Principle curvature from torsion over curvature ratio?

Question

If we have a curve $\gamma$ that is paramterized over its arc length, lets say for example $\gamma ~[a,b] \rightarrow \mathbb{R}^{3}$, can we obtain the principle curvature of its tangent surface from the ratio between the torsion the curvature? like for e.g. $$k_{1}(s,v) = \frac{\tau(s)}{k(s)|v|} $$ assuming $v$ is not $0$, and assiming $k_{2}=0$