In N H Kuiper's paper "A New Knot Invariant" he says that any circular r-braid knot can be given by for $\epsilon>0$ $$\gamma_{\epsilon}:(cos(rt)(1+\epsilon \lambda_1(t)),sin(rt)(1+\epsilon \lambda_1(t)),cos^2(rt)+\epsilon \lambda_2(t)) $$ where the function is periodic in t modulo 2$\pi$ and $\lambda_1^2+\lambda_2^2\leq 1$.
How to prove the existence of such an equation? Thanks in advance.