Smoothing of Time-Optimal Feedrates for Cartesian CNC Machines

  • Casey L. Boyadjieff
  • Rida T. Farouki
  • Sebastian D. Timar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)


Minimum-time traversal of curved paths by Cartesian CNC machines, subject to prescribed bounds on the magnitude of acceleration along each axis, usually involves a “bang-bang” control strategy in which the acceleration bound is realized by one or another of the machine axes at each instant during the motion. For a path specified by a polynomial parametric curve and prescribed acceleration bounds, the time-optimal feedrate may be expressed in terms of a C 0 piecewise-rational function of the curve parameter. This function entails sudden changes in either the identity of the limiting axis, or the sign of acceleration on a single limiting axis, incurring demands for instantaneous changes of motor torque that may not be physically realizable. A scheme is proposed herein to generate smoothed C 1 (slightly sub-optimal) feedrate functions, that incur only finite rates of change of motor torque and remain consistent with the axis acceleration bounds. An implementation on a 3-axis CNC mill driven by an open-architecture software controller is used to illustrate this scheme.


Tool Path Switching Point Traversal Time Axis Acceleration Acceleration Constraint 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Casey L. Boyadjieff
    • 1
  • Rida T. Farouki
    • 1
  • Sebastian D. Timar
    • 1
  1. 1.Department of Mechanical and Aeronautical EngineeringUniversity of CaliforniaDavisUSA

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