3.6. Allowable Load of Wrist Axis
3.6. Allowable Load of Wrist Axis
The load, which will be applied to the mechanical interface of robot's wrist axis, is restricted by allowable weight, allowable load torque and allowable moment of inertia.
Allowable weight
Table 3‑3 Allowable weight
Robot model | Allowable weight |
HA006A/HA006L | 58.8 N (6kgf) or less |
Allowable load torque
Table 3‑4 Allowable load torque
Robot model | Allowable load torque | ||
R2 axis rotation | B axis rotation | R1 axis rotation | |
HA006A | 11.8 Nm (1.2kgf·m) or less | 9.8 Nm (1.0kgf·m) or less | 5.9 N·m (0.6 kgf·m) or less |
HA006L | 39.2 Nm (4 kgf·m) or less | ||
Allowable moment of inertia
Table 3‑5 Allowable moment of inertia
Robot model | Allowable moment of inertia | ||
R2 axis rotation | B axis rotation | R1 axis rotation | |
HA006A | 2.65 kgm² (0.27kgfms²) | 2.65 kgm²(0.27kgfms²) | 0.59 kgm²(0.06kgfms²) |
HA006L | 0.88 kgm² (0.088kgfms²) | ||
Refer to the Table [3-3]~[3-5] so that the load does not exceed the allowed condition.
[Fig. 3.12, 3.13] shows the allowable range where the material point can be located when you think that the assembled load has a material point. But because the actual load (End Effector) rarely is on the material point, calculate the moment of inertia of each axis to make the evaluation. The following shows an example of considering the assembling load as the material point.
(Ex) Robot type is【HA006A】and the weight of the load is 5.74Kg
Figure 3.12 2-D load model
M – Load weight
Jxx – Inertia moment in X direction from weight center of load
Jyy – Inertia moment in Y direction from weight center of load
Jzz – Inertia moment in Z direction from weight center of load
Ja4- Inertia moment from R2 axis rotation center
Ja5- Inertia moment from B axis rotation center
Ja6- Inertia moment from R1 axis rotation center
☞ Load condition:
Aluminum block with length and width of 100mm and thickness of 200mm (Mass 5.74kg)
① Permitted torque limit
Location of B axis weight center LX = 155mm、LY = 0mm、LZ = -25.5mm
If you apply the B and R1 axis length limit in the torque map, it is shown as follows.
B axis based length 
R1 axis based length 
② Permitted inertia moment limit
Inertia moment of load from the weight center JXX=0.024kgm2, JYY=0.01kgm2, JZZ=0.024kgm2
B axis inertia moment (Ja5)
R1 axis inertia moment (Ja6)
③ Conclusion
It is safe because the weight, torque and inertia moment all satisfy the limited condition.
n Allowable center location from center of R1 axis
① Allowablecenter location from allowable torque
LR1 ≤ (Allowable torque) / (Load weight)
LR1 = 5.9 N·m / (5.74Kg×9.8 m/s2) = 0.104 m
② Allowablecenter location from allowable moment of inertia
LR1 ≤ (Allowable moment of inertia/Load weight)1/2
= (0.104 kg·m2 / 5.74kg)1/2 = 0.135 m
From the above results, the distance from the center of R1 axis is limited by the allowable torque and must be within 0.104 m.
n Allowable center location from center of B axis
(The center of the B axis of this robot is on the same axis and also the allowable load torque and allowable moment of inertia have the same B axis and R2 axis values. Therefore if the allowable conditions of B axis are satisfied, the same will be satisfied for R2 axis.)
① Allowable center location from allowable torque
LB ≤ (Allowable torque) / (Load weight)
LB = 9.8 N·m / (5.74Kg×9.8 m/s2) = 0.174 m
② Allowable center location from allowable moment of inertia
LB ≤ (Allowable moment of inertia/Load weight)1/2
= (2.65 kg·m2 / 5.74kg)1/2 = 0.679 m
From the above results, the distance from the center of B axis is limited by the allowable torque and must be within 0.174m.
n Torque Map
Figure 3.13 Wrist axis torque map