U.S. patent application number 09/943169 was filed with the patent office on 2002-02-28 for linear light form with light diverting layer.
Invention is credited to Robbins, John A., Zarian, James R..
Application Number | 20020025132 09/943169 |
Document ID | / |
Family ID | 23590535 |
Filed Date | 2002-02-28 |
United States Patent
Application |
20020025132 |
Kind Code |
A1 |
Zarian, James R. ; et
al. |
February 28, 2002 |
Linear light form with light diverting layer
Abstract
The present invention relates to a fiber optic conduit having a
light diverting outer layer (22) that reflects and/or refracts
ambient light directed towards the conduit. The fiber optic conduit
includes a light transmitting core (24), cladded with a
fluoropolymer cladding (26) and subsequently jacketed with a
polymeric finish jacket (28). The light diverting layer (22) either
inserted between the cladding (26) and the jacket (28) or
surrounding the jacket (28) is included in the fiber optic conduit.
The light diverting layer (22) preferably has the property of
allowing light to be transmitted from the fiber optic surface out
of the conduit in one direction and reflecting ambient light
directed towards the conduit When reflecting ambient light, the
fiber optic conduit appears in the form of chrome trim.
Inventors: |
Zarian, James R.; (Corona
Del Mar, CA) ; Robbins, John A.; (Lake Forest,
CA) |
Correspondence
Address: |
Brian F. Drazich
Small Larkin LLP
18th Floor
10940 Wilshire Boulevard
Los Angeles
CA
90024
US
|
Family ID: |
23590535 |
Appl. No.: |
09/943169 |
Filed: |
August 30, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
09943169 |
Aug 30, 2001 |
|
|
|
09402102 |
Sep 27, 1999 |
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Current U.S.
Class: |
385/128 ;
385/126 |
Current CPC
Class: |
G02B 6/001 20130101;
G02B 6/02 20130101; G02B 6/02033 20130101; G02B 6/2852 20130101;
G02B 6/02052 20130101 |
Class at
Publication: |
385/128 ;
385/126 |
International
Class: |
G02B 006/22 |
Claims
What is claimed is:
1. A fiber optic conduit comprising: a light transmitting core; at
least one light transmitting outer layer surrounding said core; and
at least one light diverting layer surrounding said core and said
light transmitting outer layer.
2. The fiber optic conduit of claim 1 wherein said at least one
light diverting layer includes a characteristic of allowing light
transmitted through said core to pass out of said conduit and
reflecting ambient light directed toward said conduit.
3. The fiber optic conduit of claim 2 wherein said at least one
light diverting outer layer is a dichroic film.
4. The fiber optic conduit of claim 2 wherein said at least one
light diverting outer layer is a reflective film.
5. The fiber optic conduit of claim 2 wherein said at least one
light diverting outer layer is a refractive film.
6. The fiber optic conduit of claim 2 wherein said at least one
light diverting outer layer is a holographic film.
7. The fiber optic conduit of claim 2 wherein said at least one
light diverting outer layer is a polarizing film.
8. A fiber optic conduit comprising: a plurality of light
transmitting cores; a plurality light transmitting outer layers,
each of said outer layers surrounding each of said cores; a finish
jacket surrounding said cores collectively, as a bundle; and a
light diverting layer jacketed about said finish jacket; said light
diverting layer having a characteristic of allowing light to travel
from the plurality of the fiber optics to the outer surface of said
conduit in one direction and reflecting ambient light directed
toward said cores.
9. The fiber optic conduit of claim 8 wherein said light diverting
outer layer is a dichroic film.
10. The fiber optic conduit of claim 8 wherein said light diverting
outer layer is a holographic film.
11. The fiber optic conduit of claim 8 wherein said light diverting
outer layer is a polarized film.
12. A fiber optic conduit comprising: a light transmitting core; an
outer layer cladded about said core; a light control film fastened
to said outer layer; wherein said film has a characteristic of
allowing light emitted from said core to be visible at
predetermined viewing angles, while blocking light from other
viewing angles.
13. The fiber optic conduit of claim 12 wherein said light control
film is a polarizing film.
14. A method of manufacturing a fiber optic conduit comprising the
steps of: extruding a light transmitting core; extruding at least
one light transmitting outer layer about said core; and applying a
light diverting layer about said core and light transmitting outer
layer.
