We present a new concept for impact-based triboelectric nanogenerators (TENG) inspired from the electrostatic machines of the 18th century. With this system, the electrical energy converted from the mechanical domain is automatically accumulated in a large capacitance without the need of diodes. Our TENG has three electrodes and self-synchronized/self-actuated mechanical switches, which automatically and repeatedly connect the capacitances of the system according to their series and parallel configurations in order to reproduce a behaviour similar to the Bennet's charge doubler. The movable and freestanding electrode is covered with triboelectric patches that drastically decreases the start-up time. The output voltage, and so the harvested energy, increases exponentially until either the output voltage reaches the air dielectric breakdown or a saturation occurs because the electrostatic forces become comparable to the mechanical ones. We have developed a complete numerical model that takes into account both electrical and mechanical forces and is able to show the saturation phenomena due to the high electromechanical coupling occurring at high voltage. This model has been validated with practical experiments where the prototype were excited with a sinusoidal acceleration of 0.2 grms at 5 Hz. This new and diode-free concept can be applied to any TENG having at least one variable capacitor to boost the mechanical-to-electrical energy conversion.