The Way of Analyzing and Calculating Cutting Tool Angles in a Projective Plane

Abstract

In this chapter, the space planes and lines of various cutting tools are mapped onto a plane, so-called projective plane, and then the angles of the cutting tools are analyzed and calculated through the images on the plane by means of the method introduced in last chapter. A series of examples presented in this chapter has shown the validity and visualization of such planar image method. This method explains the profound in straightforward terms, and turns difficult to easy. It can visually synthesize the relationship between the various geometric angles and it’s straightforward to analyze the influence of the rotation of the cutting tool in space on its angles. This method has provided a mathematical model and a theoretical basis for the analysis and calculation of tool working angles and dynamic angles and for their on-line monitoring and optimizing design.