15. The fiber optic conduit of claim I wherein said at least one
light diverting layer includes a characteristic of directing light
transmitted through said at least one light diverting layer from
said core in a predetermined direction.
16. The fiber optic conduit of claim 15 wherein said at least one
light diverting layer includes a characteristic of reflecting
ambient light directed toward said fiber optic conduit.
17. The fiber optic conduit of claim 16 wherein said at least one
light diverting layer includes a light diffracting characteristic
in which ambient light reflected off said fiber optic conduit is
diffracted.
18. The method of claim 14 wherein said step of applying said light
diverting layer includes the step of pressing said light diverting
film onto the outer surface of the light form.
19. The method of claim 14 wherein said step of applying said light
diverting layer includes the step of embossing said light diverting
layer onto the outer surface of the light form.
20. The method of claim 14 wherein said step of applying said light
diverting layer includes the step of adhering said light diverting
layer onto the outer surface of the light form.
21. The method of claim 14 where in said step of applying said
light diverting layer uses vacuum deposition at room
temperature.
22. The method of claim 14 where in the step of applying said light
diverting layer includes reducing the air pressure surrounding said
light diverting layer.
23. The method of claim 14 wherein the step of applying said light
diverting layer includes the step of wrapping a film of said light
diverting layer about said outer layer.
24. The method of claim 14 wherein the step of applying said light
diverting layer includes the step of placing said outer layer and
core in a channel. placing said outer layer to overlie said
channel.
25. A fiber optic conduit for use on a sign comprising: a light
transmitting core; a cladding surrounding said core; a finish
jacket surrounding said cladding; and a reflective film wrapped
about said finish jacket; wherein said conduit is configured into a
desired shape and connected to said sign such that during night
time light from said light transmitting core is directed out of
said conduit and during daylight sunlight is reflected off of said
light diverting layer.
26. The fiber optic conduit of claim 4 wherein said light diverting
layer is plurality of layers including a dichroic film, a
refractive film, and a polarizing film.
Description
TECHNICAL FIELD
[0001] The present invention relates to linear light forms and
their methods of manufacture. More particularly the present
invention relates to linear light forms having a fiber optic
conduit with a light diverting outer layer and to the manufacturing
processes thereof.
BACKGROUND ART
[0002] With the advent of modern lighting systems, the demand for
fiber optic light conduits, also known as linear light forms, is
growing. In modern lighting systems it is desirable to obtain
energy efficiency and low maintenance, both of which are provided
by linear light forms.
[0003] Types of linear light forms include those having a clear
jacketing that is co-extruded tightly about single and/or multiple
large core fiber optics. The light is transmitted, or conveyed
through the fiber optics and emitted, or released, by reflection or
refraction out the sides of the fiber optic conduit. The advantages
of this configuration, in which a transmissive, finish jacket is
co-extruded tightly about the fiber optic core, are numerous. In
another type of linear light form, single or multiple thermoplastic
fiber optics are encased in a clear polymeric tubing. In yet
another type of linear light form, a reflective hollow tubing is
intertwined with single or multiple thermoplastic fiber optic
cores.
[0004] While each of the aforementioned lighting systems are
suitable for their intended lighting application, often it is
undesirable to view the lighting assembly when it is not in use,
typically during periods of daylight. When viewed by ambient light,
the linear light form often detracts from a desired daylight look
or effect. A wall or other object decorated with the linear light
form to obtain a highlighted or enhanced lighting effect at night
often may appear crowded or undesirable when viewed with ambient
light during the day.
[0005] When these linear light forms are observed in ambient light,
and without being illuminated themselves, it may be undesirable to
keep them within view because they appear as clear tubing and do
not offer a desirable aesthetic and/or functional appearance. These
disadvantages limit their desirability for use in the sign
industry, emergency vehicles, and traffic management among
others.
[0006] Another disadvantage exists in applications where the linear
light form has to be blended into a background such as side molding
of cars or on architectural structures. The linear light forms
existing today may not offer the desired aesthetic properties
and/or may actually detract from their use during the daytime.
[0007] Yet another disadvantage relates to the angle of view where
it is desirable to direct light from the illuminated linear light
forms to a desired location and/or to mask light from projection to
other locations.
