Error-envelope-optimal G² dual bézier corner transitions for high-speed five-axis CNC toolpaths

Toolpaths in practical five-axis CNC machining are typically programmed as sequences of G01 linear blocks. At block junctions, curvature discontinuities and abrupt curvature variation reduce achievable feedrates and may excite vibration in high-speed machining. This paper proposes a local corner-smoothing method that replaces each junction with parameter-synchronized dual quartic Bezier transition segments, providing G2 continuity with continuously varying tool position and orientation. An overall error envelope is defined with respect to the programmed polyline specified by G01 block endpoints, and Bezier control points are obtained by solving a constrained optimization that minimizes differential smoothness energy to suppress curvature peaks and promote a more uniform curvature distribution within tolerance. To enhance robustness near kinematic singularities, a lightweight rotary-axis stabilization strategy based on a proxy azimuth-rate signal with soft-lock blending is incorporated to stabilize rotary commands without explicit Jacobian evaluation, while maintaining computational feasibility for online interpolation. Junctions are further classified into two types according to neighboring G01 block characteristics and treated accordingly. Simulations and five-axis machining experiments on impeller and butterfly parts demonstrate improved curvature profiles, reduced feedrate fluctuation, and higher interpolation efficiency compared with conventional corner-transition schemes.