Upper bound for the power outputs of linear vibrational power harvesters: translational vs. rotational geometries

Inertial harvesters utilize the motion of a translating or rotating mass to scavenge power from ambient vibrations. For translational harvesters, analytical expressions describing the influence of size on the output power of these harvesters have been derived previously by modeling vibrations as sinusoids or white noise. In this paper, we present a general method to estimate the size-dependent power outputs of both translational and rotational harvesters for vibrations with an arbitrary power spectral density. Using the heights and widths of the peaks in the vibrational power spectral density, we derive simple analytical expressions for the maximum power output of harvesters and the minimum harvester size required to achieve it. To illustrate an application of these estimates, we analyze the case of walking-induced vibrations produced at the hip-pocket and upper-arm locations. We find that rotational designs can outperform translational ones only when the harvester is larger than 26 cm and 8 cm for the hip-pocket and arm locations, respectively.