A transmission includes a first shaft with two gears adapted for connecting to a motor and a second shaft with two corresponding gears adapted for connecting to a driveshaft; a shift drum selectively controlling torque transfer between the shafts and defining therein two grooves; a shift rod translatable along a rod axis with a driving member fixedly connected thereto and engaging one groove, at least a portion of the groove causing the driving member and the shift rod to translate along the rod axis upon rotation of the shift drum; an engagement dog disposed on the second shaft for selectively engaging the gears of the second shaft; two biasing members disposed around the shift rod; a fork rod supporting a shift fork slidably connected to the fork rod and the shift rod, the shift fork being engaged in another groove of the shift drum.