We study the inextensible flows of curves in 3-dimensional Euclidean spaceR3. The main purpose of this paper is constructing and plotting the surfaces that are generated from the motion of inextensible curves inR3. Also, we study some geometric properties of those surfaces. We give some examples about the inextensible flows of curves inR3and we determine the curves from their intrinsic equations (curvature and torsion). Finally, we determine and plot the surfaces that are generated by the motion of those curves by using Mathematica 7.

In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrix using quasi frame along a space curve.

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