## 3 Results  
Experimentally, large output amplitudes are achieved at several input frequencies ranging from 1 Hz to 200 Hz, though the details of the response show significant discrepancies with the simple model described in Section 2. Amplitudes of the largest frequency components of output motion after FFT analysis of individual time series are shown in Figure 8, along with the comparable frequency response of the PZT bender alone. Three input frequencies, near 17 Hz, 113 Hz, and 190 Hz, achieve the largest output amplitudes. As predicted by the model, corresponding output oscillations occur at much lower frequencies (10 Hz-20 Hz), and increase with higher input frequencies. Time-series plots for mechanism output at those frequencies are shown in Figure 9. The output oscillations are  
Figure 6: Solid model of compliant mechanism (frame), active PZT actuator, and passive, rigid beam for experimental prototyping. Figure 7: Photograph of the prototype impact-based amplification mechanism. The left is the active PZT actuator and the right is the rigid output beam on the compliant amplification structure. built up over widely varying numbers of impact cycles before reaching quasi-steady-state behavior, but can reach amplitudes of up to 1.2 mm, versus approximately 1 mm-2.2 mm amplitudes in simulation. In some cases, nearly sinusoidal motion is achieved. For example, in Figure 10, a sample FFT for tip displacement is shown for 194 Hz input, showing a low-frequency output of 17 Hz as the dominant oscillation component, while only a tiny secondary peak is witnessed at the input frequency. The differences between the simple simulation model and experimentally-observed behavior highlight limitations of the conceptual dynamics. First, dominant experimental output frequencies are higher than those predicted by simulation, though this may be attributed to uncertainty in material properties and layer thicknesses for the 3D-printed components. More interestingly, in experiments, fewer sub-resonant input frequencies produce large amplitudes than in simulation, while showing more uniform output oscillations than anticipated. Together, these observations suggest that there remain un-modeled dynamics that further influence stability (or lack thereof) of periodic limit-cycle behavior from the combined system. Finally, where the simulation predicts the largest output amplification at the PZT bender's resonant frequency, experimentally, the nearby output resonance occurs at a reduced frequency (189 vs. 250 Hz) and with reduced amplitude. We hypothesize that additional interfacial forces may be present that lead to brief periods of adhesion between structures, increasing effective inertia of the bender, though this has not been verified. Figure 8: Comparison between amplification mechanism and piezoelectric actuator alone for amplitude of dominant oscillations versus driving frequency. Figure 9: Displacement of the tip of the amplification mechanism when driven near prominent peaks in frequency response (from left: 17 Hz, 113 Hz, 186 Hz). Single-sided amplitudes at notable resonances are summarized in Table 2. Output amplitudes are up to 110 times the amplitude of the bender alone at low frequencies. Comparing across frequencies, maximum mechanism output is approximately 3.5 times larger than the the largest amplitude for the bender alone. In addition to large oscillation amplitudes, the repeated impacts can drive mean tip displacements significantly away from its neutral position, sometimes with little accompanying oscillation. This primarily occurs with higher frequency excitations (300-600 Hz), producing repeated impact events that cause the output beam to rotate to a height above its neutral position. The mean tip displacement is shown as a function of input frequency in Figure 11, and includes regions where tip displacements of 0.1 to 0.25 mm are achieved (versus PZT tip displacement alone of <0.01 mm) while oscillation amplitudes are small (<0.01 mm as observed in Figure 8), for a quasi-static, non-zero output displacement.