The mechanism of rectified Brownian movement is used to analyze measured data for kinesin motion along microtubules. A key component of the mechanism is the diffusive movement of the microtubule binding heads of kinesin during the adenosine triphosphate (ATP) cycle. The first-passage time distribution for this step is analyzed in detail and is shown to be responsible for observed load-velocity profiles. The ATPase activity of the kinesin heads is that of a nucleotide switch and not that of a direct chemomechanical energy converter. Experimental data acquisition, rate constants, and alternative explanations are discussed. The mechanism described in this paper is fundamental to the nanobiology of intracellular processes.