
10.TOOL FUNCTION B-63783EN-1/01
- 1140 -
- Formulas
The three-dimensional cutter compensation vector at the N2 end point
in the following program can be calculated as follows:
1. Part program
A part program may be created with a workpiece coordinate
system.
G42.5 D1 ;
N1 Xx
1
Yy
1
Zz
1
Aa
1
Cc
1
;
N2 Xx
2
Yy
2
Zz
2
Aa
2
Cc
2
;
N3 Xx
3
Yy
3
Zz
3
Aa
3
Cc
3
;
N2 Xx2 Yy2 Zz2 Aa2 Cc2 ;
N3 Xx3 Yy3 Zz3 Aa3 Cc3 ;
2. Definition of symbols
P = (x
1
, y
1
, z
1
)
Q = (x
2
, y
2
, z
2
)
R = (x
3
, y
3
, z
3
)
P
0
: Origin of the table coordinate system (parameter No. 6154)
A: Tool rotation axis
C: Table rotation axis
3. Definition of coordinate system C1 (workpiece coordinate system)
Coordinate system C1 {O; X,Y,Z} is a Cartesian coordinate
system having
O = (0,0,0) as its origin and the following unit vectors as its basic
vectors:
I = (1,0,0) (X-axis unit vector)
J = (0,1,0) (Y-axis unit vector)
K = (0,0,1) (Z-axis unit vector)
4. Conversion of program coordinates using the table rotation axis
(1) Conversion from the workpiece coordinate system to the
table coordinate system using the table rotation axis
The table coordinate system is the one that is fixed to the
table.
The table coordinate system will move with the rotation of
the table coordinate system.
Determining the vector at Q requires that P and R in the same
state as that of Q (state at the N2 end point) be determined.
The matrixes for conversion from the workpiece coordinate
system to the table coordinate system are as follows:
The conversion matrix for P is
1
1
1
1
)(
−
−
= cRM
c
The conversion matrix for Q is
1
2
1
2
)(
−
−
= cRM
c
The conversion matrix for R is
1
3
1
3
)(
−
−
= cRM
c
where
ú
ú
ú
û
ù
ê
ê
ê
ë
é
−
=
100
0cossin
0sincos
)( cc
cc
cR
c