Abstract: According to nonlinear Chebyshev approximation theory subject to constrains a computational method approximation four pieces of circular arc to ellipse is presented. By the method the maximum approximate error is decreased to the minimum. Therefore the accuracy in machining and operation of numerical control machine tools and robots is improved. Several approximate formulae that are quite accu-rate are also presented and can be taken as the formulae of the optimal radii thus the programming and iteration are avoided.

Key words: Chebyshev approximation, Ellipse, Four pieces of circular arc