A nurbs curve interpolator with jerk-limited trajectory planning

Sheng Jung Tseng, Kuan Yuan Lin, Jiing Yih Lai, Wen Der Ueng

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The control of the maximum acceleration and jerk in the trajectory planning of the CNC controller is very important because it affects the smoothness of the machined surface substantially. We proposed a parametric interpolator composed of a look-ahead stage and a real-time sampling stage for jerk-limited acceleration planning. A pre-sampling process was implemented in the look-ahead stage to identify the segment points, where the acceleration changed across zero. A check of the acceleration and jerk was implemented and the feedrate was modified accordingly. In addition, a backtracking process was carried out during the deceleration stage to ensure that the modified feedrate was satisfied. In the real-time sampling stage, an acceleration profile based on constant jerk was implemented for each region between two segment points. With this algorithm, we ensured that both the chord error and the maximum acceleration and jerk were within the allowable limits. Also, it kept the similarity of the speed profiles for adjacent cutting paths in zigzag machining.


  • CNC
  • Jerk-limited acceleration
  • NURBS interpolator
  • Variable feedrate


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