close

Вход

Забыли?

вход по аккаунту

?

Патент USA US2409604

код для вставки
Oct‘ 15, 1946.
R. w. WOOD
2,409,603
»
METHOD AND APPARATUS FOR GENERATING CURVES
Filed Nov. 22, 1945
'
BY
2 Sheets-Sheet l
‘7
_.
m 32.”; ZWW w 22%,‘,
MTORNEYJ
Oct. 15, 1946.
R, w, wool)
2,409,603
METHOD AND APPARATUS FOR GENERATING CURVES
Filed Nov. 22, 1945
2 Sheets-Sheet 2
‘
E
-'
INVENTOR.
746w‘ WOrQer‘ #1600’
BY
M 52»;
.
9%,
ATTORNEY)‘
2,409,603
Patented Oct. 15,1946
UNITED STATES PATENT OFFICE
2,409,603
METHOD AND APPARATUS FOR GENERAT
ING CURVES
RobertWarner ‘Wood, Princeton, N. J., assignor,
by mesne assignments, to Kaiser Fleetwmgs,
Inc., a corporation of California
Application November 22, 1943, Serial No. 511,291v
7 Claims.
(01. 88-24) "
2
1
ellipse.
This invention relates to the‘ generation of
The minor axis of the ellipse will vary
. ratus which are capable of producing second de-‘
with the angular positionof the opaque element
C and'the contour will be changed correspond
gree curves of the desired contour without the
necessity for arduous mathematical calculation.
ingly. Instead of a circle, it is possible to use
other conic sections such as the ellipse, parabola
In industry, curves of varying contour are use~
in] for many purposes, and particularly in the
' or hyperbola, and the ‘shadows projected will have
designing of high speed aircraft second degree
the shape of the element projected and its angu
curves and particularly to a method and appa
the correspondingly varied form, depending upon
lar position. In addition, the element projected
curves are employed in effecting the desired
streamlining of the exposed surfaces. The meth
10 may be adjusted angularly about two aXes per
od heretofore used to generate such curves in
volves complex and laborious mathematical cal~
culations. In plants where a multiplicity of dif
ferent curves is required as the basis for template
shapes, modi?cation of design frequently involves 15
additional calculations. These require consider
able time of expert mathematicians. Errors
sometimes occur in such calculations, involving
repetition of the work. The method is therefore
20
a serious item of cost and delay.
t is the object of the invention to provide a
simple and effective method of and apparatus for
generating
second ' degree
curves
which
are
pendicular to the axis w-a and its position with
respect to the source of light P and. the screen S
may be adjusted. It is not essential that the
screen S be perpendicular to a line passing
through the center of the element C, since it also
may be arranged to be tilted about horizontal
and vertical axes, although this is not normally
necessary for the practice of the invention. In
every case, and regardless of the relative adjust
ment of the element C and the screen S, the
projected shadow will be a conic.
It is well known that the edges of shadows are
not sharp and well de?ned but are somewhat
“fuzzy” owing to diffraction. If shadows are
produced by a light issuing from a point source,
mathematically accurate and available without
DO ,vi
loss of time for reproduction and use.
the phenomenon of di?'raction may easily be
Another object of the invention is the pro
observed. Di?‘raction from the edge of an opaque
object takes the form of bands of light and
shadow. It is di?icult to indicate these bands»
precisely, but I have endeavored to do so in Fig. 2.
gree curves having any desired. form.
in which 5 indicates the shadow, 5 a light band
Other objects and advantages of the invention
and 1 a dark band beyond which there are a
will be apparent as it is better understood by ref
series of light and dark bands merging into the
erence to the following speci?cation and the
space 8. These bands are more distinct when
accompanying drawings, in which
Fig. 1 is a diagrammatic illustration in per 35 the source of light is very small, while the spac
vision of a method and apparatus vwhich may
be used by a relatively unskilled operator without
mathematical training to generate second de
ing of the bands depends upon the distances from
spective of the principle involved:
Fig. 2 is an elevation illustrating ‘the diffraction
hands at the edge of a shadow;
Fig. 3 is a diagram representing the procedure
whereby the shape of the desired curve is de 40
termined; and
P to C and from C to S. This spacing can be
computed accurately. The apparatus can be ar
ranged to make the bands quite narrow, and one
of the bands can be selected to'be ?tted to the
design requirements of the desired second degree
,
Fig. 4 is a view in perspective illustrating a
practical apparatus for the application of the
invention.
My invention is based upon the principle that
projections of comics are still conics, although
the projections may have characteristics di?er
ent from the original. As a simple illustration,
curve.
'
Although the element C is shown, for purpose of
illustration, as an opaque body, the conic section
to be projected can, of course, be an opening in
an opaque body or it may be delineated as a
transparent line or slot in an opaque body, or it
in the form of a conic, in this instance a circle,
may beformed from a thin curved member such
