Siemens SINUMERIK 880 Programming Manual page 96

4 Programming of Motion Blocks
4.2.11 Coordinate transformation 2D G133, G233, G333/3D G135, G235, G335
Three-dimensional coordinate transformation
The three-dimensional coordinate transformation is composed of a translation and a rotation of
the real coordinate system about its axis.
Transformation equations:
u =a1+x(cos cos ) – y(cos sin )+z sin
v =a2+x(cos sin +sin sin cos )+y(cos cos – sin sin sin )
w =a3+x(sin sin – cos sin cos )+y(sin cos +cos sin sin )+z(cos cos )
Transformation parameter and constant:
a : offset of the real system in the u direction relative to the zero of the fictitious coordinate
1
system.
a : offset of the real system in the v direction relative to the zero of the fictitious coordinate
2
system.
a : offset of the real system in the w direction relative to the zero of the fictitious coordinate
3
system.
: angle of rotation of the real system about the x axis
: angle of rotation of the real system about the y axis
: angle of rotation of the real system about the z axis
w
a
1
u
x, y, z = real coordinate system
u, v, w = fictitious coordinate system
a , a , a = offset
1 2 3
Translation: offset of the real coordinate system (x, y, z) relative to the fictitious coordinate system (u, v, w)
Note:
In the following three figures the coordinates of the real coordinate system (x, y, z) are only
shown with indices (e.g. x
1
bearing on the transformation equations given.
4–38
v
a
2
, x , x ) for purposes of demonstration. These indices have no
2 3
© Siemens AG 1991 All Rights Reserved
z
y
x
a
3
6ZB5 410-0HD02
SINUMERIK 880, (PG)
01.93