The directrix should simultaneously translate n units in parallel to the y-axes, so its equation is l: y = n - 1/4a.
Using the above considerations, the focus and directrix are described in Figure 4.
As in the case of [[lambda].sub.2], we managed to find a focus and a directrix that do not depend on the selection of points on [[lambda].sub.3].
For curves [[LAMBDA].sub.2] and [[LAMBDA].sub.4], the directrix is parallel to the x-axis and for [[lambda].sub.3]] it is parallel to the y-axis.
The constructive parameters of the workpiece and tool and also the generation ones determine the form of the directrix
and generatrix of the polygonal processed surface.
When students have found the points that are twice as far from the focus as they are from the directrix
(r = 2 l) they can join them to form an hyperbola with eccentricity e = 2.
Use [constructions] parallel to find another point, P', which is the same distance from the directrix and from the focus.
Choose the pointer and use it to move the point A up and down the directrix. Study what happens to the points M, B, N and P as you do this.
Move the point A up and down the directrix. As you do this, the point P will trace the locus of points along a parabola with tangent MP and normal PN.
The aspects shown in this paper represent original contribution concerning the cinematic generation of the circular helix used as directrix D at the generation of real complex surfaces of the type cylindrical helical surfaces.
This theory of the cinematic generation from composition of single movements cinematically correlated by ratios [R.sub.CCIN], for the directrix curves D and for the generatrix curves G of the geometrical surfaces, permits the cinematic correlation of the mobile parts of the machine-tools with NC at the generation of the complex surfaces on them, and, in the same time, the creation of the cinematic algorithms available for the generation of the most complex forms of the real surfaces on these machine tools.