Linear and circular representations are widely used to define tool paths, however, the tangency discontinuity between the linear and circular segments leads to large fluctuations in velocity and acceleration, as a result, the machining accuracy and efficiency are degraded. It becomes the key problem in some micromachining situations where the quality of freeform surfaces is critical, such as moulds and knee implants, etc. This research aims to develop a local tool path smoothening scheme to achieve C2 continuity at the transition positions. This scheme applies to sections consisting of high density of short segments. These segments will be approximated by cubic B-splines. The approximation is carried out within the specific error tolerance. High frequency energy to be injected into the servo loop control system is greatly reduced by the C2 continuity. The proposed scheme is feasible to be implemented in real-time microcontrollers due to the computational efficiency and reliability of B-spline algorithms
