An analytical G3 continuous corner smoothing method with adaptive constraints adjustments for five-axis machine tool

In this paper, an analytical local corner smoothing method is proposed with two specially designed quartic curves to generate smooth motion trajectories of five-axis linear segments. One symmetrical quartic B-spline curve is used to smooth the tool tip position in workpiece coordinate system (WCS); meanwhile, another asymmetrical quartic B-spline curve is used to smooth the tool orientation in machine coordinate system (MCS). With the proposed method, not only the transition error of tool tip position and the smoothing error of the tool orientation are mathematically constrained in WCS, but the G3 continuity of the tool tip position and tool orientation are guaranteed along the entire toolpath. Besides, the maximum possible machining error of tool tip position caused by transition error and chord error is also controlled analytically by transition error adjustment. What's more, in feedrate scheduling, the feedrate of tool tip is moderately adjusted by smooth feedrate profile, which can limit the maximum feedrate of tool orientation and achieve continuous axial feedrate and acceleration. Finally, the effectiveness and feasibility of the proposed method have been validated via simulations.