Abstract: Two Kirchhoff plates are considered that are joined by means of two rows of rivets posed with the small period h and modeled by Sobolev point transmission conditions. A new and unexpected effect is observed, namely the almost complete clutch of the plates occurs even for an exponentially small (with respect to h) distance between the rows in the mirror symmetry case. The same effect appears in the case of rivets in chessboard order only for the power-law smallness of the distance. These results are obtained with the help of analysis of boundary layer phenomena. Conditions are found to provide the hinge joint of the plates with friction at the limit.