ATPases are a group of enzymes that can cyclically convert the free energy of ATP hydrolysis into mechanical work. GTPases are another class of enzymes that are predominantly associated with signal transduction processes, but their role in mechanotransduction is less established. It was previously shown that the binding of the GTPase Rab5 to the tethering protein EEA1 induces a large conformational change in EEA1 from a rigid, extended to a flexible, collapsed state. This entropic collapse of EEA1 gives rise to an effective force that can pull tethered membranes closer. It currently remains unclear if EEA1 can return from the collapsed to the extended conformation without the aid of chaperone proteins. Here we show that EEA1 in a bulk solution can undergo multiple flexibility transition cycles driven by the energetics of Rab5 binding and unbinding as well as GTP hydrolysis. Each cycle can perform up to 20k _B T of mechanical work. Hence, Rab5 and EEA1 constitute a two-component molecular motor driven by the chemical energy derived from the Rab5 GTPase cycle. We conclude that tethering proteins and their small GTPase partners can have active mechanical roles in membrane trafficking.