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.