DISCLOSURE OF INVENTION
[0008] It is an object of the present invention to divert ambient
light intercepting a linear light form.
[0009] It is another object of the present invention to control the
direction of light transmitted out of the linear light form.
[0010] The present invention relates to a linear light form
including light diverting outer layers. Light transmitted out of
the light form or projected onto the light form can be diverted by
the outer layers.
[0011] In one example, the present invention is embodied in a
linear light form including a light transmitting core, clad with at
least one light transmitting outer layer and the clad core jacketed
with a dichroic film. The dichroic film has the property of
allowing light transmitted within the clad core to pass out of or
be emitted from the linear light form, but of reflecting ambient
light directed toward the linear light form from an external
source.
[0012] Preferably, the linear light forms embodying the present
invention exhibit a different appearance when observed in ambient
light, or when illuminated from an outer light source compared to
their appearance when transmitting and projecting light from the
core, i.e., internally. Linear light forms with light diverting
surfaces exhibiting this characteristic are desirable in
applications where the linear light form is in public view.
[0013] Alternatively, the present invention is embodied in a linear
light form that includes a plurality of light transmitting cores,
each clad with a light transmitting outer layer and subsequently
jacketed, collectively, as a bundle, with a finish jacket. The
bundle of light transmitting clad cores is additionally jacketed
with a dichroic film whereby the film has the property of allowing
light to radiate outward from the plurality of the clad core fiber
optics to the outer surface of the linear light form in one
direction; but to reflect ambient light directed toward the
jacketed bundle from outside the clad core.
[0014] In another alternative embodiment of the present invention,
a linear light form includes a thermoset, light transmitting core,
clad with an outer layer which is covered with a light control
film. The film has the property of allowing light emitted from the
fiber optic surface to be visible at a certain viewing angle, while
blocking the light from other viewing angles.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] Other objects and advantages of the invention will become
apparent from the foregoing detailed description taken in
connection with the accompanying drawings, in which
[0016] FIG. 1 is a partial perspective view of a linear light form
of the present invention with a light diverting layer underlying a
jacket to divert ambient light;
[0017] FIG. 2 is a partial perspective view of an alternative
embodiment of the present invention with a light diverting layer
surrounding a jacket to divert ambient light;
[0018] FIG. 3 is a partial perspective view of another alternative
embodiment of the present invention with a light diverting layer
formed on a cladding to divert ambient light;
[0019] FIG. 4 is a partial perspective view of an alternative
embodiment of the present invention transmitting light;
[0020] FIGS. 5 and 6 are partial perspective views of alternative
embodiments of present invention transmitting light in
predetermined directions; and
[0021] to FIG. 7 is a cross-sectional end view of an alternative
embodiment of the present invention housed in a channel and covered
by a polar mirror.
BEST MODE FOR CARRYING OUT THE INVENTION
[0022] As shown in the drawings for purposes of illustration, the
invention relates to a is linear light form 20 having a light
diverting layer 22. The linear light form 20 (FIGS. 1-4) includes,
generally, a fiber optic core 24 or cores, a light transmissive
fluoropolymer cladding layer 26 about the core(s) 24. A jacket
material 28 of the polymeric type is formed about the core(s) 24
and cladding material 26. Advantageously, the light diverting layer
22 includes reflective, refractive or dichroic and/or polarizing
materials that alone or in combination cause light to be diverted
in a desired direction. Reference to the terms "reflective" and
"refractive", when used to describe the novel features of the light
diverting layer of the present invention, refer to characteristics
of the layer that refract or reflect ambient light or light being
transmitted out of the fiber directed toward the core, but from
outside of and through the jacket and clad, rather than light 36
transmitted through the core by an illumination system 30. For
example, ambient light, indicated by line 32, may be provided in
the form of sunlight from the sun 34, and the light diverting layer
22 is said to refract or reflect this light.
[0023] The position of the light diverting layer 22 may be
immediately overlying the cladding layer 26 (not shown), on a film
22 encompassing the cladding layer 26 (FIG. 1);
[0024] directly on the exterior surface of jacketing material 28
deposited onto the cladding 26 (FIG. 2), inter-layered between
jacketing materials encompassing the clad-core (not shown) or on
the outer surface of the jacketing(s) 28 (FIG. 2).
