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• How to calculate "Center of gravity position" and "moment of inertia at center of gravity"
S U P P L E -
for plural mass.
M E N T
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 sys-
tem etc.
1. Divide the tool into some parts as the weight and the center of gravity posi-
tion 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 supple-
ment: "The own moment of inertia calculation for hexahedron and cylinder"
for how to calculate the own moment of inertia.)
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 =
Iy =
Iz =
wi: Weight of the i-th parts [kg]
(xi, yi, zi): Center of gravity of the i-th parts
Icxi, Icyi, Iczi: Own mome
2
{ w1 * ((y1 - yg)
2
+
{ w2 * ((y2 - yg)
.....................
2
+
{ wi * ((yi - yg)
+ (zi - zg)
2
{ w1 * ((x1 - xg)
2
+
{ w2 * ((x2 - xg)
.....................
2
+
{ wi * ((xi - xg)
+ (zi - zg)
2
{ w1 * ((x1 - xg)
2
+
{ w2 * ((x2 - xg)
.....................
2
+
{ wi * ((xi - xg)
+ (yi - yg)
inertia
nts of
of the i-th parts [kg*m
2
-6
+ (z1 - zg)
) * 10
+ Icx1}
2
-6
+ (z2 - zg)
) * 10
+ Icx2}
2
-6
) * 10
+ Icxi}
2
-6
+ (z1 - zg)
) * 10
+ Icy1}
2
-6
+ (z2 - zg)
) * 10
+ Icy2}
2
-6
) * 10
+ Icyi}
2
-6
+ (y1 - yg)
) * 10
+ Icz1}
2
-6
+ (y2 - yg)
) * 10
+ Icz2}
2
-6
) * 10
+ Iczi}
3-59
3.11 ARM Control
[mm]
(On flange coordinates)
2
]
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