4 Programming of Motion Blocks 01.93
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
1
: offset of the real system in the u direction relative to the zero of the fictitious coordinate
system.
a
2
: offset of the real system in the v direction relative to the zero of the fictitious coordinate
system.
a
3
: offset of the real system in the w direction relative to the zero of the fictitious coordinate
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
a
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x, y, z = real coordinate system
u, v, w = fictitious coordinate system
a
1
, a
2
, a
3
= offset
u
a
a
w
v
a
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a
1
a
a
a
2
x
a
a
a
3
y
z
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
, x
2
, x
3
) for purposes of demonstration. These indices have no
bearing on the transformation equations given.
4–38
© Siemens AG 1991 All Rights Reserved 6ZB5 410-0HD02
SINUMERIK 880, (PG)
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