## 3 Validation
### Computer Simulation  
The computer simulation provided a more accurate approximation of the manipulator's workspace as it took into consideration the geometry and material of the manipulator. The simulation employed a similar configuration for the arm tendon retraction mechanism. To simplify the simulation, the pulley retracting the arm tendon was placed on the ACTR, rather than the top base of the manipulator. The simulation was performed through finite element analysis (FEA) using SolidWorks [26]. The simulation process involved two steps. The first was to convert the manipulator design into a computer-assisted design (CAD) model, while the second step employed FEA to calculate the performance of the CAD model and its response during operation. In the first step, each component was created separately, and then all the components were assembled to form the manipulator. Table 1 provides a list of the components used in the simulation. The dimensions used in the assembly reflected the physical manipulator to be fabricated; hence, the arm was 500 mm long, 100 mm wide, and 0.8 mm thick. To facilitate layering on the winch pulley, the tendon was simulated as a band with a width of 6 mm and a thickness of 0.1 mm. The arm-tip pulley provided directional freedom for the arm's distal end as the angle of the arm's tip changed from zero to over 90 degrees during the simulation. Figure 7: The manipulator’s volumetric workspace based on the mathematical model calculations. The second step of the simulation involved specifying the settings to correspond to the real-life boundary conditions. Hence, the manipulator's top end was fixed, while its lower end was free to move in response to the tendon's pulling. The ACTR was fixed to provide a stable tendon retraction. Figure 8 illustrates the simulation and the response of the arm when the ACTR is 250 mm from the lower end of the arm. The materials chosen for the arm and other components reflected the ones that would be used to fabricate the manipulator. Since most of the manipulator parts would be 3D printed, Acrylonitrile Butadiene Styrene (ABS) was used for most of the parts in the simulation. Polycarbonate plastic would be used to fabricate the arm due to both its flexibility and high tensile strength. Table 2 lists the materials used and their properties. The meshing resolution in the simulation was set differently for each component based on size, location, and level of stress the component may experience. High-resolution meshing was used for the ends of the tendon, as it pulls the arm's tip, and thus experiences the highest stresses relative to its size. Relatively coarse meshing was used for the arm's body and ACTR due to their size and the relatively mild stresses they would experience. Table 3 lists the different meshing resolutions for each component. \begin{table}
\begin{tabular}{l l l} \hline \hline \multicolumn{1}{c}{**Object**} & \multicolumn{1}{c}{**Purpose**} \\ \hline Arm & To deliver the tip to a desired location. \\ \hline ACTR & To constrain the arm and hold the winch pulley. \\ \hline Winch Pulley & To pull the tendon. \\ \hline Tendon & To pull the arm from its tip. \\ \hline Arm-Tip Pulley & To provide a swivel connection between the arm’s tip binder and the tendon. \\ \hline Arm Tip-Binder & To connect the arm to the tendon through the swivel pulley. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of parts and their purpose in the FEA simulation. Figure 8: The manipulator during FEA simulation. The images indicate the bending percentage. \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multicolumn{1}{c}{**Object**} & \multicolumn{1}{c}{**Material**} & \multicolumn{1}{c}{**Density**} & \multicolumn{1}{c}{**Tensile Strength**} & \multicolumn{1}{c}{**Modulus of Elasticity**} \\ \hline Arm & Polycarbonate Plastic & 1175.0 Kg/m3 & 66.2 MPa & 2.2 GPa \\ \hline All others & ABS & 1110.0 Kg/m3 & 41.4 MPa & 2.0 GPa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Objects’ material type for the FEA simulation.