Design Variable Cross Section Roll-forming Part Using Bezier Curve

Abstract

This paper proposes a continuous stitching Bezier curve interpolation algorithm to assure the bending curve of a variable cross-section roll forming parts is smooth and continuous. By proposed algorithm the recursive equation is derived into solving the problem of Bezier curve control points. In order to make the bending curve smooth at each interpolation point, the continuity condition of two combined Bezier curve in Euclidean space curves is analyzed. With the proposed method, the accuracy and G2 continuity of the whole bending curve are obtained. Due to abandoning the traditional method which utilized straightly line segments and arc segments to construct the bending curve, the propose method can improve the design accuracy and realize the parametric design. The simulation using Mathematics soft demonstrates the feasibility of part design based on the proposed method. The research provides the theoretical basis for the control system of the variable cross section roll-forming part design.