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Path Planning for CNC Machines Considering Centripetal Acceleration and Jerk

In planning an s-curve speed profile for a computer numerical control (CNC) machine, centripetal acceleration and its derivative have to be considered. In a CNC machine, these quantities dictate how much voltage and current should be applied to servo motor windings. In this paper, the necessity of considering centripetal jerk in speed profile generation especially in the look-ahead mode is explained. It is demonstrated that the magnitude of centripetal jerk is proportional to the curvature derivative of the path known as "sharpness". It is also explained that a proper limited jerk motion is only possible when a G2-continuous machining path is planned. Then using a simplified mathematical representation of clothoids, a novel method for approximating a given path with a sequence of clothoid segments is proposed. Using this method, a semi-parallel G2-continuous path with adjustable deviation from the original shape for a sample machining contour is generated. Maximum permissible feed rate for the generated path is also calculated.