Approximation of involute curves for CAD-system processing

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

*この研究の対応する著者

研究成果: Article査読

9 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)207-214
ページ数8
ジャーナルEngineering with Computers
23
3
DOI
出版ステータスPublished - 2007 9 1
外部発表はい

ASJC Scopus subject areas

  • ソフトウェア
  • モデリングとシミュレーション
  • 工学(全般)
  • コンピュータ サイエンスの応用

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