Vibration energy harvesting technology can capture ambient energy forms. Using an energy harvesting shock absorber (EHSA) is one of the methods to achieve this function. The EHSA with mechanical motion rectifier (MMR) has motion bifurcation, which can improve energy harvesting performance and reduce the impact between gears. However, the motion bifurcation makes it difficult to quantitatively predict the vibrational energy dissipation and energy harvesting of the MMR−EHSA. Evaluating the performance of an MMR−EHSA during the design phase becomes highly complex. In this paper, a novel nonlinear dynamics model of MMR−EHSAs is established to solve motion bifurcation and quantitative power flow. Furthermore, the proposed MMR−EHSA prototype is fabricated, and dynamics testing is initiated to verify the theoretical model under harmonic vibration. The testing results show that the theoretical model can predict the working characterization of MMR−EHSAs. The resistance of optimal harvesting energy and maximum damping power is revealed by the quantitative power flow model under harmonic vibration. In addition, the working performance under random vibration is discussed. The proposed nonlinear dynamics model has advantages when solving random vibration input and has potential for practical application.