
2.3 Equation for three-dimensional coordinate conversion
The following equation expresses the relationship between (x,y,z) on the program coordinate
system and (X,Y,Z) on the original coordinate system (workpiece coordinate system).
El =!-‘1 El +!I
If the coordinate system is converted twice, the relationship is expressed as follows:
El -(-1 i4 D+L”9 El +El
X ,Y ,Z
: Coordinates in the original coordinate system (workpiece coordinate system
or machine coordinate system)
x ,Y 2
: Coordinate specified by a program (coordinate in the program coordinate
system)
xl ,yl ,zl : Center of rotation in the first conversion
ay2,z2
: Center of rotation in the second conversion (value in the coordinate system
produced after the first conversion)
Ml : Matrix for the first conversion
M2 : Matrix for the second conversion
Ml .and M2 are conversion matrices determined by the angular displacement and axis of rotation.
They are generally expressed as shown below:
i
n12 + (l- n12)cos8 nln2(Lcos@ - n3sin8
nln3(1 -cosO) + n2sin8
nln2(Lcos8)+n3sin8 n22 +(1-n22)cos8
n2n3(1- cost?) alsin@
nln3( 1 - cos0) - n2sinB n2n3(1-cosB)+nlsin8
n32 + (1- n32)cos4Y
I
i
nl
: Cosine of the angle between the X-axis and the axis of rotation -
P
: Cosine of the angle between the X-axis and the axis of rotation -
j
n2
P
k
n3 : Cosine of the angle between the X-axis anb the axis of rotation -__
P
0 : Angular displacement
Value p is obtained by the following :
P
-
-
1
l 2 + j’ + k2
TrTLEFANUC Series 16/l 8-TC
FANUC Series 16i/l8i_TA
Three dimentional coordinate convertion
Specifications
DRAW. NO.
A-60545-E
cuST.
3DIT.
DATE
DESK.
DESCRIPTION
FANUC LTD SHEET 6’14