Recently, with the fast developments of metamaterials, uniformly tuning techniques for metamaterials and periodic structures over large scales attract lots of attentions. In this research, we proposed a linkage mechanism for mechanically tuning the frequency responses of planar periodic structures where all the unit cells are connected with links. By actuating the two driving links, each unit cell is tuned continuously and synchronously to obtain the desired frequency deviations without redesign and additional fabrications. A prototype was designed and fabricated with a size of 20 by 20 unit cells. It was demonstrated that each unit of the structure was controlled synchronously without individual biased circuit or actuator and achieved a frequency of 1 GHz (14.5% in terms of fractional bandwidth).