## 5 Experimental Verification  
To validate the analytical model, experimental tests were also conducted on a prototype of the RCC mechanism with \(l=12.5\) mm, \(D=1.5\) mm, \(\theta=45^{\circ}\), and \(|OO_{1}|=10\) mm, which can be rapidly manufactured by 3D laser printing technique (selective laser sintering, SLS). The chosen material of the prototype was nylon PA 2200 with a Young's modulus of 1646 MPa and the Poisson's ratio of 0.33. The photography of the prototype is shown in Figure 8a. A digital dial gage (1 \(\upmu\)m resolution) was employed to measure the displacement, while a series of standard weights were used to apply the pull forces to the end-effector of the RCC mechanism.  
The experimentation includes two steps. In the first step (Figure 8b), the applied force generated by the weights was parallel to the \(Z\) axis of the mechanism. As the applied force does not pass through the \(Z\) axis, a \(Z\) directional force and a \(Y\) directional moment can be generated. The dial gage can measure displacement at a certain point, and the displacement originated from the \(Z\) axial compression was neglected, so \(C_{\theta_{X},\,M_{X}}\) and \(C_{\theta_{Y},\,M_{Y}}\) can be obtained from the test.  
In the second step (Figure 8c), the applied force generated by the weights was vertical to the \(Z\) axis of the mechanism. The digital dial gage is firstly pre-compressed, and then released after the force is applied. As the force does not pass through the end point \(O\), the variations of X directional force and Y directional moment can be caused by the hanging weights. Due to the small deformation of the RCC mechanism, the movements of the fixtures used to hang the weights can be neglected. Therefore, the theoretical applied force and moment can be calculated by the known hanging weights and moment arm. Both the applied force and the corresponding displacement at a certain point can be known from the measurement condition. \(C_{\theta_{X},\,M_{X}}\) is obtained from the first test, and \(C_{X,\,M_{Y}}\) is equal to \(C_{\theta_{Y},\,F_{X}}\), so, \(C_{X,\,F_{X}}\) and \(C_{X,\,M_{Y}}\) can be calculated in two measurements at different applying and measurement points [25].  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Sample 1**} & \multicolumn{3}{c}{**Sample 2**} & \multicolumn{3}{c}{**Sample 3**} \\ \hline Compliance factors & An & FEA & Err (\%) & An & FEA & Err (\%) & An & FEA & Err (\%) \\ \(C_{X,\,F_{X}},C_{Y,\,F_{Y}}\) (mm/N) & 31.93 & 32.23 & 0.93 & 29.93 & 31.43 & 4.77 & 188.9 & 183.5 & 2.94 \\ \(C_{X,\,M_{Y}},C_{Y,\,M_{X}}\) (mm/Nm) & 2.96 & 3.07 & 3.58 & 1.08 & 1.13 & 4.42 & 15.9 & 15.4 & 3.25 \\ \(C_{Z,\,F_{Z}}\) (\(\upmu\)m/N) & 2.12 & 2.30 & 7.83 & 0.96 & 1.04 & 7.69 & 10.63 & 11.11 & 4.32 \\ \(C_{\theta_{X},\,F_{Y}},C_{\phi_{Y},\,F_{X}}\) (mrad/N) & 2.96 & 3.08 & 3.89 & 1.08 & 1.13 & 4.42 & 15.9 & 15.4 & 3.25 \\ \(C_{\theta_{X},\,M_{X}},C_{\phi_{Y},\,M_{Y}}\) (mrad/Nm) & 314.6 & 330.3 & 4.75 & 47.35 & 50.56 & 6.35 & 1391.8 & 1352.3 & 2.92 \\ \(C_{\theta_{Z},\,M_{Z}}\) (mrad/Nm) & 452.2 & 469.3 & 3.64 & 147.8 & 153.6 & 3.78 & 1163.6 & 1136.7 & 2.37 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the compliance factors between analytical (An) and Finite element analysis (FEA) results.  
Figure 7: Finite element analysis (FEA) results of the RCC mechanism in different loading cases of (**a**) Direction fixed force \(F_{X}\) and (**b**) Pure Moment \(M_{Y}\).  
Each step of the experimentation process was repeated three times. The experimental results obtained from the three repeats was averaged to the final values of the compliances. The comparisons of analytical and experimental results are listed in Table 3. It can be seen that the errors between the three results are all small enough to verify the effectiveness of the proposed analytical model.