[0025] Conventional linear light forms 20 may be prepared in
accordance with the present invention using linear light forms,
apparatus, composition and methods of manufacture of the type
described in U.S. Pat. Nos. 4,763,984; 4,957,347; 5,052,778;
5,067,831; 5,149,467; 5,221,387; 5,225,166; 5,122,580; and
5,298,327 which are incorporated herein by reference. The process
of manufacturing of linear forms with a light diverting layer can
be done in a continuous or static (discrete) manner and by the use
of adhesives, deposition, painting, co-extrusion, tandem extrusion
and other equivalent means.
[0026] The linear light forms of the type described above that are
particularly beneficial can include, but are not limited to, light
forms composed of: a thermoset light transmitting core cladded by a
fluoropolymer; a plurality of thermoset light transmitting cores
each cladded by a fluoropolymer; a thermoplastic light transmitting
core clad with a fluoropolymer; a plurality of thermoplastic light
transmitting cores each clad with a fluoropolymer; a reflective or
refractive linear configuration intertwined within a plurality of
light transmitting cores each clad with a fluoropolymer; a
thermoset light transmitting core clad by a fluoropolymer and
jacketed with a polymeric finish jacket such as poly(vinyl
chloride), polyacrylate, polymethacrylate, polycarbonate, silicone,
among other suitable polymers; a plurality of thermoset light
transmitting cores each clad with a fluoropolymer and jacketed with
a polymeric finish jacket such as poly(vinyl chloride),
polyacrylate, polymethacrylate, polycarbonate, silicone, among
other suitable polymers; a thermoplastic light transmitting core
clad with a fluoropolymer and jacketed with a polymeric finish
jacket such as poly(vinyl chloride), polyacrylate,
polymetbacrylate, polycarbonate, silicone, among other suitable
polymers; a plurality of thermoplastic light transmitting cores
each clad with a fluoropolymer and in combination held together by
a polymeric material and jacketed by a polymeric finish jacket such
as poly(vinyl chloride), polyacrylate, polymethacrylate,
polycarbonate, silicone, among other suitable polymers; a
reflective or refractive linear configuration intertwined within a
plurality of light transmitting cores each clad with a
fluoropolymer and in combination held together by a polymeric
material and jacketed with a polymeric finish jacket such as
poly(vinyl chloride), polyacrylate, polymethacrylate,
polycarbonate, silicone, among other suitable polymers; and any
combinations thereof.
[0027] The reflective, refractive, polarizing or dichroic materials
particularly beneficial as a light diverting layer 22 (FIGS. 1-4)
can include, but are not limited to: films that have a reflective
or refractive surface; polarizing materials that divert light at a
certain angle; dichroic materials that filter out some frequencies
of light while allowing other frequencies of light to pass through;
holograms specifically designed to project an image; refractive
materials capable of refracting light in certain direction;
reflective materials placed at intervals onto or within the linear
light form.
[0028] In order to provide a more detailed description of the
present invention, the following examples and embodiments
illustrate the linear light form having a light diverting layer and
provide a description of the unique effects achieved from using a
light diverting layer.
EXAMPLE 1
[0029] A 1.2 m section of a linear light form of the type sold
under model No. FC-501 (jacketed clad core) manufactured by
Lumenyte International Corporation, Costa Mesa, Calif., was
combined with a light diverting layer. Onto the middle of the 1.2 m
section, a length of approximately 0.6 m long reflective film of
the type sold under model No. HRS 241 (Gila Sunshine Window Film)
manufactured by Courtaulds Performance Films, Martinsville, Va.,
was applied according to the instructions provided by the
manufacturer. The combination was then connected to an illumination
system 30 (FIG. 4) and energized to transmit light out of the
conduit. When the illuminated combination was viewed in the dark
illumination provided by a conventional illumination system of the
type sold under model No. PH-1000 illuminator with and/or wheel, by
Lumenyte International Corp., the light transmitting properties and
color changing characteristic inherent in conventional linear light
forms was observed. The light diverting layer had little or no
effect on the light transmitting properties of the linear light
form. When the illuminator was turned off, and the combined linear
light form with light diverting layer was observed in ambient light
(FIG. 2), the middle 0.6 m section to with the light diverting
layer appeared as reflective while the uncovered areas appeared
clear. Additionally, when the combination was kept illuminated, and
in turn illuminated by an external fiber optic source, the area
covered reflected the light coming from the external light source,
whereas the area appeared as a clear tubing.
