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

Authors:
Mohammad Mahdi Emami;Behrooz Arezoo
Affiliations:
Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave Tehran, Iran;Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave Tehran, Iran
Venue:
Computer-Aided Design
Year:
2010

Citing 2
Cited 2

An introduction to NURBS: with historical perspective

An introduction to NURBS: with historical perspective
Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery

Computer-Aided Design

A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk

Robotics and Computer-Integrated Manufacturing
Efficient time-optimal feedrate planning under dynamic constraints for a high-order CNC servo system

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Abstract

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.