Abstract: In order to acquire a universal multi-point contact machining alogrithm and reduce the computation cost, the prin toroidal outter and the machining surface is analyzed. And the method positioning the toroidal cutter is derived. A novel algorithm, for machining error controlling in multi-point contact machining, is proposed. In the algorithm, a function equation having the radius of the circle of the parameter difference between two contact points as the independent variable is constructed to control the maximal undercut error occurring within the two contact points in multi-point contact machining. The secant algorithm is utilized to solve the equation after iterations，and then the optimal value of the circle radius and cutter location is derived. It is proved by a computational example that very wide path intervals can be acquired when secant algorithm is applied in tool position calculation with multi-point method. The time cost of secant algorithm is much less than that of Hermite method. And it is more effective in the application on the sculpture surface machining.

Key words: Multi-point contact machining Secant algorithm, NC machining, Tool position calculation