Conceptual design of a rotational mechanical time base with varying inertia

Flexure pivot oscillators have the potential to advantageously replace the traditional balance wheel-spiral spring oscillator used in mechanical watches due to their significantly lower friction. However, they have inherent nonlinear elastic properties that can introduce a variation of their frequency with amplitude called isochronism defect. Previous research has focused on controlling the elastic behavior of flexure pivot oscillators to reach isochronism. We present a new way of minimizing the isochronism defect of rotational oscillators by varying their inertia. This principle is embodied in a new family of oscillators we call rotation-dilation coupled oscillator (RDCO). Their architecture also presents a rotational symmetry that is advantageous for minimizing the effects of gravity on their period. We present a description of this new oscillator family, give conceptual tools for tuning its isochronism and show examples of physical implementations.