We study transport properties of the helical edge states of 2D integer and fractional topological insulators (TI/ FTI), via one and two constrictions (quantum point contacts). Such constrictions can be made by adding a gate to the systems where the coupling between edge states on either side of 2D sample is electronically tuned by this gate. We focus on two gate regimes where the interacting electrons or quasiparticles are perfectly transmitted (weak backscattering limit) and perfectly reflected (weak tunneling limit) from the constrictions.  Moreover, we explore even richer physics that occurs when double impurity is on resonance which gives rise to total transmission in the weak backscattering limit and Kondo physics in the weak link regime in Luttinger liquid. Using renormalization group and duality mapping, we analyze phase diagrams for the following cases: (i)  single constriction in TI which was reported by Teo and Kane in PRB 79, 235321, (ii) single constriction in FTI, (iii) double constriction in TI, and (iv) double constriction in FTI. We find different behaviors depending on interaction strength and particularly a regime where conductance is non-monotonic as a function of temperature in the experimentally accessible parameter regime.