dear all, are the following two curves

$\displaystyle r(t)=(t+\sqrt{3}t,2\cos t,\sqrt{3}t-\sin t)$

and

$\displaystyle \tilde r(t)=(2\cos\frac{t}{2},2\sin\frac{t}{2},-t)$

being equivalent?

Here, equivalence means that the two curves coincide after a rigid motion.

I find the second curve has curvature $\displaystyle 1/4$, and torsion $\displaystyle -1/4$. However, it is difficult to solve the first one, and seems the result is not the same as the second one.

3x.