EXAMPLE 2
[0030] A 1.2 m section of a linear light form of the type sold
under model No. RB-501 (clad core, no finish jacket) and
manufactured by Lumenyte International Corporation, Costa Mesa,
Calif., was combined with the same reflective film, and applied as
in Example 1 above. The same results were observed.
EXAMPLE 3
[0031] A 1.2 m section of a linear light form of the type sold
under model No. FC-501 and manufactured by Lumenyte International
Corporation, Costa Mesa, Calif., was selected, the finish jacketing
was slit open along the length of the linear light form, the
poly(vinyl chloride) jacket was removed, and fiber optic with the
fluoropolymer cladding exposed was used as the starting linear
light form with the same reflective film, and applied as in Example
1 above. The removed poly(vinyl chloride) was placed back onto the
combination. The same results were, observed as outlined in Example
1, except that the reflective layer, between the cladding and
jacket did not appear as shiny as in Examples 1 and 2.
EXAMPLE 4
[0032] A section of a linear light form of the type sold under
model No. WN-400 optic (a core surrounded by a teflon.RTM. clad)
and manufactured by Lumenyte International Corporation, Costa Mesa,
Calif., was selected, a 15 cm portion of the linear light form was
wrapped with a layer of light diverting film sold under model,
Edmund Scientific Holographic No. 52990 and supplied by Edmund
Scientific, Barrington, N.J. The wrapped portion when exposed to
sun light exhibited a extremely slight varying color (like a
rainbow). When the linear light form was illuminated with an
illumination system similar to the combination described in Example
1 in the dark, the color changing characteristics inherent in
conventional linear light forms were observed and the section
wrapped by the film appeared to produce illumination in
substantially the same way as the rest of the linear light
form.
EXAMPLE 5
[0033] A section of a linear light form 80 of the type sold under
model No. WN-400 optic, and manufactured by Lumenyte International
Corporation, Costa Mesa, Calif., was combined with a polarizing
mirror light diverting layer 82, 5 cm in length and approximately 1
cm in width of type sold under model, Edmund Scientific Polar
Mirror No. 43683 and supplied by Edmund Scientific, Barrington,
N.J. The light diverting layer was fastened conventionally to the
linear light form (FIG. 7). The polar mirror material comprising
the light diverting layer could not be wrapped because of the
thickness of the film. It was discovered that the linear light form
can be placed in a channel 84, conventionally, and the light
diverting layers thereafter could be arranged exterior to, and
overlying, the channels. The linear light form was observed under
the same light conditions as Example 1 and the same light diverting
results as in example 1 where observed.
EXAMPLE 6
[0034] A section of a linear light form (FIG. 5) of the type sold
under model No.
[0035] WN-400 optic, and manufactured by Lumenyte International
Corporation, Costa Mesa, Calif., was combined with a light
diverting layer 22, 5 cm in length and approximately 1 cm in width
of type sold under model No. 3 M Light Control Film (0 degree
angle) 52391 by Edmund Scientific, Barrington, N.J. The Light
Control Film allows light to be directed out of the linear light
form at an angle 30 degrees from normal. The light diverting layer
22 was fastened to the linear light form such that the light
diverting layer was overlying or covering the linear light form.
The portion covered with the control film when illuminated by an
illumination system 30, as in Example 1, could not be viewed
perpendicular to the longitudinal axis of the linear light form, or
from one direction parallel to the longitudinal axis of the linear
light form at any angle; however it could only be observed to be
illuminated, i.e. transmitting light 36, from the opposite
direction within an arc, or a narrow angle range generally at 30
degrees from perpendicular.
EXAMPLE 7
[0036] A section of a linear light form (FIG. 6) of the type sold
under model No.
[0037] WN-400 optic, and manufactured by Lumenyte International
Corporation, Costa Mesa, Calif., was combined with a light
diverting layer, 5 cm in length and approximately 1 cm in width of
the type sold under model No. 3 M Light Control Film (0 degree
angle) 52390 by Edmund Scientific, Barrington, N.J. The Light
Control Film allows light to be directed out of the linear light
form at an angle normal to the surface of the film. The light
diverting layer was fastened to the linear light form such that the
light diverting layer was overlying or covering the linear light
form. The portion of the linear light form covered with the control
film when illuminated by an illumination system 30 was viewed to
transmit light 36 perpendicular to the longitudinal axis of the
linear light form, but as the viewing angle was moved from
perpendicular in either direction, the light 36 transmitted from
linear light form seemed to be dimmer and eventually the light
became invisible after about 30 degrees from perpendicular.
