A connector includes an insert including contacts having free parts to receive homologous flat contacts of a plug. The insert further includes a rotation axis about which the insert can be rotated and spring means urging the insert toward the position that it assumes when no plug is present. The insert can include, at the sides, long curved contacts and, in a central portion, shorter curved contacts, the points of contact of the contacts of the insert with the flat contacts of a plug being substantially aligned over all the contacts.