Optimal Joint Path Planning of a New Virtual-Linkage-Based Redundant Finishing Stage for Additive-Finishing Integrated Manufacturing
Abstract
:1. Introduction
2. Design of AFM and Kinematics Analysis
3. Redundancy Optimization for Joint Path Planning
3.1. Minimum Euclidian Norm Solution for Optimal Joint Space Solution for Given Tool Path
3.2. Tool Path Generation of the Inflated CAD Model of 3D Print with CURA Slicer
Algorithm 1 Tool path generation | |
1: | Input (3D point surface coordinate Ni(xi,yi,zi)) |
2: | for i = 1 to n do |
3: | if , then |
4: | for j = 1 to n do |
5: | layer_points_x = Nj(0) |
6: | layer_points_y = Nj(1) |
7: | end |
8: | surface_spline = RectBivariateSpline(layer_points_x, layer_points_y, ) |
9: | z_point = surface_spline(x, y, grid=False) |
10: | Calculate |
11: | dx = surface_spline(x, y, dx = 1, dy = 0, grid = False) |
12: | dy = surface_spline(x, y, dx = 0, dy = 1, grid = False) |
13: | normal_vector |
14: | return normal_vector |
15: | end |
3.3. Frameworks of Optimal Joint Path Planning and Motion Control
4. Results and Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
References
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Frame i | |||
---|---|---|---|
1 | (0, 0, 0) | (0, 0, 0) | (0, 0, 1) |
2 | (0, 0, 1) | (0, 0, 0) | (0, 0, 0) |
3 | (0, 0, 0) | (−L3, 0, 0) | (1, 0, 0) |
4 | (0, 0, 0) | (−L3, 0, 0) | (0, 1, 0) |
5 | (0, 0, 1) | (−L3, 0, 0) | (0, L3, 0) |
6 | (0, 1, 0) | (−L3, 0, 0) | (0, 0, −L3) |
Case 1 | Case 2 | |||
---|---|---|---|---|
Distance Error [RMS (Peak)] | Orientation Error [RMS (Peak)] | Distance Error [RMS (Peak)] | Orientation Error [RMS (Peak)] | |
Cross shape | 152.33 (201.00) × 10−9 m | 2.04 (2.62) × 10−9 rad | 95.49 (137.62) × 10−9 m | 0.57 (0.77) × 10−9 rad |
Ellipse shape | 5.38 (8.29) × 10−9 m | 0.07 (0.17) × 10−9 rad | 2.78 (4.27) × 10−9 m | 0.01 (0.03) × 10−9 rad |
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Yu, J.; Jeon, H.; Jeong, H.; Lee, D. Optimal Joint Path Planning of a New Virtual-Linkage-Based Redundant Finishing Stage for Additive-Finishing Integrated Manufacturing. Mathematics 2023, 11, 4995. https://doi.org/10.3390/math11244995
Yu J, Jeon H, Jeong H, Lee D. Optimal Joint Path Planning of a New Virtual-Linkage-Based Redundant Finishing Stage for Additive-Finishing Integrated Manufacturing. Mathematics. 2023; 11(24):4995. https://doi.org/10.3390/math11244995
Chicago/Turabian StyleYu, Jiwon, Haneul Jeon, Hyungjin Jeong, and Donghun Lee. 2023. "Optimal Joint Path Planning of a New Virtual-Linkage-Based Redundant Finishing Stage for Additive-Finishing Integrated Manufacturing" Mathematics 11, no. 24: 4995. https://doi.org/10.3390/math11244995