Classical analogy between mechanical and electrical systems has a small inconsistency in terms of the mass element. This leads to the invention of the inerter which makes the synthesis of arbitrary passive mechanical network possible based on the established circuit theory. In this paper, we attempt to improve the energy efficiency of periodic motion with a passive mechanism including the inerter. In the research of power assist control of electric bicycle, it is shown that a better energy efficiency is achieved by reducing the velocity fluctuation arising from the human pedaling torque pulsation thorough experiments. The same idea is extended to fully passive control of normal bicycle having an additional mechanical network in the drive train. We verify the effectiveness of the proposed design by the multi-body dynamics simulations.