# 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
Peripheral equipment includes an Arduino Mega 2560 board running Marlin firmware, a hotbed, and an end effector for printing. The end effector similar to the standard 3D printer nozzle, mounting on the robot's flange. The upper computer is a personal computer running Ubuntu and Robot Operating System (ROS) and translates the print path into robot script and gcode. By sending gcode through the serial port to the Arduino board, the upper computer can control peripheral devices' running state, such as extrusion length and print temperature. Although different types of robot arms use different script languages, many robot manufacturers provide ROS interfaces, making our algorithm portable. We printed several demonstration parts and test parts through our platform. The demonstration parts showed the platform's printing capability for continuous fibers, global path planning, and spatial curve path. Then, we carried out the tensile and flexural experiment on the test parts to compare the printing path's influence on mechanical properties. Figure 5: Nozzle orientation example for the spatial path. Figure 6: Multi-DOF FFF printing platform for multi-axis continuous path printing. ### Model Printing

We used continuous polyester fibers prepreg with PLA to print the parts shown in Figure 7 to verify the global continuous path planning method. The parts were printed at the temperature of 210 \({}^{\circ}\)C, 5 mm/s speed, and 0.3 mm layer thickness. These parameters refer to the experiment of [PERSON] et al. [30]. The length, width and height of the model are 35 mm, 17 mm, and 9 mm. Compared to the conventional path planning method in Figure 7a, our proposed method has less empty travel between layers and more convenient post-processing parts (Figure 7b). A curved part is printed on the support using the spatial Fermat spiral path (Figure 8). The length, width, and thickness of the part are 50 mm, 10 mm, and 3 mm, respectively. Compared to the planar slicing method, this method significantly improves the printed parts' surface quality, eliminates the staircase effect, and simplifies the continuous fiber parts' printing path on the curved surface. As shown in Figure 9, the test part contains an arch bridge structure in the middle. The total length of the test parts is 75 mm, the width is 10 mm, and the thickness is 3 mm. This shape was chosen because standard test pieces usually have regular shapes that cannot accentuate multi-DOF printing advantages. Figure 8: The printing process of the global continuous path. Figure 7: Example for spatial printing sequence generation for continuous fibers. (**a**) Conventional printing sequence. (**b**) Scheduled printing sequence. The test parts for mechanical test were respectively sliced and printed using a multi-DOF continuous path with Fermat spiral and conventional slicing along the \(X/Y/Z\) direction with Zigzag infill, as shown in Figure 10. We used our multi-DOF print platform to print the continuous path test parts, while a general FFF printer printed the XYZ direction sliced test parts. All test parts are printed by a 0.6 mm nozzle with polylactic acid (PLA) at 210 \({}^{\circ}\)C, 30 mm/s, 0.2 mm layer thickness, and 100% infill density. Figure 11 shows the printed test parts. ### Mechanical Test

Tensile tests and flexural tests were designed to verify the printed part's mechanical properties between the different slice types. We printed groups' test parts for each of the slice types in the experiment and then obtained their average values. Table 1 and Figure 12 show the result of the tensile test. The distance between the two clamps is 60 mm, and the test speed is 2 mm/min on the equipment shows in Figure 13.

Figure 11: Printed test parts with PLA. Figure 9: Continuous fiber part printed using spatial Fermat spiral path on curve layer. ### Result and Discussion

The result shows that our method avoids the strength decrease caused by anisotropy.