# Kinematics Model Optimization Algorithm for Six Degrees of Freedom Parallel Platform
## 2 Materials and Methods
### Dataset  
Table 1 shows the coordinate parameters of the connection points of each parallel manipulator arm, the moving platform, and the static platform at the initial position.  
To reduce the impact of operating system multitask scheduling and task-switching time on the algorithm calculation time-consuming evaluation, this experiment used a large sample batch calculation method to evaluate the algorithm time-consuming evaluation. Each independent sample consists of two parts, input and output. The output is the six-degree-of-freedom attitude of the parallel platform workspace, which is randomly selected on a specific closed subinterval, using the Monte Carlo method. We then performed kinematic inverse solution on the output attitude data. The lengths of six groups of parallel manipulators were obtained as the input information of this sample. When the algorithm was executed, the length information of the mechanical arm of each sample was input, and the kinematics forward solution algorithm was executed. Moreover, we compared the output information obtained by the algorithm with the output information of the sample to find the absolute error \(|e(\mathbf{X_{tar}}-\mathbf{X_{k}})|\).  
Before the execution of the MPR (Multivariate Polynomial Regression) algorithm, all polynomial coefficients need to be solved offline. Therefore, the selected sample set needs to be composed of two parts: the training sample set and the test sample set. Among  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Coordinate Points** & \(\mathbf{p_{x}}\) **(mm)** & \(\mathbf{p_{y}}\) **(mm)** & \(\mathbf{p_{z}}\) **(mm)** \\ \hline A1 & \(-25\) & \(184\) & \(52.5\) \\ A2 & \(25\) & \(184\) & \(52.5\) \\ A3 & \(171.85\) & \(-70.35\) & \(52.5\) \\ A4 & \(146.85\) & \(-113.65\) & \(52.5\) \\ A5 & \(-146.85\) & \(-113.65\) & \(52.5\) \\ A6 & \(-171.85\) & \(-70.35\) & \(52.5\) \\ B1 & \(-84.01\) & \(74.49\) & \(325.4\) \\ B2 & \(84.01\) & \(74.49\) & \(325.4\) \\ B3 & \(106.51\) & \(35.51\) & \(325.4\) \\ B4 & \(22.50\) & \(-110\) & \(325.4\) \\ B5 & \(-22.50\) & \(-110\) & \(325.4\) \\ B6 & \(-106.51\) & \(35.51\) & \(325.4\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical motor parameters.  
Figure 2: Top view of the parallel platform in zero state.  
them, the training sample set needs to contain at least 1554 linearly independent sample points. Use the Monte Carlo method to randomly select 100,000 sample points of attitudes in the closed subspace \([x\pm 10\text{ mm},\ y\pm 10\text{ mm},\ z\pm 10\text{ mm},\ \alpha\pm 10^{\circ},\ \beta\pm 10^{\circ},\ \gamma\pm 10^{\circ}]\) of the workspace. Moreover, through the inverse kinematics solution, the length of the manipulator corresponding to each sample point is obtained as the first training sample set (Test Set 1). In the same sample space, 10,000 sample points are selected as the first test sample set. In order to verify that the Newton iterative algorithm and the MPR algorithm have global convergence, using the same method, in the closed subspace \([x\pm 40\text{ mm},y\pm 40\text{ mm},z\pm 40\text{ mm},\ \alpha\pm 40^{\circ},\ \beta\pm 40^{\circ},\ \gamma\pm 40^{\circ}]\) of the workspace, randomly select 100,000 sample points to form the second training sample set (Test Set 2). Then, in the same sample space, select 10,000 sample points to form the second test sample set.