When the cutting edge and minor cutting edge are all on the rake face, like Fig.1.11, γ?0、λ ?s can be educed from γ0、λs、κr、κ ?r，and it is called derived angles. There are 6 independent marked angles for lathe cutting tool. In addition，as required in analysis, there are some other derived angles, which are：
wedge angleβ0：measured in main section,formed by rake face and flank.
β0＝90°－（γ0＋α0）
（1.6）
tool tip(nose) angleεr：the angle formed by cutting edge and minor cutting edge in the reference plane.
εr＝180 °－（κr＋κ’r ）
（1.7）
The sign of γ0、α0 、λs、κr、κ’ris specified as in Fig.1.12：in the main section, if rake face is parallel to the reference plane, γ0=0, ，if the angle is less than 90°, it is positive, otherwise, it is negative. The sign of the inclination angle is shown in Fig.1.12 .
(a)λs＝0
(b)－λs
Fig.1.12 the sign of inclination angle
(c)+ λs
1.1.3 Tool angle conversion in different system
It is necessary to convert the marked angle from one system to another system in tool design and manufacturing. i.e, among main section system,normal
section system, transverse system and longitudinal system
1.1.3.1 tool angle conversion from main section to normal section
This conversion is used in tool design, manufacturing,tool grinding and inspection,especially for large inclination tool, the angles must be marked in normal section system.
tanγn=tanγ0.cosλscotαn=cotα0.cosλs
1.1.3.1 conversion from main section to normal sectionTaketherakeangleconversionasexample,itiseducedas：tan?n?tan?o?acMaabMatan?nacMaac????cos?stan?oMaababtan?n?tan?o?cos?s1.1.3.2 angle conversion from main section to any sectionrake angle γθin any section Pθ：tanγθBD?DCBCEF?DC???ABABABAEtan?0?DCtan?s?ABAEDF?.tan?0?.tan?sABABthentanγθ＝tanγ0.sinθ+tanλs.cosθ （1.10）