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Power Series Solution for Isoscallop Tool Path Generation on Free-form Surface with Ball-end Cutter

Power Series Solution for Isoscallop Tool Path Generation on Free-form Surface with Ball-end Cutter In this paper we propose a method to compute symbolically a curve of constant scallop height on the surface swept by a ball-end cutter when it traces a free-form cutter-contact curve on a free-form surface. We give explicit formulas for power series solutions to the curve of constant scallop height and the next cutter-contact curve, when the initial cutter-contact curve is given. To make the symbolic results useful in practice, we propose a method to approximate the solutions unilaterally in the parametric plane by piecewise Chebyshev polynomials and exponential functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics in Computer Science Springer Journals

Power Series Solution for Isoscallop Tool Path Generation on Free-form Surface with Ball-end Cutter

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References (8)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Basel AG
Subject
Mathematics; Computer Science, general; Mathematics, general
ISSN
1661-8270
eISSN
1661-8289
DOI
10.1007/s11786-012-0124-7
Publisher site
See Article on Publisher Site

Abstract

In this paper we propose a method to compute symbolically a curve of constant scallop height on the surface swept by a ball-end cutter when it traces a free-form cutter-contact curve on a free-form surface. We give explicit formulas for power series solutions to the curve of constant scallop height and the next cutter-contact curve, when the initial cutter-contact curve is given. To make the symbolic results useful in practice, we propose a method to approximate the solutions unilaterally in the parametric plane by piecewise Chebyshev polynomials and exponential functions.

Journal

Mathematics in Computer ScienceSpringer Journals

Published: Aug 30, 2012

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