# Design and Performance of L-CaPaMan2
## 3 CAD Design and Simulation  
L-CaPaMan2 kept the structure of the first prototype. The scheme of the structure is shown in Figure 2a. The closed-loop parallel mechanism with 3 d.o.f. includes three limbs with rotational, translational, and spherical joints each. The input joint of each limb is the rotational joint at the base. The lengths of the links are marked as \(\mathrm{l_{ji}}\), where \(j\) is a part number and \(i\) is the limb number; \(\mathrm{l_{ki}}\) is a distance to point K on the translational joint, and \(\mathrm{l_{GH}}\) is a distance from the spherical joint to the central point of the platform H. Following this structure, a new prototype has been designed in Autodesk Inventor 2021 Professional [22], as presented in Figure 2b. The proposed research aims at improving, with a low-cost and lightweight design, the previous L-CaPaMan. As such, the main impact of the reported work is a new L-CaPaMan that manages to achieve the same performance of the previous versions in a more compact form design. Table 1, with the design parameters of the robot, is added to the paper for a direct size comparison. The constraints to the lengths of the mechanism parts prevent collision between the parts. The previous design of the translational joint [23], which was also built with 3D-printed components, and the real tests [24] show that in some cases the joint fails due to disassembly. In the new solution, the translational joint must be protected from disassembling during operation. Finally, it must have three idle (rotational) d.o.f. to avoid redundancies and associated vibrations. Following these requirements, the model has been designed with the dimensions, listed in Table 1.  
Figure 2: A design scheme of L-CaPaMan2 solution: (**a**) the scheme; (**b**) CAD design. The translational joint has been redesigned for 3D-printing; the model structure is shown in Figure 3a. The joint includes two printed parts and three manufactured bearings, which are connected to the part by pins from PLA. In the complete assembly, two wheels are placed on the rail and called \"top wheels\" and one, which is called \"bottom wheel\", is under the rail and constrains relative vertical movements. Translational movements are restricted with the border on one side of the rail, and by the bottom wheel pin they make contact with the other part on the other side, as shown in Figure 3b. Although the rolling bodies are placed on one surface, the stability of the construction is provided by the borders for the wheels, with 0.1 mm tolerance \(h_{1}\) and a 0.5 mm gap \(h_{2}\) on each side of printed parts. In order to analyze the behaviour of the designed system, dynamic simulation has been carried out with the parameters that are chosen and presented in Tables 2 and 3. From [25], the operating speed of the motor for 6 V power supply is 0.14 s/60 deg, and angular velocity \(\omega_{\rm n}\) for the input motion in the simulation is obtained as 427.571 deg/s. The input joint for four-bar linkage in limbs moves from \(\alpha-\)45 to 45 deg. A dry friction coefficient k\({}_{\rm df}\) has been set for the wheels in the prismatic joint of each limb. Stiffness and damping coefficients are marked as k\({}_{\rm st}\) and k\({}_{\rm damp}\), respectively. Time \(\Delta\)t is defined as the whole time of simulation divided by the number of scanning intervals. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **l\({}_{11}\), mm** & **l\({}_{21}\), mm** & **l\({}_{41}\), mm** & **l\({}_{51}\), mm** & **l\({}_{61}\), mm** & **l\({}_{6H}\), mm** \\ \hline L-CaPaMan2 & 40 & 60 & 30 & 90 & 70 & 75 \\ L-CaPaMan [23,24] & 70 & 60 & 25 & 90 & 70 & 60 \\ CaPaMan (2017) [21] & 40 & 100 & n. a. & 60 & 58 & 55 \\ CaPaMan (1997) [13,14] & 80 & 200 & n. a. & 120 & 116 & 109.5 \\ \hline n. a.—not available. & & & & & & \\ \end{tabular}
\end{table} 
Table 1: Design parameters for L-CaPaMan2 as compared with previous designs, Figure 1.  
Figure 3: CAD translational joint view: (**a**) scheme, (**b**) structure, and (**c**) CAD design.