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7 Appendix
Appendix 1: Inertia calculation method
An allowable moment of inertia in the mechanical interface at the tip of the robot arm is determined. If a load
exceeding the allowable moment of inertia is put, on the tip of the arm, vibration during operation and an
overload alarm may occur. Therefore, consider the matching/appropriateness of the hand and load to be
mounted on the tip of the arm for the robot specifications when you select a robot. The following describes
the load inertia calculation method.
For the vertical multi-joint robot, consider the load moment and the load inertia on the wrist axes (J4 to J6
axes). To consider them, calculate the load moment and load inertia applied on each of J4 to J6 axes in con-
sideration of the posture of the hand and workpiece. The following figures show the examples.
(1) Load moment calculation example (for J5 axis with flange facing downwards)
The items shown in the right picture are defined as follows.
Hand mass
Center of gravity of the hand
Workpiece mass
Center of gravity of the workpiece
The load moment applied to the J5 axis is calculated as follows.
Where g is gravitational acceleration (m/s
Load moment about the J5 axis : M (Nm)
= W
× L
× g + W
1
1
Check that the value of M is equal to or less than the allowable load moment of
the target model.
(2) Load inertia calculation example (for J6 axis)
The items shown in the right picture are defined as follows.
Hand mass
Distance between the center of J6 axis and
the center of gravity of the hand
Workpiece mass
Center of gravity of the workpiece
Assume that both hand and workpiece are rectangle. When their surface areas
can be expressed as follows, respectively: a1 × b1,
and a2 × b2 (where a = height, b = width), the load inertia about the J6 axis is
calculated as follows.
Load inertia about the J6 axis of the hand : I
= Iz
+ W
× L
1
1
Load inertia about the J6 axis of the workpiece : I
= Iz
+ W
× L
2
2
Total load inertia about the J6 axis of both hand and workpiece : I (kg•m
Check that the value of I is equal to or less than the allowable load moment of the target model.
Note) When the robot changes its posture significantly in a direction other than the vertical downward direction, check the load
moment inertia about the J4 axis as well.
: W
(kg)
1
: L
(m)
1
: W
(kg)
2
: L
(m)
2
2
).
× L
× g
2
2
1 2
2
2
= W
× (a1
+ b1
)/12 + W
1
2 2
2
2
= W
× (a 2
+ b 2
)/12 + W
2
: W
(kg)
1
: L
(m)
1
: W
(kg)
2
: L
(m)
2
2
(kg•m
)
1
1 2
× L
1
2
(kg•m
)
2
2 2
× L
2
J5 axis
Hand W
Center of gravity
of the hand
L
1
Center of gravity
of the workpiece
L
2
J6 axis
Hand W
Center of gravity
of the hand
L
1
L
2
2
) = I
+ I
1
2
Inertia calculation method Appendix-109
7 Appendix
kg
1
Workpiece W
kg
2
kg
1
Workpiece W
kg
2
Center of gravity
of the workpiece
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