Fig. 1.
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Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Geometric parameters of ABB IRB 2400 manipulator according to modified Denavit-Hartenberg notation
| ai (m) | αi (rad) | di (m) | θi (rad) | |
|---|---|---|---|---|
| Link 1 | 0 | 0 | d1 = 0.615 | q1 |
| Link 2 | a1 = 0.1 | 0 | ||
| Link 3 | a2 = 0.705 | 0 | 0 | q3 – q2 |
| Link 4 | a3 = 0.135 | d4 = 0.755 | q4 | |
| Link 5 | 0 | 0 | q5 + π | |
| Link 6 | 0 | 0 | q6 | |
| Tool 0 | 0 | 0 | d7 = 0.085 | 0 |
Physical parameters of the spindle
| Parameter | Sym. | Spindle |
|---|---|---|
| Mass (kg) | mT | 12.7 |
| Centre of mass (mm) | STx | -38.3 |
| STy | 0 | |
| STz | 129.3 | |
| Moments of inertia (kgm2) | ITxx | 0.269 |
| ITyy | 0.274 | |
| ITzz | 0.193 | |
| ITxy | 0 | |
| ITxz | 0 | |
| ITyz | 0 |
Accuracy parameters from the Robot’s “Birth certificate”
| Parameter | Value (mm) |
|---|---|
| Average Absolute Error | 0.18 |
| Maximum Absolute Error | 0.38 |
| Standard Deviation | 0.07 |
Friction model parameters for each joint
| Joint | Fs [Nm] | Fc [Nm] | Fv [Nms/rad] | ωst [rad/s] |
|---|---|---|---|---|
| 1 | 36.3 | 24.2 | 11.85 | 0.0085 |
| 2 | 39.2 | 31.2 | 8.323 | 0.0031 |
| 3 | 25.3 | 16.9 | 9.3613 | 0.0094 |
| 4 | 19.2 | 7.9 | 7.1228 | 0.0175 |
| 5 | 39.7 | 13.7 | 7.2654 | 0.0176 |
| 6 | 17.5 | 8.8 | 2.323 | 0.0162 |
Physical parameters of the robot
| Parameter | Sym. | Link 1 | Link 2 | Link 3 |
|---|---|---|---|---|
| Mass (kg) | mi | 192 | 26.5 | 25.7 |
| Centre of mass (mm) | Six | 21 | 253.4 | 139.5 |
| Siy | 22 | 47.7 | -99.5 | |
| Siz | -188.5 | 7 | -9.7 | |
| Moments of inertia (kgm2) | Iixx | 9.82183 | 0.23517 | 0.0143 |
| Iiyy | 6.16127 | 1.22338 | 0.01412 | |
| Iizz | 8.30224 | 1.16539 | 0.00892 | |
| Iixy | 0.50571 | 0.58498 | -0.0259 | |
| Iixz | -1.0596 | 0.22733 | 0.01089 | |
| Iiyz | 0.10946 | 0.56479 | -0.0003 | |
| Link 4 | Link 5 | Link 6 | ||
| Mass (kg) | mi | 29.7 | 2.8 | 0.8 |
| Centre of mass (mm) | Six | 0.131 | -0.587 | 0.208 |
| Six | -1.81 | -0.245 | 0.035 | |
| Siz | -296.7 | 0.540 | 72.270 | |
| Moments of inertia (kgm2) | Iixx | 0.74128 | 0.0034 | 0.00002 |
| Iiyy | 0.71936 | 0.00332 | 0 | |
| Iizz | 0.09626 | 0.00419 | 0 | |
| Iixy | 0.208 | 0.00023 | 0 | |
| Iixz | 0.035 | 0.00023 | 0 | |
| Iiyz | 0.000711 | 0.0003 | 0 | |
Accuracy indicators for each joint
| Joint | MAE (Nm) | RMSE (Nm) | AVG(ureal) (Nm) | RMSE/AVG [%] |
|---|---|---|---|---|
| 1 | 3.16 | 4.08 | 35.13 | 11.61 |
| 2 | 8.52 | 10.89 | 319.60 | 3.41 |
| 3 | 2.9 | 3.79 | 102.91 | 3.69 |
| 4 | 0.73 | 1.17 | 13.69 | 8.56 |
| 5 | 0.58 | 0.78 | 10.03 | 7.80 |
| 6 | 0.64 | 0.81 | 8.96 | 9.06 |