Improvements in or relating to the Production of Parabolic Surfaces.
Year: 1893

page_text: Date of Application, 10th Oct., 1893-Accepted, 13th Jan., 1894
COMPLETE SPECIFICATION.
Improvements in or relating to the Production of Parabolic
Surfaces.
I, ALEXANDER WACKER, a Director of the Elektrizitäts-Aktiengesellschaft
(formerly Schuckert & Co.) of Nürnberg, Germany, do hereby declare the
nature of this invention and in what manner the same is to be performed, to
be particularly described and ascertained in and by the following statement :-
In the machines hitherto employed for grinding or producing parabolic surfaces,
the grinding tool has been moved in a parabolic path by a suitable mechanism,
while a parabolic surface has been rotated against it. Working in this manner,
the grinding process is limited to a point, or to the immediate neighbourhood of a
point. As it is evident that the tool must present to the work a surface instead of
a mathematical point, (which surface cannot be chosen too small to avoid abnormal
wear), the exact result is easily disturbed, and instead of the true geometrical
parabolic form, an irregular form is produced. The object of the invention is to
improve the grinding process in such a manner that, instead of a mere point, a
whole line is worked on at the same time. The result will be more exact, because
the tool acts more as a knife, instead of a point, and can therefore be taken smaller
without danger of wear. In addition, there is the advantage that inaccuracies
are corrected by the procedure itself; and that the time required for finishing
the work will be much smaller; an important item, as the grinding requires
several days.
The mathematical principle of the invention is as follows. If a paraboloidal
surface of rotation is cut by planes parallel to the axis, the curves of intersection
are parabolas of the same focal distance (see Fig. 1). This is easily proved The
equation of the paraboloidal surface being x + y² = 2pz and to the said plane = a
we get for the intersection y² = 2 pz" a that is, a parabola with the focal
distance p.
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2
The tool, as shown in Figs. 2 and 3, is of a corresponding form; that is, bounded
by a parabola of the desired size. Its movement is in the direction normal to its
own plane; in the figures from 1 to m, from the edge to the centre of the parabolic
shell or surface. Now by the theorem proved before, the tool must touch the
shell or surface always in a parabolic line.
Instead of bounding the tool by an exact parabola, we may substitute for it a
circle, with a radius equal to the radius of curvature. Such an arrangement is
shown in Figs. 4 and 5. The grinding mechanism to produce parabolic movement
can be one of the known mechanisms, such as that shown in Fig. 5, and others shown
and described in the Specifications numbered 18733 and 18734 dated 19 October
1892. The tool is of a disc form, rotated by a driving rope, belt, or equivalent
means, as shown in Figs. 4 and 5; and, as before stated, the tool must be moved in
a direction from the edge of the shell to its centre, while the shell is rotating.
arrangement may be modified so that the rotating disc tool his guided along a
straight line, while the rotating shell is lifted or lowered so that the paraboloidal
surface will be produced.
This
It is further to be observed that instead of a complete disc tool h, a part or
sector of the circle can be provided, and given an oscillating movement instead of
a rotating one; the length of the oscillating pendulum being equal to the radius of
curvature.
An advantage of the present improvement is that in the centre of the shell or
parabolic surface the tool has a movement independent of the movement of rotation

page_text: given to the shell or surface; so that an effective grinding is given at the central
part thereof.
Having now particularly described and ascertained the nature of the said inven-
tion, and in what manner the same is to be performed, I declare that what I
claim is ;-
1. The herein described improvement in producing parabolic surfaces, consisting
in the combination of a plane tool bounded by a parabola, a parabolic surface
arranged and adapted to be acted upon by the said tool, means for rotating the
said surface and a mechanism for guiding the said tool in a parabolic path whereby
every point of the grinding surface of the said tool is caused to describe a parabola,
substantially as and for the purpose described.
2. The herein described improvement in producing parabolic surfaces, consisting
in the combination of a disc and means for rotating the same, a parabolic surface
arranged and adapted to be acted upon by the said tool, means for rotating the said
surface and a mechanism for guiding the said tool or the said surface in a parabolic
path, substantially as and for the purpose described.
3. A grinding tool for use in producing parabolic forms consisting of a rotating
disc, or an oscillating sector of a circle, substantially as and for the purpose herein
-described.
Dated this 10th day of October 1893.
FAIRFAX & WETTER,
433, Straud, London, Agents for the Applicant.