Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
CA 02471970 2004-07-09
HIGH DEFINITION THERMAL INK-JET PRINTER
The present invention relates generally to computer
hardcopy printers and more particularly to ink-jet
printers. The predominant current usage of the improved
thermal ink-jet printer assembly of the present invention
is as a means of obtaining high definition color
printouts of computer generated text and graphics.
BA(',$GROUND ART
With the advent of computers came the need for
devices which could produce the results of computer
generated work product in a printed form. Early devices
used for this purpose were simple modifications of the
then current electric typewriter technology. But these
devices could not produce picture graphics, nor could
they produce multicolored images, nor could they print as
rapidly as was desired.
Numerous advances have been made in the field.
Notable among these has been the development of the
impact dot matrix printer. While that type of printer is
still widely used, it is neither as fast nor as durable
as is required in many applications. Nor can it easily
produce high definition color printouts. The development
of the thermal ink-jet printer has solved many of these
problems. U.S. Pat. No. 4,728,963 issued to S. O.
Rasmussen et al., and assigned to the same assignee as is
this application, teaches an example of this type of
printer technology.
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Thermal ink-jet printers operate by employing a
plurality of resistor elements to expel droplets of ink
through an associated plurality of nozzles. In
particular, each resistor element, which is typically a
pad of resistive material about 50um by 50um in size, is
located in a chamber filled with ink supplied from an ink
reservoir. A nozzle plate, comprising a plurality of
nozzles, or openings, with each nozzle associated with a
resistor element, defines a part of the chamber. Upon
the energizing of a particular resistor element, a
droplet of ink is expelled by droplet vaporization
through the nozzle toward the print medium, whether
paper, fabric, or the like. The firing of ink droplets
is typically under the control of a microprocessor, the
signals of which are conveyed by electrical traces to the
resistor elements.
The pen containing the nozzles is moved repeatedly
across the width of the medium to be printed upon. At
each of a designated number of increments of this
movement across the medium, each of the nozzles is caused
either to eject ink or to refrain from ejecting ink
according to the program output of the controlling
microprocessor. Each completed movement across the
medium can print a swath approximately as wide as the
number of nozzles arranged in a column on the pen
multiplied times the distance between nozzle centers.
After each such completed movement or swath, the medium
is moved forward the width of the swath, and the pen
begins the next swath. By proper selection and timing of
the signals to the nozzles, the desired print is obtained
on the medium.
In order to obtain multicolored printing, the column
CA 02471970 2004-07-09
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of nozzles in the pen can be allocated to the
distribution of different colored inks. For instance, a
pen with a column of nozzles 48 nozzles in length may be
constructed such that the first twelve nozzles can be
supplied with cyan ink, the next twelve nozzles can be
supplied with magenta ink, the next twelve with yellow
ink, and the last twelve with black ink. Using this
arrangement, each complete movement or swath of the pen
across the medium could print four color bands, each band
being twelve nozzle spacings or index positions wide.
The medium would then be advanced twelve index positions
so that the next swath would have the magenta ink nozzles
moving over the same medium positions as were the cyan
ink nozzles on the previous swath. By continuing to
advance the medium by twelve index positions before each
swath of the pen, each of the print positions on the
medium could, if directed by the microprocessor, be
printed by each of the ink colors. Using this
arrangement, any given individual position on the print
medium is addressed four times on four consecutive
swaths. But the print medium will have advanced twelve
index positions between each swath. Therefore, the
information from the computer concerning this print
position has to be temporarily stored and used on the
four consecutive swaths, each of which is separated by
twelve index positions. This is referred to as a data
index of twelve lines. Using this arrangement, it is
possible to produce reasonably high quality multicolored
printed images of both alphanumeric characters and
graphics at a reasonably high rate of speed.
But thermal ink-jet printer technology is itself not
without problems, and considerable need has existed for a
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means of solving some of these problems. The most
obvious problem associated with thermal ink-jet printers
has been the tendency of the print produced to be of a
less than desirable definition or quality. Highest
character definition could be achieved if ink were
deposited on the media only where intended and if the ink
would stay where it is deposited without migrating.
Unfortunately, because of phenomena such as that of the
wet ink being drawn into the surrounding dry media by
capillary action, the edges of the printed characters
tend to become less defined. Also, when inks of
differing colors are printed adjacent to each other, the
different colored inks tend to bleed into each other.
Further, the wet ink on print media that have a low
absorption rate (i.e., transparency film) tends to clump
together in small puddles due to surface tension, thus
creating a phenomenon called ink coalescence. Another
problem encountered in ink-jet printing is paper cockle.
