In five-axis machining the trajectory is composed of linear path which has the feature of tangential discontinuity, so that the velocity will be abrupt or be equal to zero at the corner of the adjacent segments. This problem greatly effects the machining efficiency and quality. So a pair of double cubic NURBS curves satisfying the predefined fitting accuracy are used to fair the corners of the adjacent five-axis linear segments and generate the smooth tool path. On the basis of the proposed transition model, the parametric synchronization of the smoothed double NURBS trajectories and the remained two linear segments are respectively constructed to realize the smoothing variation along the tool trajectory. The approximation error has an analytical relationship with the transition length of the smoothed curve. It is easily to construct the analytical double NURBS curves satisfying the pre-defined error limit. The simulation and experiment examples show that the proposed transition algorithm can satisfy the error constraint, generate the curvature-continuous double NURBS tool path, make local corner transition smooth and improve the machining quality.
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