Mechanical watch with isochronic position insensitive rotary resonator

A resonator mechanism for a timepiece movement having an input wheel train mounted to pivot around an axis of rotation and subjected to a driving torque, and having a central wheel train fixed in rotation to said input wheel train around said axis of rotation and arranged to turn continuously, wherein said resonator mechanism has a plurality of N inertial elements, each being movable in relation to said central wheel train, and restored to said axis of rotation by elastic restoring means belonging to said resonator mechanism, which are arranged to cause a restoring effort on the centre of mass of said inertial element, wherein said resonator mechanism has a rotational symmetry of order N, wherein said resonator mechanism has kinematic linkage means between all said inertial elements that are arranged to maintain at any time the centres of mass of said inertial elements at the same distance from said axis of rotation, and also wherein said elastic restoring means, which are rotational and borne by said resonator mechanism, cause an elastic potential wherein by the following equation:

• V=½·(dα0/dt)2·Σ(MjRj2)
• where:
• V is the elastic potential
• Σj is the sum of the quantity between parentheses
• (dα0/dt) is the speed of rotation to be imposed
• Rj is the distance of the axis of rotation from the centre of mass G of said inertial element
• Mj is the mass of said inertial element.