YASKAWA MOTOMAN YRC1000 - Page 120

System Setup
9 - 120
<Example 3>
If there are two or more heavy loads such as double welding guns (see the figure below):
1. Set the center of gravity if the center of gravity for the whole tool has been determined
approximately. Set the moment of inertia at the center of gravity that has been
calculated through approximation of the whole tool in the shape of a hexahedron or
cylinder (this setting is sufficient as a rule).
2. Alternatively, if the weight of each load and the center of gravity are known, the center
of gravity and the moment of inertia at the center of gravity of the whole tool can be
calculated (see "Calculation of the center of gravity and moment of inertia at the center
of gravity for multiple loads" above).
In this example, the calculation is shown using method 2.
Weight: W = w1 + w2 = 3 + 6 = 9 = approx. 10 kg
Center of flange
(Gun 1) Weight: w1 = 3 kg Center
of gravity x1 = 100 mm y1 = 50 mm
z1 = 40 mm
View from above
(Gun 2) Weight: w2 = 6 kg x2 = 100
mm y2 = 150 mm z2 = 70 mm
Center of gravity:
Xg = (w1 * x1 + w2 * x2) / (w1 + w2) = (3 * 100 + 6 * 100) / (3+6) = 100.0 [mm]
Yg = (3 * 50 + 6 * (-150)) / (3+6) = -83.333 [mm]
Zg = (3 * 40 + 6 * 70) / (3+6) = 60.0 [mm]
The moment of inertia at the center of gravity:
Ix =
{w1 * ((y1 - Yg)2 + (z1 - Zg)2) * 10
-6
+ Icx1}
+ {w2 * ((y2 - Yg)2 + (z2 - Zg)2) * 10
-6
+ Icx2}
= 3 * ((50 - (-83))2 + (40 - 60)2) * 10
-6
+ 6 * (((-150) - (-83))2 + (70 - 60)2) * 10
-6
= 0.082 = approx. 0.100
Iy =
3 * ((100 - 100)2 + (40 - 60)2) * 10
-6
+ 6 * ((100 - 100)2 + (70 - 60)2) * 10
-6
= 0.002 = approx. 0.010
Iz =
3 * ((100 - 100)2 + (50 - (-83))2) * 10
-6
+ 6 * ((100 - 100)2 + ((-150) - (-83))2) * 10
-6
= 0.080 = approx. 0.100
1
Y
F
40
70
Gun 1
Gun 2
X
F
Z
F
Y
F
X
F
100
50 150
2
3
4