Approximation of involute curves for CAD-system processing

Fumitaka Higuchi, Shuuichi Gofuku, Takashi Maekawa*, Harish Mukundan, Nicholas M. Patrikalakis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


In numerous instances, accurate algorithms for approximating the original geometry is required. One typical example is a circle involute curve which represents the underlying geometry behind a gear tooth. The circle involute curves are by definition transcendental and cannot be expressed by algebraic equations, and hence it cannot be directly incorporated into commercial CAD systems. In this paper, an approximation algorithm for circle involute curves in terms of polynomial functions is developed. The circle involute curve is approximated using a Chebyshev approximation formula (Press et al. in Numerical recipes, Cambridge University Press, Cambridge, 1988), which enables us to represent the involute in terms of polynomials, and hence as a Bézier curve. In comparison with the current B-spline approximation algorithms for circle involute curves, the proposed method is found to be more accurate and compact, and induces fewer oscillations.

Original languageEnglish
Pages (from-to)207-214
Number of pages8
JournalEngineering with Computers
Issue number3
Publication statusPublished - 2007 Sept 1
Externally publishedYes


  • Bézier curves
  • Chebyshev approximation formula
  • Circle involute curves
  • Involute gears

ASJC Scopus subject areas

  • Software
  • Modelling and Simulation
  • Engineering(all)
  • Computer Science Applications


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