Shaking force balancing of a 2-DOF isotropic horological oscillator

Despite centuries of research and significant advances, the escapement mechanism used to count maintain oscillations mechanical time bases remains a complex major source energy losses. We showed in previous work that, instead widely rotational one degree-of-freedom (DOF) oscillators, 2-DOF flexure oscillators have potential revolutionizing watchmaking by eliminating traditional escapement, replacing it simple crank driving pin. Additionally, using flexures increases quality factor base, leading further improvements timekeeping accuracy consumption. However, challenge these new is their balancing such that influence external accelerations on frequency minimized, necessary condition for accurate portable applications. This article presents novel planar oscillator called Wattwins demonstrates how can be made insensitive linear as gravity. For this purpose, approach shaking force developed based decomposition perturbations into effects corresponding different orders center mass displacement. A full analytical model tuning derived pseudo-rigid-body assuming decomposed two independent 1-DOF oscillators. The results are validated finite element method show practical watch specifications theoretically reached. physical prototype was also constructed preliminary experimental confirm theory well simulations.