as a wire. The only important consideration is
that the element C be capable of casting the
shadow of a conic section when disposed in a
beam of light and rotatable about one or more
is disposed in the beam and rotated partially
axes, preferably three, in order to facilitate modi
if a beam of light from a point source P is pro
jected onto a screen S and an opaque element 0
?cation of the curvature of the shadow to ?t the
about an‘ axis a—a, a shadow X will be projected
upon the screen and will have the form of an 55 desired conditions.
2,409,603
3
4
Just as a straight line is determined uniquely
by two points or by one point and a tangent line
at that point, a second degree curve is deter
24. It is not necessary, of course, to use the en
tire outline of a conic section. Any selected por
tion thereof may be projected in the manner de
mined uniquely by ?ve points, by four points and
scribed until a curve is found which conforms to
a tangent line at one of them, or by three points 5 the ?ve conditions which are initially marked
and tangent lines at two of them. The latter
condition is indicated in Fig. 3, in which 9, I0
and II are predetermined points, and I2 and I 3
tangents at the points 9 and II. The curve M
‘upon the surface 24.
It remains only to ?x the curve of the pro
jected shadow. The simplest procedure when all
adustments have been made is to shut off the
is a conic conforming to these conditions. In 10 source of light, substitute a photosensitized sur
designing curved surfaces such, for example, as
face for the surface 24!, and then expose the sur
those used in streamlining airplanes, it is pos
face to light from the source for a sufficient inter
sible to ?x the ?ve conditions which determine
val to secure a photographic image. This opera
the desired curve. Heretofore, as already indi
tion must be conducted obviously without inter
cated, it has been the practice, when the ?ve
ference from extraneous light or otherwise in a
conditions have been determined, to proceed by
dark room. Instead of photographing the image,
elaborate mathematical calculations, to ?x
it may be ?xed by marking points on the surface
enough remaining points on the curve so that
24, which may be subsequently connected to de
it could be accurately drawn. My invention
lineate the desired curve. Any other procedure
avoids this di?iculty by the practical application
may be utilized to obtain a ?xed representation
of the principles hereinbefore discussed in the
of the curve which may be utilized subsequently
simple apparatus hereinafter described.
in the form of templates or other mechanical
Referring to Fig. 4, I5 indicates a housing for
means for reproducing the curve.
The curve as
a light source such as an are between carbons
?xed may be enlarged to any desired scale before
l6 and H which are supplied with electric cur
rent through conductors I8 and I9 from any
suitable source. A condenser lens 20 directs a
it is translated to a template or other device.
The apparatus as illustrated affords the nec
essary elements in simple form adapted to secure
beam of light from the source through a small
universality of adjustment to reproduce substan
aperture 2|.
tially every available second degree curve. Some
. The housing I5 is connected by a track 22 to 30 of the adjustments can, of course, be eliminated
an easel 23 carrying a surface 24 which is prefer
where the range of desired second degree curves
ably white. The easel 23 may be fixed or movable
is limited or where great accuracy is not essen
on the track 22. It is preferably movable to
tial. The elements illustrated need not be in the
permit relative adjustments as may be required.
Between the housing I5 and the easel 23, a
particular form in which they are shown.
For
‘ example, any source of light and means for pro
block 25 is supported for longitudinal movement
jecting a beam thereof through a small aperture
along the track 22. It is provided with a groove
may be utilized. Many forms of such devices are
26 in which a block 21 is adjustable transversely
well known. Likewise, the means for adjusting
of the track 22. A standard 28 on the block 21
the element 36 about its three axes and otherwise
40
supports a spindle 29 which is capable of vertical
may be modi?ed, the form illustrated being
and rotational adjustment and is held in the
merely a simple and satisfactory arrangement.
desired position by a set screw 30. Mounted on
The easel 23 may be supported ?xedly or may
the spindle 29 is a frame 3| to which a second
be made adjustable by any of the ordinary de
frame 32 is pivotally connected at 33. The frame
vices available for that purpose.
32 carries a support 34 having a pivot 35 for the p. U Various changes may be made, therefore, in the
element 36 corresponding to the element C of
procedure as described and particularly in the
Fig. 1, that is, an element having the outline of
apparatus employed without departing from the
a conic section. As will be readily apparent, the
invention or sacri?cing the advantages thereof.
element 36 is adjustable about the three axes X,
I claim:
'
Y and Z of the adjacent diagram by rotating the 0 1. An apparatus for generating curves com
