A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length

Mohammad Mahdi Emami, Behrooz Arezoo

Research output: Contribution to journalArticle

41 Citations (Scopus)


There are currently no analytical methods available which determine the exact arc length for NURBS curves and for this reason, a smooth feedrate profile with desired trajectory cannot be achieved. Numerical methods used to calculate the arc length are time-consuming processes which make generating a feedrate profile with desired accelerations difficult in real-time. This paper introduces a look-ahead trajectory generation method which determines the deceleration stage according to the fast estimated arc length and the reverse interpolation of each curve at every sampling time. This results in a feedrate trajectory generation with jerk-limited acceleration profiles for the NURBS curves. The feedrate profile is adjusted dynamically according to the geometrical path constraint determined by chord error for the curved path. A NURBS curve by two different kinematics conditions was used as a means to test the feasibility of the developed interpolation scheme and command generator.

Original languageEnglish
Pages (from-to)625-632
Number of pages8
JournalCAD Computer Aided Design
Issue number7
Early online date16 Apr 2010
Publication statusPublished - 1 Jul 2010


  • Feedrate profile
  • Jerk-limited acceleration
  • Parametric interpolation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

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