Motion Planning of a Stepping-Wriggle Type Piezoelectric Actuator Operating in Bending Modes

A new non-resonant-type piezoelectric actuator with unlimited stroke was proposed, in which two transducers operated in hybrid bending modes were used to generate the desired displacements with micrometer scale. Compared with the PZT stack, both positive and negative dc voltages can be applied on the PZT elements to achieve large displacement. The vertical bending movement was used to control the contact state between the foot and the runner, whereas the runner was pushed by the horizontal bending movement. The operating principle of the stepping-wriggle driving was discussed. The motion planning of the bending transducers with eight steps was developed. The duty ratios and the phase difference of the two signals applied on the vertical PZT elements were 1/3 and 180°, respectively, which insured the reliable positioning of the runner. Excitation voltages with different rise times were applied on the PZT elements to discover its effects on the responses of the bending movements by a transient analysis. It was found that the transducer cost about 2 ms to reach the steady state, in spite of the difference of the rise times, but the rise time showed a significant effect on the oscillation amplitude of the bending motion. The motion trajectories of the driving tip were nearly rectangles with horizontal and vertical steady displacements of $\sim 6.10$ and 5.52 $\mu \text{m}$ , respectively. This paper can provide the guidance for the design of non-resonant-type piezoelectric actuator by bending modes.