element on the pivot 35, rotating the frame 32
prising a plane surface on which a plurality of
on the pivots 33 and rotating the spindle 29 on
points not in'a straight line and through which
the standard 28. In other words, the element
the curve is to pass may be indicated, a support
having the outline of the conic section is uni
for said surface, a point-light source mounted to
versally adjustable about the three axes. It also 55 project a beam of light toward said surface, a
may be moved longitudinally and transversely of
curved outline, a support on which said curved
the track 22 to vary its relative position with
outline is mounted in the beam of light, and
respect to the source of light and the easel 23.
means for adjusting the angle of the plane of
In carrying out the invention, the points 9, I0
said outline relative to the axis of the beam of
light.
and II, and the tangents I2 and I3, which are
to determine the desired curve, are marked upon
2. An apparatus for generating curves compris
the surface 24. The element 35 is then adjusted
ing a plane surface on which a plurality of points
about its three axes, and its relative position with
not in a straight line and through which the curve
respect to the source of light and the easel 23 is
‘is to pass may be indicated, a support for said
modi?ed until the selected diffraction band of
surface, a point-light source mounted to project
the shadow coincides with the points 9, Ill and I I
a beam of light toward said surface, a curved
and is tangent to the lines I2 and I3. The re
outline, a support on which said curved outline
sulting outline of the diffraction band is the pre
is mounted in the beam of light, means for ad
cise curve desired. If the desired curve cannot
justing the angle of the plane of said outline rela
be obtained by the described adjustments of the 70 tive to the axis of the beam of light, and means
element 36, another element of conic outline may
for adjusting the support for said outline bodily
be substituted therefor. Thus, outlines of a cir
relatively to the point-light source.
cle, ellipse, hyperbola or parabola may be used
3. An apparatus for generating curves com
to secure shadows which are modi?cations of
prising a plane surface on which a plurality of
these conic sections projected upon the surface 75 points not in a straight line and through which
5
2,409,603
the curve is to pass may be indicated, a support
for said surface, a point-light source mounted to
project a beam of light toward said surface, a
curved outline, a support on which said curved
6
angle of the plane of said surface relative to the
axis of the beam of light.
6. An apparatus for generating curves com
prising a track, a plane surface on which a plu
outline is mounted in the beam of light, and
rality of points not in a straight line and through
which the curve is to pass may be indicated,
means for adjustably supporting said surface
lar axes relative to the axis of the beam of light.
from said track, a point-light source mounted to
4. An apparatus for generating curves compris
project a beam of light toward said surface, a
ing a plane surface on which a plurality of points 10 curved outline, a support adjustably mounted on
not in a straight line and through which the
said track on which said curved outline is mount
curve is to pass may be indicated, a support for
ed in the beam of light, and means for adjusting
said surface, a point-light source mounted to pro
the angle of the plane of said outline relative to
ject a beam of light toward said surface, said
the axis of the beam of light.
surface being mounted substantially normal to
'7. .An apparatus for generating curves com
means for adjusting the angle of the plane of
said outline about three respectively perpendicu
the axis of the beam of light, a curved outline, a
support on which said curved outline is mounted
in the beam of light, and means for adjusting
prising a track, a plane surface on which a plu
rality of points not in a straight line and through
which the curve is to pass may be indicated, a
the angle of the plane of the outline relative to
support for said surface, a point-light source
the axis of the beam of light.
20 mounted to project a beam of light toward said
5. An apparatus for generating curves compris
surface, a curved outline, a support on which
ing a plane surface on which a plurality of points
said curved outline is mounted in the beam of
not in a straight line and throuh which the curve
light, said last-named support being mounted on
is to pass may be indicated, a support for said sur
the track and adjustable there along between the
face, a point-light source mounted to project a 25 point-light source and said plane surface, and
beam of light toward said surface, a curved out
means for adjusting the angle of the plane of the
line, a support on which said curved line is mount
outline relative to the axis of the beam of light.
ed in the beam of light, and means for adjusting
the angle of the plane of said outline, and the
ROBERT WARNER WOOD.
Документ
Категория
Без категории
Просмотров
0
Размер файла
506 Кб
Теги
1/--страниц
Пожаловаться на содержимое документа