## 2 Background and Driving Principles  
### Structure of Typical PAMTs  
Figure 1 provides a schematic diagram of a typical PAMT structure. The main components of PAMTs include the tool platform, planar flexible hinges, hinge fixation devices, piezoelectric actuator, piezoelectric actuator fixation devices, preload screws, and preload \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Nonlinear Factors** & **Solution** & **Advantage** & **Limitation** \\ \hline \multirow{4}{*}{Hysteresis} & Improved Preisach hysteresis model [16] & & \begin{tabular}{c} Only consider the nonlinear \\ effect of hysteresis on \\ features and dead zone issues \\ in hysteresis characteristics. \\ \end{tabular} & \begin{tabular}{c} Only consider the nonlinear \\ effect of hysteresis on \\ piezoelectric actuators, \\ without taking into account \\ creep characteristics \\ \end{tabular} \\ \hline \multirow{4}{*}{C creep} & Logarithmic creep models [19] & & \begin{tabular}{c} The models are simple and \\ easy to implement, suitable \\ for open-loop control. \\ \end{tabular} & \begin{tabular}{c} Poor dynamic adaptability; \\ reliance on \\ empirical parameters \\ \end{tabular} \\  & \begin{tabular}{c} A feedforward controller \\ based on the LTI creep model \\ and hysteresis operator [22] \\ \end{tabular} & \
\begin{tabular}{c} They provide a more \\ comprehensive description of \\ nonlinearity (such as operator \\ superposition, adaptive \\ combination). \\ \end{tabular} &
\begin{tabular}{c} Complex calculations and \\ insufficient real-time \\ performance; most of them \\ did not consider strong \\ coupling effects \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of existing methods. nuts. Among these, dual parallel flexible hinges are used to achieve high-precision motion transmission. The flexible hinges enable elastic deformation motion within the nanometer range while eliminating friction, ensuring efficient transmission of force and motion. Before machining, the required preload force can be applied to the piezoelectric actuator using the preload screws to optimize their performance. The vibration isolation platform is used to isolate external vibrations from affecting the tool holder, stabilizing the tool holder and ensuring machining accuracy. Since tensile and shear forces significantly impact the performance and lifespan of a piezoelectric actuator, the piezoelectric actuator cannot directly drive the cutting tool. Therefore, a guiding mechanism is designed to protect the piezoelectric actuator. The guiding mechanism must accurately transmit the displacement of the piezoelectric actuator to the tool under high-frequency motion while ensuring stability and precision. This structural design, through the combination of flexible hinges and guiding mechanisms, achieves efficient motion transmission between the piezoelectric actuator and the cutting tool while preventing damage to the piezoelectric actuator due to direct force application. This enhances the system's reliability and machining accuracy. The PAMT requires a micro-positioning stage with high precision, large stroke, and high stiffness. It typically employs a coarse and fine two-stage feed system, where constant-velocity motion ensures the best machining quality. Generally, a micro-positioning stage with a stroke range of 0 to 40 nm can meet the requirements of fine feed. The designed stage must have high stiffness to counteract machine tool vibrations and cutting forces during the machining process, ensuring machining accuracy and stability. The specific technical parameters of PAMTs are listed in Table 2.