TY - JOUR
T1 - Approximation of involute curves for CAD-system processing
AU - Higuchi, Fumitaka
AU - Gofuku, Shuuichi
AU - Maekawa, Takashi
AU - Mukundan, Harish
AU - Patrikalakis, Nicholas M.
PY - 2007/9/1
Y1 - 2007/9/1
N2 - 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.
AB - 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.
KW - Bézier curves
KW - Chebyshev approximation formula
KW - Circle involute curves
KW - Involute gears
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U2 - 10.1007/s00366-007-0060-3
DO - 10.1007/s00366-007-0060-3
M3 - Article
AN - SCOPUS:34547432456
VL - 23
SP - 207
EP - 214
JO - Engineering with Computers
JF - Engineering with Computers
SN - 0177-0667
IS - 3
ER -