We investigate the effect of quantisation of vibrational modes on a system in which the transport path is through a quantum dot mounted on a cantilever or spring such that tunnelling to and from the dot is modulated by the oscillation. We consider here the implications of quantum aspects of the motion. Peaks in the current–voltage characteristic are observed which correspond to avoided level crossings in the eigenvalue spectrum. Transport occurs through processes in which phonons are created. This provides a path for dissipation of energy as well as a mechanism for driving the oscillator, thus making it easier for electrons to tunnel onto and off the dot and be ferried across the device.