Fig. 1.
Transformation of tool frame related to workpiece frame in robotic machining system
Fig. 2.
Rotation around fixed global coordinate system
Fig. 3.
Flowchart of the proposed tool path smoothing method
Fig. 4.
Corner smoothing of tool tip position
Fig. 5.
Corner smoothing of tool orientation
Fig. 6.
Tool orientation error in the WCS
Fig. 7.
The deviation between spline segment and linear segment
Fig. 8.
Synchronization of the tool tip position and orientation
Tab. 1.
Parameters of the testing tool path
| No. of corners | No. of tool path | Tool tip position (x, y, z)(mm) | Tool orientation(α,β,γ) (rad) |
|---|---|---|---|
| 1 | 1 | (240, 200, 220) | (0.6283, 0.5236, 0.3142) |
| 2 | (230, 240, 250) | (1.0472, 0.7854, 0.3927) | |
| 2 | 3 | (270, 230, 252.2) | (0.3142, 0.1571, 0.2094) |
| 3 | 4 | (250, 210, 242) | (0.6283, 0.7854, 0.5236) |
| (235, 230, 246.8) | (0.3142, 0.3927, 0.5236) |
Fig. 9.
The testing tool path utilized in numerical simulation
Fig. 10.
The smoothed tool tip position and tool orientation
Tab. 2.
Deviation errors of the tool tip and tool orientation with error tolerances εp = 0.8mm and ε0 = 0.01rad
| No. of corners | 1 | 2 | 3 | |
|---|---|---|---|---|
| Tool tip Position error | εp (mm) | 0.8 | 0.8 | 0.8 |
| εp(mm3) (κ,λ) | 5.4858e-06 (0.48, - 5.4e-4) | 2.3160e-06 (0.51, -1.4e-4) | 3.9818e-05 (0.47, 5.3e-4) | |
| Tool orientation error | ε0 (rad) | 0.01 | 0.01 | 0.01 |
| ε0 (rad3) (κ,λ) | 2.2647e-11 (0.46, -2.4e-3) | 1.2184e-10 (0.49, 7.2e-3) | 2.8408e-11 (0.47, -3.0e-3) | |
Tab. 3.
Deviation errors of the tool tip and tool orientation with error tolerances εp = 1.2mm andε0 = 0.005rad
| No. of corners | 1 | 2 | 3 | |
|---|---|---|---|---|
| Tool tip Position error | εp (mm) | 1.2 | 1.2 | 1.2 |
| ep (mm3)(κ,λ) | 1.8557e-05 (0.48, -8.1e-4) | 7.8179e-06 (0.51, -2.2e-4) | 1.3406e-04 (0.47, 7.9e-4) | |
| Tool orientation error | ε0 (rad) | 0.005 | 0.005 | 0.005 |
| e0 (rad3) (κ,λ) | 2.8111e-12 (0.46, -1.2e-3) | 1.5905e-11 (0.49, 3.6e-3) | 3.5244e-12 (0.47, -1.5e-3) | |
Fig. 11.
Synchronization errors of the tool orientation with respect to the tool tip displacement with εp = 0.8mm and ε0 = 0.01rad
Fig. 12.
Synchronization errors of the tool orientation with respect to the tool tip displacement with εp = 1.2mm andε0 = 0.005 rad
Fig. 13.
Kinematic profile after interpolation
Fig. 14.
Kinematic profiles of each joint of robot
