<p>In traditional machining of complex surfaces, discontinuity problem of linear toolpath generated by computer-aided manufacturing systems result in low machining efficiency, and also trigger tool vibration, reducing machining accuracy and surface quality. Therefore, Linear motion commands need to be smoothed at the transition corners. Analytical and shape-controllable corner smoothing path that satisfied the axis motion limits should be found. The paper proposes two corner path planning algorithms, including the arc corner transition and the Bezier corner transition. These algorithms give the maximal deviation error and corner running time. The effectiveness of the proposed algorithm is verified by the calculation and simulation of several different angles. Finally, the two algorithms proposed in the paper are verified by two model machining experiments, and measurement results show that the proposed algorithm has certain advantages in machining efficiency and machining surface accuracy.</p>