An overspeed emergency brake system includes an overspeed detector magnet generating a brake actuation force and a kinematic constraint element guiding the movement of the magnet. The magnet and a kinematic constraint element in the brake system are arranged such that a linear brake actuation force is generated at a normal operating speed condition (i.e in a first position of the magnet with respect to the kinematic constraint element), due to the movement of the kinematic constraint element when guiding the magnet along a reaction surface and the kinematic constraint element converts the linear speed-force relationship into a nonlinear speed-force relationship in an overspeed condition (i.e a second position), while the magnet translates with respect to the kinematic constraint element generating a sharply increasing force for triggering the overspeed emergency brake.