Abstract: Spherical tools are generally used in the field of numerical control (NC) machining. Arc
fitting method has therefore been applied to machining of non-circular curved surfaces. The
machining error is determined by the fitting accuracy, and arc fitting ellipse has infinite solutions.
Since there is no accurate error calculation algorithm currently for fitting ellipse with eight-center
arcs, accuracy of such fitting ellipse is uncertain. To resolve the issue, this research puts forward a
concept of arithmetic fitting arc based on the theory of graphics. The definite solution interval of
eight-center arcs for fitting ellipse has been identified. A transcendental equation has been derived for
normal error of the eight-center arcs for fitting ellipse, and it is solved using dichotomy method. The
process has been programmed in Visual LISP language in AutoCAD to solve for the minimum error
band of the eight-center arcs for fitting ellipse in terms of normal error, so as to optimize the solution
of eight-center arcs for the fitting ellipse. The paper thus provides a criterion for judging whether
eight-center arcs can fit the ellipse for given form tolerances.

Key words: eight-center arcs, arithmetic fitting, ellipse, optimal solution