Harmonic Drive FHA Mini Series, Manual

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Appendix 3 Moment of inertia
FHA-mini
- 45 -
Appendix 3 Moment of inertia
3-1 Calculation of mass and moment of inertia
(1) Both centerlines of rotation and gravity are the same:
The following table includes formulas to calculate mass and moment of inertia.
m: mass (kg); Ix, Iy, Iz: moment of inertia for rotation center of x-, y-, z-axis respectively (Kg
･
m
2
);
G: distance from gravity center to the surface;
ρ
: specific gravity
Unit Length: m; Mass: kg; Inertia: kg
･
m
2
Object form Mass, inertia, gravity center Object form Mass, inertia, gravity center
Cylinder Circular pipe
Slanted cylinder Ball
Ellipsoidal cylinder Cone
Rectangular pillar Square pipe
R
L
z
x
y
ρ L R π m
2
=
2
R m
2
1
Ix =








+ =
3
L
R m
4
1
Iy
2
2








+ =
3
L
R m
4
1
Iz
2
2
R
1
L
R
2
z
x
y
R
1
:outer,
R
2
:inner
( )
ρ π
L R R m
2
2
2
1
− =
( )






+ − =
3
L
R R m
4
1
Iy
2
2
2
2
1
( )
2
2
2
1
R R m
2
1
Ix
− =
( )






+ − =
3
L
R R m
4
1
Iz
2
2
2
2
1
B
L
z
x
y
C
ρ L BC m
4
π
=
( )
2 2
C B m
16
1
Ix + =








+ =
3
L
4
C
m
4
1
Iy
2 2








+ =
3
L
4
B
m
4
1
Iz
2 2
R
L
z
x
y
G
ρ π
L R
3
π
m
2
=
2
R m
10
3
Ix =
( )
2 2
L 4R m
80
3
Iy
+ =
( )
2 2
L 4R m
80
3
Iz + =
4
L
G =
z
x
y
C
B
A
ρ
A
BC m =
( )
2 2
C B m
12
1
Ix + =
( )
2 2
A C m
12
1
Iy
+ =
( )
2 2
B A m
12
1
Iz + =
D
B
A
z
x
y
( )
ρ
D - B 4AD
= m
( )
 
2
2
D D - B m
3
1
Ix + =
( )
 
2 2 2
D D - B A m
6
1
Iy + + =
( )
 
2 2 2
D D - B A m
6
1
Iz
+ + =
ρ L R π m
2
=
( )  
θ θ
2 2 2 2
sin L cos 1 3R
m
12
1
I
+ + 
=

R
L
θ
R
ρ π
3
R
3
4
m =
2
R m
5
2
I =