Engineering with Computers

, Volume 23, Issue 3, pp 207–214 | Cite as

Approximation of involute curves for CAD-system processing

  • Fumitaka Higuchi
  • Shuuichi Gofuku
  • Takashi Maekawa
  • Harish Mukundan
  • Nicholas M. Patrikalakis
Original Article


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.


Circle involute curves Involute gears Chebyshev approximation formula Bézier curves 


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Copyright information

© Springer-Verlag London Limited 2007

Authors and Affiliations

  • Fumitaka Higuchi
    • 1
  • Shuuichi Gofuku
    • 1
  • Takashi Maekawa
    • 1
  • Harish Mukundan
    • 2
  • Nicholas M. Patrikalakis
    • 2
  1. 1.Department of Mechanical Engineering, Digital Engineering LaboratoryYokohama National UniversityYokohamaJapan
  2. 2.Department of Mechanical Engineering, Design LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

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