# On the Control and Validation of the PARA-SILSROB Surgical Parallel Robot
## 2 Materials and Methods  
### Experimental Model of the Parallel Robot PARA-SILSROB  
The parallel robot PARA-SILSROB was developed based on the medical protocol [3] and the requirements set forth by surgeons [43]. This robot was developed in accordance with the master-slave concept and this chapter focuses on presenting the architecture of the robotic system, beginning with the kinematic scheme and concluding with the mechanical assembly. The development stages of the experimental model are illustrated in Figure 3 (kinematic scheme of the robot), Figure 4 (3D design of the robot), and Figure 5 (experimental model of the robot). The kinematic scheme of the robot was defined, presented, and detailed in [20], and resulted in a parallel structure of the type **3-PCRRS-PCRR**, which consists of 3 identical kinematic chains mounted on a triangular frame. The next stage in the development of the parallel robot involved designing the 3D model based on the kinematic scheme detailed in [3]. The final stage consisted of assembling the mechanical structure using the information obtained from the first two stages (the kinematic scheme and the 3D design). Figure 3: The kinematic scheme of the PARA-SILSROB robot. The kinematic scheme shown in Figure 3 illustrates the three identical kinematic chains (\(KC_{i}\), \(i=1\ldots 3\)) and provides a detailed view of the mobile platform (MP) of the PARA-SILSROB robot. The fixed coordinate system (OXYZ) is positioned on the first kinematic, which consists of two active translational joints (\(q_{1},q_{2}\)) connected by two cylindrical joints (\(C_{11}\), \(C_{12}\)). One cylindrical joint serves the main link (denoted as \(l_{1}+l_{2}\)--the length between the revolute joint \(C_{11}\) and the spherical joint \(S_{1}\)), while the other serves the secondary  
Figure 4: The 3D design of the PARA-SILSROB robot. Figure 5: Experimental model of the PARA-SILSROB robot including the main components and the movements of the serial modules: (1) PARA-SILSROB; (2) Mobile platform; (3) Torso training; (4) Graphical user interface for engineers; (5) Graphical user interface for surgeons; (6) 3D Space Mouse devices with keyboard and mouse; (7–9) Serial modules used for instrument handling). link (denoted as \(l_{1}\)--the length between the revolute joint C\({}_{12}\) and the revolute joint \(R_{12}\)). Additionally, the chain includes four passive revolute joints (\(R_{f1}\), \(R_{11}\), \(R_{12}\), \(R_{13}\)) and a passive spherical joint (\(S_{1}\)), which connects the kinematic chain to the mobile platform. The structural synthesis analysis of the PARA-SILSROB robot is detailed in [20], which means that the system has six degrees of freedom (6-DOF). This capability allows for the manipulation and orientation of instruments along the three axes (\(OX\), \(OY\), \(OZ\)). The active instruments and the laparoscope are mounted on the mobile platform of the PARA-SILSROB robot using three serial modules. Two of these modules each provide 3-DOF for the orientation and insertion of the active instruments (two active revolute joints for the left and right module denoted as \(q_{1 ms1}\) and \(q_{1 ms2}\), and four active prismatic joints denoted as \(q_{2 ins1}\) and \(q_{3 ms1}\) for the left module and \(q_{2 ins2}\) and \(q_{3 ins2}\) for the right module). Additionally, there is a third module with 1-DOF dedicated to the insertion of the laparoscope (denoted as \(q_{lap}\)). These modules were specifically designed to ensure that the RCMs (remote centers of motion) of the instruments are architecturally constrained, which is a critical feature for robotic-assisted surgery [44]. Figure 4 illustrates the 3D CAD model of the PARA-SILSROB robot and a detailed view of the mobile platform. The modeling was performed using the Siemens NX software program (Version 12 provide by Siemens PLM Software, founded in 1963 in Torrance, CA, USA, country Germany, Office Plano, TX, USA) [45].