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I just started taking Differential Geometry and I'm stuck on this question: "Mark off the line segments of fixed length on the binormals to a simple helix. Find the equation of a curve that is traced by the endpoints of these line segments."

I know how to find a binormal vector (i.e. $\beta= \frac{r' \times r''}{|r' \times r''|}$) but I basically have no clue how to do that with this question.

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    Hint: If the fixed lenght is $k$, then the final point can be $r(t)+\beta(t)k$, for each parameter $t$. – 2017-02-21

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