Question:
Show that when the curve $c_1=c_1(t)$ has constant torsion $\tau$, the curve $$c_2=c_2(t)=-\frac{1}{\tau}N+\int_{t_0}^{t}B(u)du$$ has constant curvature $-\tau$ or $+\tau$.
What I know:
$$\dot T=\kappa N$$ $$\dot{N}=-\kappa T +\tau B$$ $$\dot B=-\tau N$$
In fact, I posted what i did. But, I am not sure. There may be some mistakes.