Abstract: The backlash-free reducing mechanism, includes a fixed flange insidely provided with a toothed ring with which meshes a first toothing of a double planet wheel, a mobile flange having an inner toothed ring intended for cooperating with a second toothing of the double planet wheels. The mobile flange is maintained free in rotation in the fixed flange by a circular member. The double planet wheels are maintained in the reducing mechanism by a central planet wheel holding piece having resilient means and are centered on a side of the toothed ring of one of the flanges by a resilient floating idle pinion.