## 6 Experiments on Robotic Cutting of Artificial Vertebrae  
To validate the efficacy of our method for fabricating artificial vertebral bodies based on bone density predictive modeling, a robotic vertebral plate cutting experiment was devised. The experimental setup comprises a 6-DOF EC66 collaborative robot (Elite Corporation, Shanghai, China), a type of KWR75B six-axis force sensor (Kunwei, Changzhou, China), a ball end milling cutter (China Dezhou Lansuo Medical Equipment Co., Dezhou, China), and a computer for control and data acquisition (HP ProBook, Beijing, China). During the experiment, the 3D-printed artificial vertebrae are securely mounted on a fixture. An overview of the experimental platform is illustrated in Figure 21.  
The 6-DOF collaborative robot, equipped with a ball end milling cutter, executes transverse feed cutting along the \(Y\)-axis. The transverse feed rate and the longitudinal  
Figure 21: Robot cutting experiment platform. Figure 20: Artificial vertebrae model. (**a**) Cancellous bone model; (**b**) cortical bone model; (**c**) composite model; (**d**) composite model overall diagram. depth of the cut are controlled by the collaborative robot's controller and the host computer. The rotation speed of the end mill, set at 5000 rpm, is achieved by commanding the integrated servo motor through the host computer interface. Cutting trials are conducted on both the printed cortical and cancellous bone sections. Throughout the process, a six-axis force sensor is employed to monitor and record the cutting forces exerted by the end mill. For this specific experiment, parameters are set as follows: a rotation speed of 5000 rpm, a feed rate of 3 mm/s, and a depth of the cut of 0.2 mm. A porcine spine, exhibiting a density akin to that of the artificial vertebra, is chosen for comparative cutting experiments. Utilizing CT scanning, the bone densities of various layers within the porcine spine are determined. The comparative density analysis, summarized in Table 11, reveals relative errors all confined within a 4% margin. This substantiates the suitability of the porcine spine for implementation in the cutting comparison tests. To corroborate the hypothesis that distinct bone qualities yield differential force signals during the cutting process, the robot performs cuts on differing bone layers of both the artificial vertebral plate and the porcine spine. The outcomes demonstrate that the force signals indeed vary in response to the varying bone properties. Illustrations of the robotic cutting procedure on the porcine spine are depicted in Figure 22, while the analogous procedure on the artificial vertebral plate is showcased in Figure 23.  
Considering the y-direction milling force for comparison, Figure 24 displays the plots of the cutting force signal data for the cortical bone and cancellous bone models, respectively. Similarly, Figure 25 illustrates the cutting force signal data for the cortical and cancellous bone segments of the actual porcine spine. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Bone Type**} & **Artificial Vertebra** & **Porcine Spine** & **Relative Error** \\  & **Density (mg/cm\({}^{3}\))** & **Density (mg/cm\({}^{3}\))** & **(\%)** \\ \hline Cortical bone & 340.98 & 353.26 & 3.60 \\ Cancellous bone & 1169.78 & 1152.36 & 1.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison of artificial vertebral density with porcine spine density. Figure 22: Effect of robotic cutting of porcine backbone. (**a**) Cortical bone cutting effect; (**b**) cancellous bone cutting results. Figure 23: Effect of robotic cutting of artificial vertebral plate. (**a**) Cortical bone model cutting effect; (**b**) cutting effect of cancellous bone model. Figure 24: Cutting force signals for cortical and cancellous bone models. (**a**) For cortical bone model; (**b**) for cancellous bone model.