Linear motion commands of multi-axis computer numerical control (CNC) machine tools need to be smoothed at the transition corners, because the velocity discontinuities at corners can result in fluctuations on machine tool motions and lead to poor surface quality. However, no research has been reported on local corner smoothing algorithm for four-axis CNC machine tools with two rotary axes by considering their special kinematic characteristics. To this end, this paper proposes an analytical C3 continuous local corner smoothing algorithm for four-axis CNC machines with two rotary axes. After coordinates transformation, the tool tip positions and tool orientations are smoothed by locally inserting specially designed three-dimensional (3D) quintic B-splines and one-dimensional (1D) quintic B-splines into the corners between linear motion segments, respectively. The smoothing algorithm guarantees C3 continuity of the tool tip position and C3 continuous synchronization of the tool orientation related to the tool tip position, through analytically evaluating control points of the inserted microsplines. The maximum error tolerances of the tool tip position and tool orientation are mathematically constrained. Experiments on an in-house developed four-axis machine verify the efficacy of the proposed algorithm, where maximal errors caused by the local corner smoothing algorithm are constrained, the synchronization of the tool orientation and the tool tip position are achieved, and the proposed C3 continuous corner smoothing algorithm has lower jerk and jounce but higher tracking and contour accuracy than C2 continuous algorithm.

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