## 4 Discussion
### System Integration  
To use compliant amplification of a piezoelectric transducer in a small, mobile robot, one goal would be to couple transducer vibration into oscillations of a compliant appendage structure that produces a useful gait or function, such as terrestrial or aquatic locomotion. Inspired by results from submersion of the basic mechanism, a simple bio-inspired aquatic robot was constructed as a proof-of-concept for integrating the impact-based mechanism into a small robot. It is important to note that no design or analysis for effective fluid dynamics behavior has been attempted at this time. Rather, the current experiment is intended to provide only basic insights into amplification mechanism integration into more complex systems.  
The actuation mechanism was mounted in an elliptical frame carved by hand from balsa wood, with a fin-like acrylic structure attached to the output beam shown in Figure 15. As in earlier experiments, significant displacement amplification is observed, along with frequency down-conversion. Figure 16 shows motion of the assembled system in air. After assembly, natural frequency of the bender alone was found to decrease to 165 Hz, likely due to compliance in the bender mounting to the wooden frame. Under square-wave amplification, a maximum angular displacement of the fin was approximately 5 degrees, with highest amplitude for a 19 Hz square-wave input and 10 Hz dominant output frequency. Notably, the inertial coupling between structures was sufficient to oscillate the entire body relative to the fin when resting on a smooth surface.  
Figure 16: Oscillation in air of a fish-inspired geometry with tail fin driven by impact-based amplification mechanism. Red and green lines indicate angle of body and fin midlines, with approximately 5 degree body rotation and 5 degree fin rotation relative to the body.  
Figure 14: Amplification mechanism with output passive beam immersed in water.  
Figure 15: (a) Schematic illustration of fish robot, showing impact amplification structure relative to manually carved balsa wood frame; (b) enclosing elements for operation in water, with polyethylene wrap and modeling clay ballast; (c) overhead images captured near maximum oscillation when partially-immersed in water, with approximately 1.5 degree bend angle.  
The fish-inspired geometry was then enclosed by adhering a polyethylene film around the wooden frame, with epoxy applied to complete waterproof sealing where the output beam and fin extend through the film. Unfortunately, in the current assembly, this procedure was found to substantially impede motion, due to excessive epoxy needed to prevent the film from separating during operation. Nonetheless, after attaching additional mass sufficient to achieve approximately 50% submersion of the frame and fin and increasing driving amplitude to 100 V, maximum oscillation amplitudes of 1-2 mm remained achievable. In the half-submerged position, output fin frequency was estimated at 5 Hz from video capture data, with resonances observed under input frequencies of 5 Hz, 13 Hz, 19 Hz, and 65 Hz. Substantial further development is required to translate the proposed mechanism into effective locomotion, but these preliminary experiments suggest that there is some possibility for coupling piezoelectric bender vibration into variable fin oscillation frequencies even with substantial inertial and viscous loads.