YASKAWA DX100 - Page 112

8 System Setup
DX100 8.4 ARM Control
8-47
<Setting>
• W : 100.000 kg
• Xg : 0.000 mm
• Yg : 0.000 mm
• Zg : 250.000 mm
• Ix : 10.000 kg.m
2
• Iy : 3.500 kg.m
2
• Iz : 10.500 kg.m
2
SUPPLE
-MENT
How to calculate "Center of gravity position" and "moment of inertia at center of
gravity" for plural mass
The center of gravity position and the moment of inertia
at the center of gravity of the
entire tool can be calculated by the weight and the center of gravity position of each
mass when the tool can be thought that the tool consists of two or more big mass like
the twin gun system etc.
1. Divide the tool into some parts as the weight and the center of gravity position can
be roughly presumed. It is not necessary to divide in detail. The tool is
approximated in construction of rough parts.
2. Calculate the weight and the center of gravity position of the each parts on flange
coordinates. It does not care by a rough value. Calculate the own moments of
inertia of the big parts. (If parts are small, it is not necessary to calculate the own
moments of inertia. Refer to above-mentioned supplement: "The own moment of
inertia calculation for hexahedron and cylinder" for how to calculate the own
moment of inertia.)
wi : Weight of the i-th parts [kg]
(xi, yi, zi) : Center of gravity position of the i- th parts
(On flange coordinates)[mm]
Icxi, Icyi, Iczi : Own moments of inertia of the i-th parts [kg*m
2
]
3. The center of gravity position of the entire tool is calculated by the next
expression.
xg = {w1 * x1 + w2 * x2 + .... + wi * xi} / (w1 + w2 + .... + wi)
yg = {w1 * y1 + w2 * y2 + .... + wi * yi} / (w1 + w2 + .... + wi)
zg = {w1 * z1 + w2 * z2 + .... + wi * zi} / (w1 + w2 + .... + wi)
4. The moment of inertia at the center of gravity position of the entire tool is
calculated by the next expression.
Ix = { w1 * ((y1 - yg)
2
+ (z1 - zg)
2
) * 10
-6
+ Icx1} + { w2 * ((y2 - yg)
2
+
(z2 - zg)
2
) * 10
-6
+ Icx2}
...................
+ { wi * ((yi - yg)
2
+ (zi - zg)
2
) * 10
-6
+ Icxi}
Iy = { w1 * ((x1 - xg)
2
+ (z1 - zg)
2
) * 10
-6
+ Icy1} + { w2 * ((x2 - xg)
2
+
(z2 - zg)
2
) * 10
-6
+ Icy2}
.....................
+ { wi * ((xi - xg)
2
+ (zi - zg)
2
) * 10
-6
+ Icyi}
Iz = { w1 * ((x1 - xg)
2
+ (y1 - yg)
2
) * 10
-6
+ Icz1} + { w2 * ((x2 - xg)
2
+
(y2 - yg)
2
) * 10
-6
+ Icz
.....................
+ { wi * ((xi - xg)
2
+ (yi - yg)
2
) * 10
-6
+ Iczi}
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