An analytical method for corner smoothing of five-axis linear paths using the conformal geometric algebra

Abstract

The chain of linear path segments is widely used in five-axis machining, but the tangential discontinuity of the path reduces machining efficiency and accuracy. This paper proposes an analytical G 3 continuous corner smoothing method based on the conformal geometric algebra. Based on the locations of the tooltip point and a tool axis point, the toolpath is represented in the 6-dimensional Euclidean space. With the help of the representation of conformal transformations and circles in conformal geometric algebra, the path in the 6-dimensional space is smoothed by G 3 continuous circle-based splines under the constraints of the maximum deviation error tolerance. The proposed approach can generate a smooth toolpath that passes through the discrete cutter locations given in the original linear segments analytically. The cycle time of machining is improved thanks to the small curvature and G 3 continuity of the toolpath. The effectiveness and efficiency of the proposed method are validated by simulations and experiments. • A new analytical method for smoothing of 5-axis linear paths based on the conformal geometric algebra is proposed. • The proposed method generates G 3 continuous paths that satisfy the smooth error tolerance and pass through the initial discrete cutter locations. • The proposed method performs high efficiency and significantly improves the feedrate of the tool.