## 5 Example and Verification Experiment
### Experiments  
The printing code of the workspace was generated with the proposed kinematics model and the multisolution method by setting V\({}_{\mathrm{U}}\) = [0,0,0]T. The multijoint-industrial-robot-based 3D-printing system then printed its own workspace. The simulation are proposed with the printing code by setting the layer height as 10 mm and 5 mm, respectively as shown in Figure 13. It was found here that it was difficult to print the actual size of the workspace, because the end-effector approached singularities near the boundaries of its workspace, where it lost rigidity and precision. In addition, the layer height setting may make printing time be too long, which will waste time and printing materials.  
The entire workspace was scaled by 10 times in equal proportion, so the robot could print its workspace. The origin of the base of the robot was chosen as the origin of the scaling, as shown in Figure 14. After scaling, the height dimensions became Z\({}_{\mathrm{max}}\) = 38.2924 mm and Z\({}_{\mathrm{min}}\) = \(-17.5947\) mm. The total height was 55.8871 mm. For printing, the scaled workspace model was translated to the print platform, as shown in Figure 14. First, the model was translated from the origin of the base to the origin of the WCS with vector V\({}_{\mathrm{a}}\) = [225, \(-70\),12]T mm. At this time, the height of a part of the model was negative. The model was then translated with vector V\({}_{\mathrm{p}}\) = [70, 70, 5.5947]T mm to make the model on the print platform. The printing code with joint angles of the robot was generated based on the model and the proposed multisolution method. Vector V\({}_{\mathrm{U}}\) = V\({}_{\mathrm{a}}\) + V\({}_{\mathrm{p}}\) was used for the calculation of the all possible joint-angle groups. With the printing code, the scaled workspace was printed with this multijoint robot. The printing material was PLA. The layer height was set to 0.2 mm, and feed velocity was 50 mm/min. The printed model of the scaled workspace is shown in Figure 15. The results showed that the workspace visualization method produced the real workspace, and the proposed kinematics and multisolution method can be used for 3D printing with such a robot.  
The proposed method can be used to obtain and visualize a detailed workspace of a multijoint industrial robot by using a 3D-printing layering concept. There are some possible industrial applications. For example, multijoint industrial robots play a great role in automatic production lines, such as in automation welding, automatic material delivery, and automatic assembly. Detailed workspace models of such robots can be a great help for the arrangement of the robots. The trajectory of the welding or the material delivery should be in the workspace of the robot. The workspace also provides a restricted area for path planning and reliable control of the robot in an automatic production line.  
Figure 13: Workspace printing path: (**a**) setting the height to 10 mm; (**b**) set the height to 5 mm.  
In addition, multijoint industrial robots can be used for 3D printing to manufacture complex freeform surfaces. The visual workspace can help to determine and optimize the locations of the printed parts. The printing trajectories are also limited by the workspace of the robot.