NDLI: Approximation of involute curves for CAD-system processing

Content Provider	Springer Nature Link
Author	Higuchi, Fumitaka Gofuku, Shuuichi Maekawa, Takashi Mukundan, Harish Patrikalakis, Nicholas M.
Copyright Year	2007
Abstract	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.
Starting Page	207
Ending Page	214
Page Count	8
File Format	PDF
ISSN	01770667
Journal	Engineering with Computers
Volume Number	23
Issue Number	3
e-ISSN	14355663
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-04-19
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Circle involute curves Involute gears Chebyshev approximation formula Bézier curves ApplicationMathematics/Computational Methods of Engineering Mechanics Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Math. Applications in Chemistry Computer-Aided Engineering (CAD, CAE) and Design
Content Type	Text
Resource Type	Article
Subject	Engineering Computer Science Applications Modeling and Simulation Software

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