Spontaneous rotation in a driven mechanical system

We show that a mass free to circulate around a shaken pivot point exhibits resonance-like effects and large amplitude dynamics even though there is no natural frequency in the system, simply through driving under geometrical constraint. We find that synchronization between force and mass occurs over a wide range of forcing amplitudes and frequencies, even when the forcing axis is dynamically, and randomly, changed. Above a critical driving amplitude the mass will spontaneously rotate, with a fractal boundary dividing clockwise and anti-clockwise rotations. We show that this has significant implications for energy harvesting, with large output power over a wide frequency range. We examine also the effect of driving symmetry on the resultant dynamics, and show that if the shaking is circular the motion becomes constrained, whereas for anharmonic rectilinear shaking the dynamics may become chaotic, with the system mimicking that of the kicked rotor.