Space corner smoothing of CNC machine tools through developing 3D general clothoid

Tool paths defined by G01/G02/G03 commands need to be smoothed to eliminate the discontinuities of velocity, acceleration and jerk at the junction points. Because of inherent problems of curve fillets, traditional corner smoothing strategies are limited to the smoothing of corners in plane. This article presents a method to smooth the space corners through blending the position, tangent, curvature and sharpness of the adjacent trajectory segments based on 3D general clothoid splines, which are analytically developed by proposing 3D clothoid with G³ continuity. The 3D general clothoid realizes extending the traditional clothoid from 2-dimension to 3-dimension, and reserves some good properties of the traditional clothoid, i.e. the curve length parameterization and the analytically expressed curvature. It can also achieve higher degree of continuity compared to the traditional 2D clothoid. Based on the proposed 3D general clothoid, a corner smoothing algorithm, which is suitable for the smoothing of any planar or space line-line, line-arc or arc-arc pairs with G³ continuity, is proposed. At the same time, a smoothing-error-constraining-algorithm is developed to constrain the smoothing error within the tolerance. Simulation and experimental results, which are obtained from the smoothing of trajectories containing space corners, trajectories containing planar corners with G02/G03 commands, and trajectories containing planar corners with only G01 commands, demonstrate that the proposed corner smoothing algorithm can effectively increase the machining quality and efficiency.