Cutting tool trajectory generation is critical in precision machining of workpiece on machine tools. The generated tool path can trigger the natural frequencies of the machine tool and servo motor system and interfere with precision machining. Therefore, the generated tool path should not only give the desired path, but also the required continuity. It is usual for natural frequencies to be triggered if velocity and acceleration continuity is not maintained at the junction of consecutive segments. The tool path algorithm developed in this study can perform linear and circular interpolation by operating at the time of the servo motor control loop. In addition, the algorithm provides C2 continuity by generating micro-curves between consecutive segments, regardless of linear or circular. This allows rapid and smooth transition between segments. Micro curves used in the transition regions between segments in the tool path algorithm are created using a fifth degree polynomial with limited acceleration and jerk. Circular and linear tool paths generated outside the transition zones are generated with a trapezoidal acceleration profile with jerk limit. The developed algorithm was tested by cutting a star profile on a 3-axis Gantry type milling machine and the machining results were examined.