A one-step corner smoothing formulation for five-axis G01 trajectories using jerk-smooth kinematic profile blending

While existing one-step corner smoothing methods for five-axis G01 commands achieve greater computational efficiency compared to two-step approaches, they often employ jerk-limited profiles with only second-order continuity. This inherent jerk discontinuity adversely affects motion smoothness and surface quality. To overcome these limitations, this study presents a one-step formulation based on jerk-smooth kinematic profile blending, delivering superior motion smoothness. A trigonometric-based kinematic profile is developed as a smooth basis function, ensuring continuous differentiability of jerk while maintaining a concise analytical expression. To tackle the challenge of over-constrained kinematic parameters, a two-phase strategy is developed, involving geometry-driven prediction of the blending interval and decoupled adjustment using asymmetric profiles, enabling independent and systematic control of acceleration and deceleration phases. Furthermore, a geometric error control methodology is integrated to maximize smoothing errors within predefined limits. Using the tangential condition between resultant velocity and admissible area, an efficient method is constructed to determine the maximum blending time, which is applicable across various kinematic profiles. Experimental results, through comprehensive comparisons with representative approaches such as classical blending-based smoothing, advanced finite impulse response (FIR) filter-based smoothing, and high-order spline-based smoothing methods, demonstrate that the proposed method effectively improves motion smoothness and machining efficiency while strictly satisfying kinematic and geometric constraints.