Now we show that [alpha](t) is a circular helix in [E.sup.2n+1.sub.v].

So, we can say that [alpha] (t) is a circular helix.

It is easy to show that the curve [alpha](t) is the circular helix.

If both [kappa] and [tau] are non-zero constants, it is called a circular helix.

Hence a circular helix is a Bertrand curve (see [7]).

The circular helix characteristic to the reference worm is the helix corresponding to the reference cylinder and is named the mean circular reference helix of the worm; it has the pitch [p.sub.E] and the inclination [[theta].sub.0] having the size:

The right line d is inclined posed towards the basic cylinder with the angle [[theta].sub.b] that is the inclination angle of the circular helix described by the right line d on the base cylinder.

So, a W-curve of rank 1 is a straight line, a W-curve of rank 2 is a circle, and a W-curve of rank 3 is a right

circular helix.

If k and r are positive constants along C, then C is called a circular helix with respect to the Frenet frame.

C is a circular helix with respect to the Frenet frame {[partial derivative]/[partial derivative]v, n, b}, if and only if

In that sense, at the generation of the helical cylindrical surfaces where the theoretic directrix curve D is a circular helix, it is used the composition of a rotation movement with the rectilinear translation movement of the generating element in order to generate a helical circular trajectory in conditions of cinematic correlation (Sandu & Strajescu, 2004), (Botez, 1967).

that represent the known parametric equations of the circular helix and in which