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We show that two-terminal transport can measure the Luttinger liquid (LL)parameter $K$, in helical LLs at the edges of two dimensional topologicalinsulators (TIs) with Rashba spin-orbit coupling. We consider a Coulomb draggeometry with two coplanar TIs and short-ranged spin-flip inter-edgescattering. Current injected into one edge loop induces circulation in thesecond, which floats without leads. In the low-temperature ($T \rightarrow 0$)perfect drag regime, the conductance is $(e^2/h)(2 K + 1)/(K + 1)$. At higher$T$ we predict a conductivity $\sim T^{-4K+3}$. The conductivity for a singleedge is also computed.

Helical Quantum Edge Gears in 2D Topological Insulators