures overbraiding non-cylindrical prisms based on surface transformation

• Obtain the braiding surface based on the surface transformation.
• Establish the geometrical modeling method based on the intersection of braiding surface and helical surface.
• Build the geometrical models for complicated braids overbraiding mandrels generated by extruding, sweeping, revolving and lofting.

This paper presents the geometrical modeling methods for braided structures overbraiding non-cylindrical prisms. This modeling method comes from the motion analysis of braiding process. The motion of strands in braiding process could be decomposed into circumferential motion, radial motion and axial motion based on the movements of carriers and take-up roller. These motions could be re-composed to form two independent surfaces: the braiding surface and helical surface, which include all information of strand movements in braiding process. Therefore, the strands could be obtained by the intersections of these two surfaces. The helical surfaces define the position of strands and the pitch while the braiding surfaces define the interlacing patterns and the outline of braids. For different braids overbraiding complicated structures, the simulated braids could be obtained by changing the braiding surfaces. Based on this theory, this paper illustrated the modeling methods for braids overbraiding prisms, which generated by extruding, sweeping, revolving and lofting respectively.