A study on the precision of mechanical watch movement with Tourbillon

Despite its long history, detailed studies on the dynamics of mechanical watch movement are still lacking. In this paper, extending our previous mechanics model, the dynamical wave motion of the hairspring—balance wheel assembly, the core of the timekeeping mechanism called the escapement, is analyzed by partial differential equations. It is found that the corresponding eigenfunctions may be formulated into a Fourier series, through which the …