Spontaneous spinning of a rattleback placed on vibrating platform

Abstract

The spontaneous spinning of a rattleback placed on a vibrating platform is investigated. The rattleback is a toy with some curious properties. When placed on a surface with reasonable friction, the rattleback has a preferred direction of spin. If rotated anti to it, longitudinal vibrations are set up and spin direction is reversed. In this paper, the dynamics of a rattleback placed on a sinusoidally vibrating platform are simulated. We can expect base vibrations to excite the pitch motion of the rattleback, which, because of the coupling between pitch and spin motion, should cause the rattleback to spin. Results are presented which show that this indeed is the case- the rattleback has a mono-peak spin resonance with respect to base vibrations. The rattleback, thus, transduces translating vibrations into continuous rotary motion and, therefore, is ideal for applications in Energy harvesting and Vibration sensing. The dynamic response of the rattleback was found to be composed of two principal frequencies that appeared in the pitch and rolling motions. One of the frequencies was found to have a large coupling with the spin of the rattleback. Spin resonance was found to occur when the base oscillatory frequency was twice the value of the coupled frequency. A linearized model is developed which can predict the values of the two frequencies accurately and analytical expressions for the same in terms of the parameters of the rattleback have been derived. The analysis, thus, forms an effective and easy method for obtaining the spin resonant frequency of a given rattleback. Novel ideas for applications utilizing the phenomenon of spin resonance, for example, an energy harvester composed of a magnetized rattleback surrounded by ferromagnetic walls and a small scale vibration sensor comprising an array of several magnetized rattlebacks, are included.