Methodology for obtaining C3 continuity on tool trajectory featuring acceleration and jerk constraint on computer numerical control machine

High-quality material manufacture requires the improvement of the computer numerical control (CNC) machine performance. Such task can be achieved by considering the tool trajectory, in which it is important to minimize the acceleration and jerk levels. Previous research works are focused on providing smooth movements at most with C2 continuous trajectories, and the results of using C3 continuity in the trajectory are not evaluated. The contribution of this study is the design of a methodology for obtaining C3 tool trajectories while acceleration and jerk levels are constrained through adaptive feed-rate. C3 and C2 trajectories are executed in a CNC machine. Speed, acceleration, and jerk are monitored in order to validate the proposed methodology and to analyse and quantify the differences between using C2 and using C3 trajectories.