Chapter 5 - End of Arm Tooling
58 AdeptSix 300CR Robot Instruction Handbook, Rev. A
The steps below describe how to calculate the center of gravity, including the moment of
inertia, based on the center of gravity of the plural mass. This can be calculated based on
the weight and the center of gravity of each mass, when the tool is considered to consist of
two or more large mass objects, like a dual gun system.
1. Divide the tool into individual parts, so as to calculate the weight and center of
gravity of each part.
2. Calculate the weight and center of gravity of each part, based on the tool flange
coordinates. Refer to “Example 1” on page 54 for details on how to use the
hexahedron and cylinder examples to calculate these values.
Wi: Weight of the i-th parts (kg)
(xi, yi, zi): Center of gravity of the i-th parts (mm)
lcxi, lcyi, lczi: Moment of inertia of each i-th parts (kg.m²)
3. The position of the center of gravity for the entire tool is calculated using the
following formula.
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 for the entire tool is calculated
using the following formula.
lx = {w1*((y1-yg)²+(z1-zg)²)*10
-6
+lcx1}
+ {w2*((y2-yg)²+(z2-zg)²)*10
-6
+lcx2}
………………………………….
+ {wi*((yi-yg)²+(zi-zg)²)*10
-6
+lcxi}
ly = {w1*((x1-xg)²+(z1-zg)²)*10
-6
+lcy1}
+ {w2*((x2-xg)²+(z2-zg)²)*10
-6
+lcy2}
………………………………….
+ {wi*((xi-xg)²+(zi-zg)²)*10
-6
+lcyi}
lz = {w1*((x1-xg)²+(y1-yg)²)*10
-
6 +lcz1}
+ {w2*((x2-xg)²+(y2-yg)²)*10
-
6 +lcz2}
………………………………….
+ {wi*((xi-xg)²+(yi-yg)²)*10
-6
+lczi}
