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.

Piezo-actuated stick-slip micro-drives (PASSMDs) are often used in microrobotic applications due to their advantages of a straightforward design and good operational characteristics. In this work, influences of fabrication tolerances on operational characteristics of PASSMDs are theoretically investigated. A dynamic model describing the whole macroscopic movement of the driver’s runner and the actuators, and the microscopic behavior of the frictional contacts using the method of dimensionality reduction, was used. Three essential parameters of the drives including the angle between working surfaces of the runner, the alignment angle between two actuator blocks on each side of the runner, and the stiffness of an individual actuator, whose values are impacted by the tolerance of the fabrication and assembly process, were considered as the input of the investigation. By performing hybrid-dynamic simulations, influences of these parameters on the drives' operational characteristics, including the repeatability of the step length, the critical amplitude phenomenon, and the maximal-achievable driving frequency/velocity, were evaluated. Simulation results show that these parameters significantly influence on the characteristics of the drives. The contribution of this work is so important that several important phenomena of PASSMDs, which are experimentally detected, are physically explained for the first time. The results of this work could help designers to optimize for better generations of PASSMDs.

This paper presents an enhanced pseudo-rigid body model (PRBM) integrated with the LuGre friction law to analyze the dynamic behavior of flexure-hinge-based piezoelectric stick–slip actuators (PSSAs). The PRBM captures flexure compliance through Lagrangian dynamics, while Newtonian mechanics describe the piezoelectric stack and slider motion. Non-linear contact effects, including stick–slip transitions, are modeled using the LuGre formulation. A mass–spring–damper model (MSDM) is also implemented as a baseline for comparison. The models are solved in MATLAB Simulink version R2021a and validated against experimental data from a published prototype. The enhanced PRBM achieves strong agreement with experiments, with a root mean square error of 20.19%, compared to 51.65% for the MSDM. By reformulating the equations into closed-form expressions, it removes symbolic evaluations required in the standard PRBM, resulting in one to two orders of magnitude faster simulation time while preserving accuracy. Stable transient simulations are achieved at fine time steps ($\Delta t={10}^{-8}$ s). A systematic parametric study highlights preload force, flexure stiffness, friction coefficients, and tangential stiffness as dominant factors in extending the linear frequency–velocity regime. Overall, the PRBM–LuGre framework bridges the gap between computationally intensive finite element analysis and oversimplified lumped models, providing an accurate and efficient tool for design-oriented optimization of compliant piezoelectric actuators.