Owing to their wide spectrum of in vivo functions, motor proteins, such as kinesin-1, show great potential for application as nanomachines in engineered environments. When attached to a substrate surface, these motors are envisioned to shuttle cargo that is bound to reconstituted microtubules - one component of the cell cytoskeleton - from one location to another. One potentially serious problem for such applications is, however, the rotation of the microtubules around their longitudinal axis. Here we explore this issue by labelling the gliding microtubules with quantum dots to simultaneously follow their sinusoidal side-to-side and up-and-down motion in three dimensions with nanometre accuracy. Microtubule rotation, which originates from the kinesin moving along the individual protofilaments of the microtubule, was not impeded by the quantum dots. However, pick-up of large cargo inhibited the rotation but did not affect the velocity of microtubule gliding. Our data show that kinesin-driven microtubules make flexible, responsive and effective molecular shuttles for nanotransport applications.