YASKAWA DX200 - Page 135

8-48
182582-1CD
182582-1CD
8 System Setup
8.4 ARM Control
MH900, DX200 Controller
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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