High-speed contouring control with NURBS-based C2 PH spline curves

Javad Jahanpour, Mi-Ching Tsai, Ming-Yang Cheng

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

This paper presents a C2 Pythagorean hodograph (PH) spline curve constructed by the non-uniform rational B-spline (NURBS) curve for high-speed contouring control. With the knot vector, weights, and control points given, the C2 PH spline curve is defined to be a "good" interpolant for Hermit data obtained from a NURBS curve of degree 3 specified by the same control polygon, weights, and the knot vector. To this end, the first- and second-order derivatives are evaluated at the nodal points on the NURBS curve. These boundary conditions are imposed on the PH segments of degree 9 to preserve continuity between the connecting segments. The S-curve motion planning architecture with variable feed rate for a planar NURBS-based C2 PH spline curve is also developed in this paper. In particular, C1 cubic feed acceleration/deceleration is imposed on the first and last PH segments. Several NURBS-based C2 PH spline curve-following tasks were conducted to verify the effectiveness of the proposed interpolation algorithm. Experimental results show that the proposed interpolator is not only feasible for machining the complicated parametric curves represented in the NURBS-based C2 PH spline form but also yields satisfactory contouring performance under variable feed rate control.

Original languageEnglish
Pages (from-to)663-674
Number of pages12
JournalInternational Journal of Advanced Manufacturing Technology
Volume49
Issue number5-8
DOIs
Publication statusPublished - 2010 Jul 1

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Speed control
Splines
Weight control
Deceleration
Motion planning
Interpolation
Machining
Boundary conditions
Derivatives

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Software
  • Mechanical Engineering
  • Computer Science Applications
  • Industrial and Manufacturing Engineering

Cite this

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High-speed contouring control with NURBS-based C2 PH spline curves. / Jahanpour, Javad; Tsai, Mi-Ching; Cheng, Ming-Yang.

In: International Journal of Advanced Manufacturing Technology, Vol. 49, No. 5-8, 01.07.2010, p. 663-674.

Research output: Contribution to journalArticle

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