Geometry-feedrate co-optimization for 3-D non-planar corner smoothing in 5-axis CNC machining

In five-axis machining, standard G01/G02/G03 toolpaths inherently exhibit geometric and kinematic discontinuities at segment junctions, degrading accuracy and limiting feedrate. Existing corner smoothing approaches are largely restricted to planar configurations, while practical machining trajectories involve non-planar (3D) Line-Arc and Arc-Arc corners. Moreover, state-of-the-art methods use sequential planning, fixing the geometric transition before scheduling feedrate, which neglects the interdependence between path geometry and motion kinematics, resulting in conservative cycle times. To overcome this, a unified co-optimization framework for simultaneous 3D corner smoothing and time-efficient feedrate scheduling is introduced. A generalized quintic Bézier curve-based strategy is developed to handle non-planar Line-Arc and Arc-Arc transitions with C² continuity under prescribed error bounds. Furthermore, geometric parameters and S-curve parameters are co-optimized using Particle Swarm Optimization under drive constraints, explicitly exploiting the geometry-motion synergy to minimize cycle time. Simulation and experimental validation on YCM 5-Axis Machine Tool shows that the proposed framework achieves shorter cycle time while maintaining smooth motion and reduced contour errors vs established methods, demonstrating the advantages of unified geometry-feedrate planning for efficient and precise five-axis machining of complex 3D trajectories.