The tool path composed of consecutive short linear segments (G01 blocks) is still the widespread tool path representation form in five-axis machining. The inherent shortcoming of linear tool path is first-order discontinuity at the corner, which is the bottleneck to achieve high-speed and high-accuracy machining. In this article, a dual-Bézier path smoothing algorithm for five-axis linear tool path in workpiece coordinate system is proposed. There are three steps involved in our method. First, the corner error distribution model is introduced to assign the given tolerance to the smoothing approximation error constraint and the chord error constraint to ensure the interpolation trajectory error within the given tolerance. Second, segment junctions of the linear tool path in workpiece coordinate system are smoothed by double G 2 continuous cubic Bézier curves. One cubic Bézier curve is used to round the corner of the tool tip point path, and the other Bézier curve is used to round the corner of the tool axis point path. This algorithm takes the conditions of approximation error constraint, the parameterized synchronization constraint, and continuous curvature constraint into consideration. Hence, the tangency and curvature continuities are both guaranteed in the new path. Third, an adaptive feedrate scheduling method is introduced to interpolate the new path. Simulation and experiment are performed to verify the effectiveness of the proposed method in five-axis tool path smoothing, speed smoothing, and trajectory accuracy controlling.

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A numerical control (NC) tool path of digital CAD model is widely generated as a set of short line segments in machining. However, there are three shortcomings in the linear tool path, such as discontinuities of tangency and curvature, huge number of line segments, and short lengths of line segments. These disadvantages hinder the development of high speed machining. To smooth the linear tool path and improve machining efficiency of short line segments, this paper presents an optimal feed interpolator based on G 2 continuous Bézier curves for the linear tool path. First, the areas suitable for fitting are screened out based on the geometric characteristics of continuous short segments (CSSs). CSSs in every area are compressed and fitted into a G 2 Continuous Bézier curve by using the least square method. Then a series of cubic Bézier curves are generated. However, the junction between adjacent Bézier curves is only G 0 continuous. By adjusting the control points and inserting Bézier transition curves between adjacent Bézier curves, the G 2 continuous tool path is constructed. The fitting error is estimated by the second-order Taylor formula. Without iteration, the fitting algorithm can be implemented in real-time environment. Second, the optimal feed interpolator considering the comprehensive constraints (such as the chord error constraint, the maximum normal acceleration, servo capacity of each axis, etc.) is proposed. Simulation and experiment are conducted. The results shows that the proposed method can generate smooth path, decrease the amount of segments and reduce machining time for machining of linear tool path. The proposed research provides an effective method for high-speed machining of complex 2-D/3-D profiles described by short line segments. which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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