A periodical driving system includes a circular wheel having a plurality of radial recesses defined in an outer periphery of the wheel and each recess is defined by two inner sides and each inner side includes an inward curved section so as to form a convergent opening in the outer periphery of the wheel. A driving disk has two driving pins extending therefrom and each driving pin has a cylindrical base portion extending from the disk and a protrusion extends axially from a distal end of each base portion. The driving pins enter into the recesses via the openings so as to push the inner sides of each recess. The two protrusions are in contact with the two curved sections of the two recesses when the wheel is in stationary status.