## 6 Performance Analysis  
The analytical model was established to analyze the influences of the geometric parameters and the material properties on the compliance factors and rotation center shifts. The designed geometric parameters of the mechanism were chosen as \(l\), \(D\), \(\theta\), and \(|OO_{1}|\). It can be noticed that all compliance factors of the mechanism vary inversely with the elastic Young's modulus \(E\), and increase with the increase of \(l\) and the decrease of \(D\).  
To evaluate the influences of the other two parameters \(\theta\) and \(|OO_{1}|\) on the compliance factors, three dimensional plots of all compliance factors in terms of the two geometric parameters mentioned above are shown in Figure 9. Each time that the two parameters are varied, the other parameters are considered to be constant. These constant values are: \(E=1646\) MPa, \(l=12.5\) mm, \(D=1.5\) mm. It can be seen from Figure 9 that the two geometric parameters also have significant effects on the compliance factors, and several conclusions can be derived as follows to provide a useful and accurate reference for the design and manufacture of satisfactory RCC mechanism structures:  
1. The compliance factors \(C_{X,\;F_{X}}\) increase when \(\theta\) increases. The variation tendency of \(C_{X,\;F_{X}}\) versus \(|OO_{1}|\) is dependent on \(\theta\).
2. \(|OO_{1}|\) has no influence on the vertical compliance factor \(C_{Z,\;F_{Z}}\), which increases sensitively with the decrease of \(\theta\). \(C_{\theta_{X,\;M_{X}}}\) decreases when the two parameters increase.
3. \(C_{X,\;M_{Y}}\) varies slightly with \(|OO_{1}|\), and presents a maximum in terms of \(\theta\), around \(\theta=45^{\circ}\).  
Figure 8: The experimental setups. (**a**) Photo of the prototype, and experimental conditions of (**b**) the first step and (**c**) the second step.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Compliance Factors** & **Analytical** & **Experimental** & **Error (\%)** \\ \hline \(C_{X,\;F_{X}},C_{Y,\;F_{Y}}\) (μm/N) & 31.93 & 32.78 & 2.59 \\ \(C_{X,\;M_{Y}},C_{Y,\;M_{X}}\) (mm/Nm) & 2.96 & 3.18 & 6.91 \\ \(C_{\theta_{X,\;F_{Y}}},C_{\phi_{Y,\;F_{X}}}\) (mrad/N) & 2.96 & 3.18 & 6.91 \\ \(C_{\theta_{X,\;M_{X}}},C_{\phi_{Y,\;M_{Y}}}\) (mrad/Nm) & 314.6 & 311.8 & 0.9 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparisons of compliance factors between analytical and experimental results.  
The influences of different geometric parameters of the mechanism on the rotation center shift were also analyzed by the proposed analytical model. Although the real rotation center is very close to the ideal rotation center based on the aforementioned analytical results, the RCC mechanism is expected to minimize its center shift if it is designed for precise rotation. According to Equation (25), the locations of rotation center are the ratio functions of the compliance factors; hence, the influences of Young's modulus \(E\) of the material on the center shift are removed. The variation tendencies of the center shift with respect to the changing dimensions are all graphically represented in Figure 10. As can be seen from Figure 10a-d, the dimensions of the beam flexure have a significant influence on the center shift. The center shifts in both loading cases (direction fixed force \(F_{X}\), \(F_{Y}\) and pure Moment \(M_{X}\), \(M_{Y}\)) decrease with the increase of \(l\) and the decrease of \(D\), and vary quasi-linearly with \(|OO_{1}|\). It can be concluded from Figure 10 that the minimization of the center shifts may be achieved by increasing \(l\) or reducing \(D\), \(|OO_{1}|\), and \(\theta\).