Basic Characteristics RAPID

Example 1
A tool is orientated so that its Z’-axis points straight ahead (in the same direction as the
X-axis of the base coordinate system). The Y’-axis of the tool corresponds to the Yaxis
of the base coordinate system (see Figure 2). How is the orientation of the tool
defined in the position data (robtarget)?
The orientation of the tool in a programmed position is normally related to the coordinate
system of the work object used. In this example, no work object is used and the
base coordinate system is equal to the world coordinate system. Thus, the orientation
is related to the base coordinate system.
Figure 2 The direction of a tool in accordance with example 1.
The axes will then be related as follows:
x’ = -z = (0, 0, -1)
y’ = y = (0, 1, 0)
z’ = x = (1, 0, 0)
Which corresponds to the following rotational matrix:
The rotational matrix provides a corresponding quaternion:
Example 2
Z
X
X´
0 + 1 + 0 + 1 2
q1 = ---------------------------------- = ------ = 0,707
2 2
q2
q3
0 – 1 – 0 + 1
= --------------------------------- = 0
2
1 – 0 – 0 + 1 2
= --------------------------------- = ------ = 0,707
2 2
0 – 0 – 1 + 1
q4 = --------------------------------- =
0
2
sign q3 = sign (1+1) = +
The direction of the tool is rotated 30 o about the X’- and Z’-axes in relation to the wrist
coordinate system (see Figure 2). How is the orientation of the tool defined in the tool
data?
RAPID Reference Manual 7-orient-3
Z´
0 0 1
0 1 0
– 1 0 0