Study on manufacturing theory of helicoids based on discrete points

A new method of calculation on discrete points of shape tools for helicoids was presented. The contact equations of tool and helicoids were deduced when the discrete points of helicoids as well as those of shape tools were given. The calculation method of slope angle of each discrete point was presented based on studying the cubic parametric spline method. Calculation errors of the method were analyzed by using practical examples. The discrete data curve of shape tools were fitted by biarc after interpolating by cumulated cubic parametric spline method. The validity and feasibility of the mathematical model were proved by case studies. And this method provides a new means for reducing the machining error and it can meet to the machining needs of the high-speed and precision of helicoids.