In two dimensional systems, the non-self crossing condition leads to an excluded volume effect, and the obtained critical index，is in good agreement with the predictions of the renormalization group theory. In three dimensional systems, the condition of absence of knots should lead to new effects. However, it is observed that the probability of knot formation increases very slowly with the number of segments, and it is difficulty to find a reliable critical index. This paper makes an advancing step on this investigation.