Kinesins are microtubule-based motor proteins that power intracellular transport. Most kinesin motors, exemplified by Kinesin-1, move towards the microtubule plus end, and the structural changes that govern this directional preference have been described. By contrast, the nature and timing of the structural changes underlying the minus-end-directed motility of Kinesin-14 motors (such as Drosophila Ncd) are less well understood. Using cryo-electron microscopy, here we demonstrate that a coiled-coil mechanical element of microtubule-bound Ncd rotates approximately 70 degrees towards the minus end upon ATP binding. Extending or shortening this coiled coil increases or decreases velocity, respectively, without affecting ATPase activity. An unusual Ncd mutant that lacks directional preference shows unstable nucleotide-dependent conformations of its coiled coil, underscoring the role of this mechanical element in motility. These results show that the force-producing conformational change in Ncd occurs on ATP binding, as in other kinesins, but involves the swing of a lever-arm mechanical element similar to that described for myosins.