A prosthetic hand structure including at least one mechanical finger having a metacarpal support and a proximal stiff link connected to the metacarpal support by a proximal cylindrical joint. The mechanical finger includes a transmission member connected to the proximal stiff link. The transmission member includes a worm screw integral to the proximal stiff link. The transmission member includes a flexible rack having a first end portion, pivotally connected to the metacarpal support, and a second end portion arranged to engage with the threaded profile of the worm screw at an engagement zone of the flexible rack. The structure also includes an actuator mounted to the mechanical finger and to actuate the worm screw, causing it to rotate about its rotation axis, in such a way that, when the actuator moves the worm screw, the mechanical finger extends or flexes.