Cycloidal reducer with backlash self-adjustment and power steering system with such a reducer

A cycloidal gear reducer comprising an input shaft, mounted in rotation in a reducer casing according to an axis called main axis, an eccentric member carried by the input shaft and driven in rotation by the latter, at least one cycloidal disk which is mounted in rotation on the eccentric member and which is provided with a cycloidal toothing, at least one rim provided with a receiving toothing on which the cycloidal toothing of the cycloidal disk meshes, and an output shaft, distinct from the input shaft, which is arranged so as to be driven in rotation by the cycloidal disk, the reducer being wherein it comprises a suspension device which is arranged to elastically bias the cycloidal toothing of the cycloidal disk and the receiving toothing of the rim against each other, so as to provide an automatic adjustment of the backlash between the cycloidal disk and the rim according to at least one component radial to the main axis.