This paper mentions a detail calculation of the equivalent dynamic parameters in differential equations of motion of the electrothermal V-shaped actuator. A heat transfer model for a thin beam (including the dependence of material properties on the temperature) is applied in order to solve more exactly temperature distribution and displacement of V-shaped beam system. Comparing the values of displacement in both calculation and simulation confirmed a higher accuracy of proposed equations. Moreover, a related formula between the minimum conversion stiffness and driving voltage amplitude is analyzed and examined to avoid the buckling phenomenon may occur in V-shaped beam system while working at a high voltage.

Modeling and waveform optimization are important research topics for piezo-actuated stick–slip micro-drives. In this paper, the dynamics of piezo-actuated stick–slip micro-drives (PASSMDs) are theoretically investigated. We introduce an extended model taking the dynamics of the piezo actuators into account. The model combines the whole macroscopic movement of the drive’s runner and actuators and the microscopic behavior of the frictional contacts in a hybrid dynamic simulation. The macroscopic movements are described via Newtonian mechanics, while the microscopic behavior is computed using the method of dimensionality reduction. Two important characteristics of the drive, the critical actuation amplitude and the force generation, are systematically analyzed. The numerical simulation results show a fine agreement with experimental data of the previously published work. The critical actuation amplitude is found to depend on the behavior of the guiding contacts, the dynamics of the actuators and their interaction. Furthermore, a novel driving waveform, which allows us to increase the operational velocity for the drive, is proposed. The waveform is derived by exploiting micro-vibration and considering the dynamic contact status. Simulation results show that the average velocity of the drive is heightened by about $15\%$ . The performance of the drive is therefore improved.