Motoman PX2750, Manual

Page: 405 / 611

3.11 ARM Control
3-60
<Example 3>
When there is two or more big mass like the twin gun system like the figure below,
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)
2. Or, 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 above-mentioned supplement: "How to calculate
"Center of gravity position" and "moment of inertia at the center of gravity" for plural
mass").
How by the method of 2 to calculate the value is shown here.
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
Iz = 3 * ((100 - 100)
2
+ (50 - (-83))
2
) * 10
-6
+ 6 * ((100 - 100)
2
+ ((-150) - (-83))
2
) * 10
-6
= 0.080 = approx. 0.100
YF
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)