Installation manual

Chapter 2. ARM DESIGNATION AND MOTION
２－5
２．３ COORDINATE SYSTEM CREATION
How should the coordinate system shown in the section 2.2 be created:
Here it is explained how to assign coordinate to each link which constructs a
manipulator.
【
joint coordinate】
【
Link parameters】
Axis Axis Des. Twisting Angle
Rotation Angle X Y Z
Link 1 1st S1 Roll φ
S1
0 0 1b
Link 2 2nd S2 Pitch φ
S2
0 -1s 0
Link 3 3rd S3 Roll φ
S3
0 0 0
Link 4 4th E1 Pitch φ
E1
0 -1e 0
Link 5 5th E2 Roll φ
E2
0 0 0
Link 6 6th W1 Pitch φ
W1
0 -1w 0
Link 7 7th W2 Roll φ
W2
0 0 0
This chart shows only the 7-axis arm composition. For the 6-axis arm, there is no Link 3.
Twisting Angles
Roll ：Rotation around Z-axis of the base coordinate.
Pitch：Rotation around Y-axis of the base coordinate.
Yaw：Rotation around X-axis of the base coordinate.
Joint Coordinates
Roll coordinate：the same as the base coordinate.
Pitch coordinate：90 degrees diverted around X-axis of the base coordinate.
Yaw coordinate：90 degrees rotated around Y axis of the pitch coordinates.
＜A-Matrix＞
Any manipulator is constructed with a series of links connected by joints. At each
link (each axis) the coordinate is fixed one by one. At this point, the conversion
matrix showing the relation between a link and another one is called A-matrix. To
summarize: the A-matrix indicates a relative translation and rotation between link
coordinates.
＜T-Matrix＞
It can be indicated by the A-matrix product if seeing each link from the base
coordinate (the origin. of the manipulator coordinate.) This A-matrix product is
called T-matrix. T-matrix of each link seeing from the base coordinate is indicated
with Ｔ
ｉ
（＝
０
Ｔ
ｉ
）.
1w
1e
1s
1b
E2 E1 S3 S2
S1
W1W2
z
7
z
6
z
5
z
4
z
3
z
2
z
1
y
1
p
z
x
y
a
n
o
Mech. interface Coordinate
（Tip Coordinate）
Base
Coordinat
e
Z
X
Y
x
1
(0,0,0)
Remark