Installation manual

Chapter 2. ARM DESIGNATION AND MOTION
２－9
２．５ CONVERSION
Space conversion with a 4x4 Matrix can indicate the conversion of translation and rotation.
Using these conversions and coordinates, they designate the position and orientation of a
manipulator.
（１）Position designation
Position designation (conversion) is to translate X, Y and Z directions of the basic
coordinate T.
Trans ( x, y, z )＝ 1 0 0 x
0 1 0 y
0 0 1 z
0 0 0 1
（２）Orientation designation ( Roll, Pitch, Yaw )
Roll, pitch and yaw is generally used for the orientation designation
(conversion).
In a standard coordinate T, Yaw is the rotation around X-axis. Pitch is the
rotation around Y-axis. Roll is the rotation around Z-axis.
As these three conversions are based on the original coordinate, pay attention
to the conversion formula, the multiplication order is reversed.
R P Y ( roll, pitch, yaw )
Processing order
= Rot ( z, roll ) Rot ( y, pitch ) Rot ( x, yaw )
C
r
-S
r
0 0 C
p
0 S
p
0 1 0 0 0
= S
r
C
r
0 0 0 1 0 0 0 C
y
-S
y
0
0 0 1 0 -S
p
0 C
p
0 0 S
y
C
y
0
0 0 0 1 0 0 0 1 0 0 0 1
C
r
C
p
C
r
S
p
S
y
- S
r
C
y
C
r
S
p
C
y
+ S
r
S
y
0
= S
r
C
p
S
r
S
p
S
y
+ C
r
C
y
S
r
S
p
C
y
- C
r
S
y
0
-S
p
C
p
S
y
C
p
C
y
0
0 0 0 1
However、S
y
= sin (yaw), C
y
= cos (yaw)
S
p
= sin (pitch), C
p
= cos (pitch)
S
r
= sin (roll), C
r
= cos (roll)
Memo