Abstract: A gear shift device for a mobility machine has a plurality of gears between a first gear referred to as gear No. 1 and a top gear. The gear shift device includes a series of input pinions arranged so as to turn freely around a selection shaft with an axis X2, said selection shaft accommodating a worm screw and a shuttle. The gear shift device also includes a series of output pinions with an axis X3 that rotate conjointly with a hollow shaft a gear shift actuator arranged so as to displace the shuttle along the worm screw between a plurality of positions and to engage a selected gear. A mobility machine can include the gear shift device.