Fig. 1.
Schematic diagram of the robotic machining test stand
Fig. 2.
Physical implementation of the robotic machining test stand
Tab. 1.
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 |
Fig. 3.
Schematic diagram of the ABB IRB 2400 manipulator with coordinate frames assigned in accordance with the modified Denavit–Hartenberg convention
Tab. 2.
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 |
Fig. 4.
Centre of mass distribution of the robot’s links
Fig. 5.
Graph illustrating the friction model
Fig. 6.
Diagram of forces and torques acting on the ith link of the robot
Fig. 7.
Diagram of the procedure for determining the physical parameters of the model
Tab. 3.
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 | |
Tab. 4.
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 |
Fig. 8.
a) Angular position and velocity of joint 2 at a constant velocity, b) recorded actuator torque
Fig. 9.
Experimental and estimated friction torque values for joint 2
Tab. 5.
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 |
Fig. 10.
Inputs for simulation – joint angles and velocities (joints 1-3)
Fig. 11.
Inputs for simulation – joint angles and velocities (joints 4-6)
Fig. 12.
Modelled vs. real actuator torques for joints 1–6