Abstract: An actuation and traction system for a pedal-actuated electric vehicle like electric bicycle, electric tricycle, or electric quadricycle comprises an electric motor, a transmission comprising an epicyclic device and a variable speed drive actuated independently of the pedals wherein the variable speed drive comprises an actuator that discretizes the ratio, and two expandable pulleys wherein the transmission of the motion occurs through a cascade of gears adapted to obtain the desired transformation ratio between the electric motor that rotates at high speed, and the pinion that actuates the chain for transmitting motion to the wheel of the electric vehicle.