Isotropic springs based on parallel flexure stages

We define isotropic springs to be central springs having the same restoring force in all directions. In previous work, we showed that isotropic springs can be advantageously applied to horological time bases since they can be used to eliminate the escapement mechanism [7]. This paper presents our designs based on planar serial 2-DOF linear isotropic springs. We propose two architectures, both based on parallel leaf springs, then evaluate their isotropy defect using firstly an analytic model, secondly finite element analysis and thirdly experimental data measured from physical prototypes. Using these results, we analyze the isotropy defect in terms of displacement, radial distance, angular separation, stiffness and linearity. Based on this analysis, we propose improved architectures stacking in parallel or in series duplicate copies of the original mechanisms rotated at specific angles to cancel isotropy defect. We show that using the mechanisms in pairs reduces isotropy defect by one to two orders of magnitude.