The phenomena of self-centering accompany any contact of two bodies. For bodies with a small mass and low dynamic indicators, this phenomenon can be neglected. At high values of the dynamic indicators of the mechanical system and especially under periodic loading, the phenomenon of self-centering cannot be neglected, since its consequences accumulate. In modern society, when there is more and more talk about the space industry, the consideration of the contact between two bodies acquires particular importance. The material will shed a cursory light, without claiming to be exhaustive, on the phenomenon of self-centering in the contact of two bodies in the general case of this physical phenomenon. Two mathematical methods for sizing a contact mechanism will be described, taking into account the load on the bodies during contact.