# Design and Performance of L-CaPaMan2
## 3 CAD Design and Simulation
Three modes of movement have been analyzed. The first mode shows a simultaneous motion of the limbs; in the second mode, motion of an individual limb is set; and in the third mode, the motion of the limbs with a phase shifting between each of them has been assumed. The plot in Figure 4 illustrates the scheme of the limb's input joint motion in degrees. The plot has five characteristic points:  
A: start moving from position \(-45\) deg, \(t=t_{0}\)  
B: end moving in position \(45\) deg, \(t=t_{1}\)  
C: start moving from position \(45\) deg, \(t=t_{2}\)  
D: end moving in position \(-45\) deg, \(t=t_{3}\)  
E: end of the simulation in position \(-45\) deg, \(t=t_{e}\)  
For dynamic simulation, it is required to define the time to reach \(\omega_{\rm n}\) from \(\omega=0\) and time to reach \(\omega=0\) from \(\omega_{\rm n}\), this time has been defined as 0.1 s. Therefore, the whole time between points A-B and C-D is equal to 0.31 s. Table 3 describes motions of input joint for each limb in relation to time. Figures 5 and 6 show the behaviour of the system during the simulation in case of accelerations of the point H--central point of the platform. By controlling the speed, the accelerations values are also restricted and do not exceed 3 m/s\({}^{2}\). With the simultaneous movements of legs in Mode 1, accelerations are observed only along Z axis. On the other hand, for Mode 3 the accelerations along Z axis are less than along others, as shown in Figure 6. When only one leg is moved, distance along Z axis is less than along others. When the speed is the controlled characteristic, the torque depends on it. Figure 7a,b show the torque values changing during time. The measurements have been done for the first leg, which is placed perpendicularly to X axis. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Mode** & **Limb** & **t0 (s)** & **t1 (s)** & **t2 (s)** & **t3 (s)** & **t\({}_{\rm e}\) (s)** \\ \hline \multirow{3}{*}{1} & 1 & 0 & 0.31 & 1 & 1.31 & 2 \\  & 2 & 0 & 0.31 & 1 & 1.31 & 2 \\  & 3 & 0 & 0.31 & 1 & 1.31 & 2 \\ \hline \multirow{3}{*}{2} & 1 & 0 & 0.31 & 1 & 1.31 & 2 \\  & 2 & 0 & 0 & 0 & 0 & 0 \\  & 3 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{3} & 1 & 0 & 0.31 & 1 & 1.31 & 3 \\  & 2 & 0.5 & 0.81 & 1.5 & 1.81 & 3 \\  & 3 & 1 & 1.31 & 2 & 2.31 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time data for limbs input joint motion in dynamic simulation, Figure 4.  
Figure 4: A scheme for input motion mode of the limbs. Overall, the proposed L-CaPaMan design enables a lighter, smaller, and cheaper version of the L-CaPaMan when compared also to the 2017 and 1997 CaPaMan versions, as also shown in Table 1. Nonetheless, the kinematic performance of the novel mechanism, which is here expressed in terms of motion and acceleration, is comparable to the ones reported in previous works [18,22], with a peak acceleration of 3 m/s\({}^{2}\) for the first CaPaMan  
Figure 5: Computed results in Mode 1 in terms of accelerations of H.  
Figure 6: Computed results in Mode 3 in terms of accelerations of H.  
Figure 7: Computed results in terms of torques of D of the first leg: (**a**) in Mode 1; (**b**) in Mode 3.  
prototype (1997, made of metal), 2.5 m/s\({}^{2}\) for the first low-cost CaPaMan prototype (2017, made of 3D-printed parts), 2.3 m/s\({}^{2}\) for the novel L-CaPaMan2. The results from Figures 5 and 6 could be used for comparison with the real prototype acquired results.