Yamaha FLIP-X Series, User Manual

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Appendix
iv
Equation of moment of inertia calculation
CAUTION
The robot must be operated with correct tolerable moment of inertia and acceleration
coefficients according to the manipulator tip mass and moment of inertia. If this is not
observed, premature end to the life of the drive units, damage to the robot parts or
residual vibration during positioning may result.
Usually the R axis load is not a simple form, and the calculation of the moment of inertia is not
easy.
As a method, the load is replaced with several factors that resemble a simple form for which the
moment of inertia can be calculated. The total of the moment of inertia for these factors is then
obtained.
The objects and equations often used for the calculation of the moment of inertia are shown
below.
1. Moment of inertia for cylinder
The moment of inertia (J) for a cylinder having a rotation center such as shown below is
given by
D
h
J =
ρπ
D
4
h
32g
WD
2
8g
= (kgf.cm.sec
2
)
mD
2
8
= (kgm
2
)
ρ
g
W
m
: Density (kg/cm
3
)
: Gravitational acceleration (cm/sec
2
)
: Weight of cylinder (kgf)
: Mass of cylinder (kg)