Periodic chains of molecular gears in which molecules couple with each other and rotate on surfaces have been previously explored by us theoretically using ab initio simulation tools. On the basis of the knowledge and experience gained about the interactions between neighboring molecular gears, we here explore the transmission of rotational motion and energy over larger distances, namely, through a longer chain of gear-like passive "slave" molecules. Such microscopic gears exhibit quite different behaviors compared to rigid cogwheels in the macroscopic world due to their structural flexibility affecting intermolecular interaction. Here, we investigate the capabilities of such gear chains and reveal the mechanisms of the transmission process in terms of both quantum-level density functional theory (DFT) and simple classical mechanics. We find that the transmission of rotation along gear chains depends strongly on the gear-gear distance: short distances can cause tilting of gears and even irregular "creep-then-jump" (or "stick-slip") motion or expulsion of gears; long gear-gear distances cause weak coupling between gears, slipping and skipping. More importantly, for transmission of rotation at intermediate gear-gear distances, our modeling clearly exhibits the relative roles of several important factors: flexibility of gear arms, axles, and supports, as well as resulting rotational delays, slippages, and thermal and other effects. These studies therefore allow better informed design of future molecular machine components involving motors, gears, axles, etc.