  A twisted curve in Euclidean 3-space E^3 can be considered as a curve whose
position vector can be written as linear combination of its Frenet vectors. In
the present study we study the twisted curves of constant ratio in E^3 and
characterize such curves in terms of their curvature functions. Further, we
obtain some results of T-constant and N-constant type twisted curves in E^3.
Finally, we give some examples of equiangular spirals which are constant ratio
curves.
