YASKAWA DX100 - Page 113

8 System Setup
DX100 8.4 ARM Control
8-48
<Example 3>
When there are two or more big mass such as the twin gun system as
shown in the figure below, perform:
1. Set the center of gravity position when the center of gravity position of
the entire tool is roughly understood, and set the moment of inertia at
the center of gravity calculated by approximating the entire tool in the
shape of hexahedron or cylinder. (It is enough in this setting usually.);
or
2. When weight in each mass and the center of gravity position are
understood, the center of gravity position and the moment of inertia at
the center of gravity of the entire tool can be calculated. (Refer to
forementioned supplement column: "How to calculate "Center of
gravity position" and "moment of inertia at the center of gravity" for
plural mass".)
This example shows the calculation with the mothod 2.
Weight : W = w1 + w2
= 3 + 6 = 9 = approx. 10[kg]
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 position:
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
Y
F
40
70
Gun 1
Gun 2
X
F
Z
F
(Gun 1)
Weight: w1 = 3 kg
Center of Gravity:
x1 = 100 mm
y1 = 50 mm
z1 = 40 mm
(Gun 2)
Weight: w2 = 6 kg
Center of Gravity:
x2 = 100 mm
y2 = -150 mm
z2 = 70 mm
Y
F
X
F
Center of Flange
100
50 150
Gun 1
Gun 2
(Top View)
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