Curvature-continuous sharp corner smoothing scheme for Cartesian motion systems

In general practice, a geometric tool-path for CNC (computer numerical controlled) machine tools or NC positioning systems is mainly composed of linear motion segments, or so called the G1 commands. This approach exhibits serious limitations in terms of achieving the desired part geometry and productivity in high-speed machining. Velocity and acceleration discontinuities occur at the junction points of consecutive segments if they are not blended continuously. To solve this problem, a corner smoothing algorithm is proposed in this paper, which fits minimum curvature quintic B-splines to blend the adjacent straight lines together. The proposed transition scheme ensures C² continuity transitions and a minimum curvature geometry delivering the fastest cycle time without violating the axis acceleration limits. The cornering error is controlled analytically allowing the user to set the desired cornering tolerance. At last, a limited bell-shaped acceleration profile is generated to realize smooth feed motion.