## 3 Structure Optimization  
### Multi-Objective Optimization Models  
The SCARA robot operates at high speed in the horizontal direction, and has a high acceleration at the start and stop stages, which makes the upper arm subject to large shear force and torque. In addition, the elasticity of the bolt connector will further enhance the vibration of robot, which will cause the tiny centerline deviation of the bolt contactor, and cause the bolt contactor to wear and loosen. Therefore, the real-time clamping force of the bolt connectors should be enhanced. As shown in Figure 3, the mechanical model of the bolt connector is simplified into two groups of axial force composed of elastic force and damping force. In addition, it is considered that the elastic force and damping force act in the same direction. When the SCARA robot operates, one group of axial forces is compressed and the other group is stretched due to the effect of shear force and torque. Meanwhile, a tiny gap is produced, which causes the bolt connector to wear. The real-time clamping force can be expressed as Equation (1). \[F=\left.F_{0}\middle/(1+\frac{f_{w}K}{A}n)\right. \tag{1}\]  
where \(F_{0}\) is the pretension of bolt connector, \(F\) is the real-time clamping force of the bolt connector, and \(A\) is the equivalent contact area. It can be seen that when \(n\), \(f_{w}\) and \(K\) are constant, increasing \(F_{0}\) and \(A\) can effectively improve the real-time clamping force. However, when \(F_{0}\) increases, the pressure exerted by the bolt connector will increase. If the thickness of the clamped part is not enough, it may be damaged due to excessive \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Link i**} & \(\mathbf{\theta i}\) & \(\mathbf{di}\) & \(\mathbf{ai}\) & \(\mathbf{ai}\) \\  & **Rot z [deg]** & **Disp z [mm]** & **Disp x [mm]** & **Rot x [deg]** \\ \hline
1 & \(-120^{\circ}\leq\theta_{1}\leq 120^{\circ}\) & 0 & 200/300/400 & 0 \\
2 & \(-145^{\circ}\leq\theta_{2}\leq 145^{\circ}\) & 0 & 265 & 0 \\
3 & 0 & \(0\leq d_{3}\leq 200\) & 0 & 180\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of Denavit and Hartenberg. Figure 2: The structure diagram of reconfigurable SCARA. pressure. In addition, when the thickness of the clamped part and equivalent contact area are increased, a larger contact area will be required and the weight of module will increase rapidly. Therefore, \(F_{0}\), \(A\) and \(c\) (the thickness of the clamped part) affect each other, in a complex nonlinear relationship. To reduce the complexity of the optimization model, key factors, including \(F_{0}\) (the pretension of bolt connector), \(c\) (the thickness of the clamped part) and the width \(t\), are taken as the optimization variable based on Equation (1). \(L\) (maximum deformation), \(M\) (weight) and \(f\) (first-order natural frequency) are taken as the optimization objectives. The two modules are connected by six M4 bolts. The strength grade of the bolt is 4.8, and the maximum pretension is \(F_{0}\) = 2634 N. The material of the module is aviation aluminum alloy 7075. The range of sample groups and the initial values are determined according to the mechanical design manual and the volume of robot, which are listed in Table 2.  
The Box-Behnken experimental method is used to arrange the sample groups at high level, and avoid the wrong nonlinear fitting results between the variables and the optimization objective. According to this method, the finite element models with different sample groups are established, the partial data of which are listed in Table 3.  
Considering that the multi-objective optimization model presents as highly nonlinear, a phenomenological model based on finite element analysis data is employed to approximate the complex optimization model. The phenomenological model depicting the bolt connector should be compact and accurate.