Installation manual

Chapter 2. ARM DESIGNATION AND MOTION
２－7
（２）Mechanical Interface Coordinates
Mechanical interface coordinates (tool tip coordinate) will be created as follows:
・
First of all, create the conversion matrix A1 from the manipulator origin, indicating the S1 origin.
→The coordinate of S1 origin located at base coordinate:
Ｔ
１
＝Ｔ
０
Ａ
１
・
Then, create conversion matrix: A2 indicating the S2 origin for the S1 origin (T1 coordinate.)
→The coordinate of S2 origin located at the base coordinate:
Ｔ
２
＝Ｔ
１
Ａ
２
＝Ａ
１
Ａ
２
・
Then, create conversion matrix: A3 indicating the S3 origin for the S2 origin (T2 coordinate.)
→The coordinate of S3 origin located at the base coordinate:
Ｔ
３
＝Ｔ
２
Ａ
３
＝Ａ
１
Ａ
２
Ａ
３
・
Then, create conversion matrix: A4 indicating the E1 origin for the S3 origin (T3 coordinate.)
→The coordinate of E1 origin located at the base coordinate:
Ｔ
４
＝Ｔ
３
Ａ
４
＝Ａ
１
Ａ
２
Ａ
３
Ａ
４
・
Then, create conversion matrix: A5 indicating the E2 origin for the E1 origin (T4 coordinate.)
→The coordinate of E2 origin located at the base coordinate:
Ｔ
５
＝Ｔ
４
Ａ
５
＝Ａ
１
Ａ
２
Ａ
３
Ａ
４
Ａ
５
・
Then, create conversion matrix: A6 indicating the W1 origin for the E2 origin (T5 coordinate.)
→The coordinate of W1 origin located at the base coordinate:
Ｔ
６
＝Ｔ
５
Ａ
６
＝Ａ
１
Ａ
２
Ａ
３
Ａ
４
Ａ
５
Ａ
６
・
Then, create conversion matrix: A7 indicating the W2 origin for the W1 origin (T6 coordinate.)
→The coordinate of W2 origin located at the base coordinate:
Ｔ
７
＝Ｔ
６
Ａ
７
＝Ａ
１
Ａ
２
Ａ
３
Ａ
４
Ａ
５
Ａ
６
Ａ
７
・
Then, create conversion matrix: A tool indicating tool tip for the W2 origin (T7 coordinate.)
→The tool tip coordinate located at the base coordinate:
Ｔ
ｔｏｏｌ
＝Ｔ
７
Ａ
ｔｏｏｌ
＝Ａ
１
Ａ
２
Ａ
３
Ａ
４
Ａ
５
Ａ
６
Ａ
７
Ａ
ｔｏｏｌ
Thus, if it is successively indicated with a conversion
for new coordinates, multiply the
conversion matrix of each joint on the right.
To summarize: the finally created Ｔ
ｔｏｏｌ
（
０
Ｔ
ｔ
）matrix indicates the position / direction of
the mechanical interface coordinate (included the tool) seen from the base coordinate.
Using this matrix, it also makes the conversion from the mechanical interface coordinate
to the base coordinate.
n
x
o
x
a
x
p
x
T
TOOL
= N O A P = n
y
o
y
a
y
p
y
n
z
n
z
a
z
p
z
0 0 0 1
Tip Orientation Tip position
This is the 7-axis arm composition. For 6-axis arm, there is no A3.
P
Y
Z
X
N
0
A
Remark