Corner smoothing and trajectory generation algorithm for complex linear toolpaths

In order to solve the problems of sudden change in velocity, machine vibration and machining accuracy reduction caused by discontinuity of tangential and curvature of linear toolpath, a corner smoothing algorithm based on linear path segmentation is proposed. The algorithm constructs G² continuous smoothing models for different corner types and incorporates an error allocation mechanism to strictly control both the smoothing approximation error and the interpolation chord error, thereby improving path fidelity. On this basis, the curvature extrema are obtained through analytical calculation. By combining the kinematic constraints of the machine tool and the acceleration/deceleration control strategy, a continuous and smooth velocity curve is planned to effectively suppress the impact during machine tool operation. Simulation results show that, compared with the traditional B-spline smoothing method, the proposed method reduces the average smoothing error by approximately 38.06%, yields smoother curvature variation, and shortens machining time by about 55.20%. The method demonstrates consistent accuracy and robustness across multiple path scenarios, significantly enhancing machining efficiency and trajectory quality, and offers strong potential for practical engineering applications.