# Virtual and Physical Prototyping of Reconfigurable Parallel Mechanisms with Single Actuation
## 4 Virtual and Physical Prototyping
### Kinetostatic Analysis of a Hexapod Using CAD Modeling
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Nomenclature** & **Dimension** \\ \hline Overall dimensions of the hexapod, including the & 530 mm \(\times\) 530 mm \(\times\) 457 mm \\ maximum displacements of the platform & (LWH dimensions) \\ \hline Column height of circular guide 1 & 143.00 mm \\ \hline Diameter of circular guide 1 & 500.00 mm \\ \hline Height of circular guide 1 & 58.30 mm \\ \hline Pitch diameter of driving wheel 3 & 125.00 mm \\ \hline Number of teeth of driving wheel 3 & 50 \\ \hline Pitch diameter of gear 5 & 45.00 mm \\ \hline Number of teeth of gear 5 & 18 \\ \hline Center distance of gear transmission 3–5 & 85.00 mm \\ \hline Module of gears 3–5 & 2.50 mm \\ \hline Diameter of driving pulley 6 & 30.00 mm \\ \hline Diameter of driven pulley 8 & 60.00 mm \\ \hline Center distance of belt transmission 6–8 & 76.00 mm \\ \hline Length of crank 9 & 38.85 mm \\ \hline Length of swinging arm 11 (distance from the & \\ center of circular guide 1 to the center of spherical & 246.05 mm \\ joint 12–13) & \\ \hline Length of leg 13 & 220.05 mm \\ \hline Platform radius 14 excluding spherical joints 13–14 & 180.00 mm \\ \hline Platform radius 14 including spherical joints 13–14 & \\ (distance from the center of platform 14 to the & 193.00 mm \\ center of spherical joint 13–14) & \\ \hline Minimum/maximum angle between paired & 20\({}^{\circ}\)/100\({}^{\circ}\) \\ spherical joints 13–14 & \\ \hline Bearing 1,000,804 (13 pcs) & 20 mm \(\times\) 32 mm \(\times\) 7 mm \\ \hline Bearing 623 ZZ (18 pcs) & 3 mm \(\times\) 10 mm \(\times\) 4 mm \\ \hline Diameter of the sphere in the spherical joints & 12.00 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Geometrical dimensions of the hexapod links. Given the parameters above, we prepared the mechanism assembly (Figure 4) for dynamic modeling. Simulation results shown in Figure 5 present the calculated value of the motor torque (\(T_{M}\)) for the different cases of cranks initial positions. Notice how the torque increases to compensate for the weight contribution of the links when the platform displaces along the vertical axis. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Link/Group of Links** & **Material** & **Moment of Inertia, kg\(\cdot\)mm\({}^{2}\)** & **Mass, kg** \\ \hline \hline Shaft 2 and driving wheel 3 & Plastic ABS & 494.19 & 0.257 \\ \hline Shaft 4, gear 5 and driving pulley 6 & Plastic ABS & 20.68 & 0.091 \\ \hline Shaft 7, driven pulley 8 and crank 9 & Plastic ABS & 32.04 & 0.085 \\ \hline Slide block 10 & Plastic ABS & 0.061 & 0.003 \\ \hline \multirow{5}{*}{Swinging arm 11 (incl. elements 11a,b), and carriage 12 (incl. elements 12a,b),} & \#1 & 2545.40 & 0.052 \\ \cline{2-4}  & \#2 & 2545.66 & 0.052 \\ \cline{2-4}  & \#3 & 2545.76 & 0.053 \\ \cline{2-4}  & \#4 & steel & 2545.87 & 0.053 \\ \cline{2-4}  & \#5 & 2545.80 & 0.053 \\ \cline{2-4}  & \#6 & 2546.09 & 0.053 \\ \hline \multirow{2}{*}{Leg 13 (incl. elements 13a)} & \multirow{2}{*}{Aluminum, plastic ABS, steel} & \(\left[\begin{array}{ccc}159.87&0&0\\ 0&159.87&0\\ 0&0&0.33\\ \end{array}\right]\) & 0.022 \\ \hline \multirow{2}{*}{Platform 14 (incl. elements 14a)} & \multirow{2}{*}{Aluminum, plastic ABS, steel} & \(\left[\begin{array}{ccc}10061.20&0&0\\ 0&10061.20&0\\ 0&0&20079.61\\ \end{array}\right]\) & 1.153 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Inertial properties of the hexapod links. One should note that using CAD software to perform calculations allows for considering the links geometry and material as accurately as possible. Thereby, the CAD functionality can significantly simplify the solution process and lead to more accurate results in comparison with the analytical methods.