EXAMPLE 8
[0038] A section of a linear light form of the type sold under
model No. WN-400 optic, and manufactured by Lumenyte International
Corporation, Costa Mesa, Calif., was combined with a light
diverting layer. A 15 cm portion of the linear light form was
wrapped with a light diverting layer of the type sold under model,
Edmund Scientific Diffraction Grating No. 40267 supplied by Edmund
Scientific, Barrington, N.J. The wrapped portion when exposed to
sun light exhibited a varying color (like a rainbow) more
pronounced than the effect observed in Example #4 above. When the
linear light form was illuminated the section wrapped by the film
appeared to transmit light out of the linear light form in
substantially the same manner as the uncoated portion of the linear
light form.
[0039] Processes for Production of Linear Light Forms With Light
Diverting Layers
[0040] The techniques particularly beneficial to manufacturing a
linear light form with a light diverting layer can include, but are
not limited to, pressing dichroic films onto the outer surface of
the linear light forms, deposition of reflective or refractive
materials at reduced pressure at room temperature, embossing of
holographic patterns on the outer surface of the light forms,
application of holograms at intervals onto the surface of the
linear light forms by pressing a film including the hologram among
others. All the above techniques can be used in a continuous manner
during manufacture of the linear light form.
[0041] Other conventional techniques may be used to apply the light
diverting materials. For example, vacuum deposition both at room
temperature and under reduced pressure, or at higher or lower
temperatures, may be used to deposit a layer of a reflective
material onto the cladding or jacketing materials. Alternatively,
the light diverting layer may be applied to a film and adhered to
the cladding prior to jacketing. The film may, alternatively be
wrapped around the cladding prior to the application of a jacketing
material by a co-extrusion process, for example, to integrate the
different components into position. Yet again, a light diverting
material may be adhered to the outer surface of a jacketing
material that has already been extruded over a clad-core
combination.
[0042] Other placement combinations and/or techniques can be used
within the scope of the present invention as long as the light
diverting layer positioned and/or manufactured produces the desired
light diverting effect for the application.
[0043] The light diverting layers on linear light forms are
particularly useful in automobile, traffic management, sign,
military, architectural among other applications.
[0044] In each case when ambient light, either from sunlight light
during the day or headlights at night, is projected upon the linear
light form it will reflect or refract the ambient light thereby
providing the look of chrome trim or if a holographic reflector is
used then a fanciful design, or if reflective surface is used then
an identifiable outline. The purpose is to keep the linear light
form visibly pronounced even when receiving ambient light. This is
particularly desirable in applications where the linear light form
is used to identify a vehicle, the perimeter of roads or other
objects at night or other object at night to other motorists. In
the absence of a light diverting layer, the linear light form would
not assist in identifying the object it was intended to highlight
and/or be bleached out.
[0045] In the case of certain traffic signs or emergency vehicles,
it may be desirable to direct the path of light from the linear
light form so that only those motorists that need to view a
particular signal or sign on the freeway will be able to view the
light transmitted out of the linear light form. In such instances
the polarized light diverting layer maybe desirable.
[0046] In the case of certain traffic management applications, for
example in outlining road ways, it may be desirable to use a
reflective outer layer so that the road is outlined at night;
however, when the light from other motorists' headlights is
projected onto the light form, the surface reflects the light back
still making the outline of the road visible. Without the
reflective layer, the road outline when exposed to the headlight
will be bleached out rendering the ultimate application, namely
warning the motorist, not as effective.
[0047] While the present invention has been described in connection
with what are presently considered to be the most practical, and
preferred embodiments, it is to be understood that the invention is
not to be limited to the disclosed embodiments, but to the
contrary, is intended to cover various modifications and equivalent
arrangements included within the spirit of the invention, which are
set forth in the appended claims, and which scope is to be accorded
the broadest interpretation so as to encompass all such
modifications and equivalent structures.
* * * * *