A Two-stage CNC Interpolation Algorithm for Corner Smoothing Trajectories with Geometric Error and Dynamics Constraints

Corners among linear segments are normally smoothed in order to improve the CNC machining efficiency. The interpolation of the corner smoothing trajectories is important to guarantee high geometric accuracy and good dynamics performance. This paper proposes a two-stage interpolation algorithm for corner smoothing trajectories, which includes the off-line pre-processing stage and the on-line interpolation stage. The off-line pre-processing stage calculates the path lengths, and approximates the relation of spline parameters and spline lengths with 7th order polynomial splines within preset tolerance. The on-line interpolation stage generates interpolated drive commands with the trapezoidal acceleration profile, where chord errors and centripetal accelerations at transition corners are also constrained. Simulation and experiment results show that the proposed interpolation algorithm can improve the machining efficiency and satisfy the preset geometric error and dynamics constraints as well.