# 3D Printing of Objects with Continuous Spatial Paths by a Multi-Axis Robotic FFF Platform
## 3 Methodology
### Multi-Axis Toolpath Planning
#### 3.2.2 Global Continuous Toolpath Planning
In the tensile test, the result shows that the test part with the curve slicing path can withstand the maximum load compared to other ordinary slice types. The tensile strength of the curved sliced part is approximately 22% higher than X-direction and 167% higher than Y-direction. Parts printed in the Y and Z direction showed significant brittleness, while parts printed along curve layers showed plasticity and fractured due to bending. In the flexural test, the strength of curve slicing is second to the X direction. The result is probably due to insufficient extrusion on the surface where the parts and support contact, resulting in more pronounced stress concentration. There is little difference in the flexural strength values between different slice types, but the plasticity of parts is still obviously affected by the slice type. Compared to the work of [PERSON] et al. [24], which aims to reinforce the strength of FFF, our method provides a similar result (maximum more 100% strength increase than traditional FFF) but with a higher surface resolution and a more feasible process. The surface quality of our method is satisfactory: all the layers are well aligned to the surface and has no staircase effect. Compared to the robotic printing of [PERSON] et al. [10], our method has a smaller gap between toolpaths and eliminates the staircase on convex surfaces. Our method can be used for print parts with overhanging structures and require mechanical strength because it optimized the material deposit direction, making the toolpath along the part surface. Aerospace components, for example, usually have smooth surfaces and require high strength and lightweight, so our method can be utilized to fabricate such parts using continuous fibers. Moreover, our approach is portable and not limited to specific robot hardware or slicing software, providing a universal interface for construction. It is worth mentioning that our method does not avoid the need for support, as slice planning is based on the part surface rather than an unsupported strategy. ## 5 Conclusions

Multi-DOF printing gets rid of the limitation of traditional FFF that deposits materials along a single direction. Unlike conventional FFF printing, we propose a multi-axis continuous toolpath planning method and a process control strategy for the robotic arm-based 3D printing platform, making it possible to take full advantage of the multi-axis printing platform's advantages and improve the mechanical strength and surface quality of the printed part. Our method is based on open-source architecture and can be extended to a universal solution for multi-DOF printing. The most challenging task is to define an appropriate set of curve layers to slice the model. We flattened the model based on accessibility, then generated the toolpath with a continuous path and restored it to its original shape. The multi-axis FFF platform printed the demonstration parts and the test parts through our specially designed control architecture to verify our method. The experimental result is satisfying, showing that the continuous spatial toolpath can improve the tensile strength by 22-167% higher than that of the conventional slice type when the same printing material is used. Our method also allows the platform to print continuous reinforced fibers on the curve surfaces, further enhancing the part's strength. In the meantime, layers generated by our method are parallel to the model's surface, which effectively eliminates the staircase effect and improves the surface quality. \begin{table}
\begin{tabular}{l c c} \hline
**Slice Type** & **Max Load (N)** & **Max Deflection (mm)** \\ \hline Curve slicing & 135.70 & 5.825 \\ Z-direction & 119.70 & 6.103 \\ X-direction & 140.66 & 7.172 \\ Y-direction & 102.27 & 5.215 \\ \hline \end{tabular}
\end{table} 
Table 2: Experiment data of three-point flexural test. The major limitation of our approach is the generation of support when the model is complex.