The ink used in thermal ink-jet printing is of~a liquid
base. When the liquid ink is deposited on wood-based
papers, it absorbs into the cellulose fibers and causes
the fibers to swell. As the cellulose fibers swell, they
generate localized expansion, which, in turn, causes the
paper to warp uncontrollably in these regions. This
phenomenon is called paper cockle. This can cause a
degradation of print quality due to uncontrolled pen-to-
paper spacing, and can also cause the printed output to
have a low quality appearance due to the wrinkled paper.
Hardware solutions to these problems have been
attempted. Heating elements have been used to dry the
ink rapidly after it is printed. But this has helped
only to reduce smearing that occurs after printing.
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Prior art heating elements have not been effective to
reduce the problems of ink migration that occur during
printing and in the first few fractions of a second after
printing.
5 Other types of printer technology have been
developed to produce high definition print at high speed,
but these are much more expensive to construct and to
operate, and thus they are priced out of the range of
most applications in which thermal ink-jet printers may
l0 be utilized.
To the inventors' knowledge, no prior art solution
to the problem of lack of definition in the product of
thermal ink-jet printers has been, either singly or in
combination with other attempted solutions, successful in
bringing the overall print definition of these printers
within optimal limits.
This invention relates to an ink-jet printer having
conventional print medium, carriage, and handling
mechanisms but also having several unique features which
serve to enhance the definition of the print produced.
These features each individually contribute to the
improved definition and also each contribute to the
operation and effectiveness of the other unique features
of the inventive printer such that they function together
as a system to optimize print definition.
Briefly, the presently preferred embodiment of the
present invention is a thermal ink-jet printer having a
metal platen upon which paper is positioned for printing
and a paper feed mechanism for drawing the paper across
the platen. The platen, which may comprise a flat or
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curved surface, contains a platen heating assembly which
heats the paper prior to, during, and after printing.
The media is heated in an area covering one full swath
immediately prior to the printing area (a preheating
area) to give the medium sufficient time to come up to
temperature. It is heated in the printing area and also
in an area one full swath after the printing area to
insure that the ink is completely dried and/or fixed.
The addition of the preheating area insures that the
medium will be within temperature specifications at the
time of printing. Temperature specifications will vary
between 50°C and Z80°C, depending upon the type of medium
and the ink formulation used and the print density
required. Some minimal experimentation is required to
adjust optimum temperature within the specified range for
each new combination of medium, ink, and print density.
A partial vacuum is created in the interior of the
printer by any conventional vacuum-producing means, such
as a vacuum fan, a vacuum pump, a venturi pump, and the
like. A plurality of holes in the platen heating
assembly serve to expose the paper to this partial vacuum
and thus to draw the paper into contact with the heating
assembly for efficient conduction of heat into the paper.
A pen containing a plurality of ink-jet nozzles is moved
transversely across the paper to position the nozzles for
firing droplets of ink as directed by a microprocessor
controller.
The pen contains a plurality of nozzles for each
color ink utilized in the printer. It has been
discovered by the inventors that the problem of
coalescence of different colored inks is due in great
part to the fact that prior art methods have caused
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different colored inks to be printed simultaneously in
adjacent bands, and thus the different colored inks were
potentially on the medium and adjacent to each other
while both were still wet, and thus the colors tended to
bleed together. Therefore, the nozzles of the inventive
printer are arranged in a column such that adjacent
nozzles for the same color are placed at a uniform
spacing of one index length center to center, but that
adjacent nozzles for different colored inks are placed at
l0 a greater distance (a multiple of the index length).
This provides a physical gap between simultaneously
printed different colors and allows a drying time between
any possible application of different colors to two
adjacent print positions. Although this arrangement is
much more difficult to conceptualize than prior art
nozzle arrangements because a given position on the
medium will not simply be addressed by the similarly
positioned nozzles of each of the groups of nozzles for
different colored inks, it does not increase the
complexity of data flow to the pen since it merely
requires a simple alteration of an already existing data
index number.
In accordance with one aspect of the present
invention there is provided an ink-jet printer comprising
in associative combination:
(a) a paper traction means rigidly affixed to a
printer body for moving a medium to be printed upon in a
medium advancement direction;
(b) a printhead for printing on said medium,
mounted on a printhead carriage, said printhead carriage
being rigidly affixed to said printer body and adapted
for holding said printhead such that said printhead can
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be moved orthogonally relative to said medium advancement
direction; and
(c) a platen heater for heating said medium, said
platen heater being rigidly affixed to said printer body
adjacent to said printhead such that said medium is drawn
between said printhead and said platen heater by said
paper traction means.
An advantage of an aspect of the present invention
is that print definition is improved as compared to prior
art ink-jet printers.
Another advantage of an aspect of the present
invention is that ink migration is halted by rapid drying
of the ink on the medium.
Another advantage of an aspect of the present
invention is that inks of different colors are never
printed simultaneously adjacent to each other and thus
are never in contact with each other when both are wet,
and thus the different colored inks cannot bleed
together.
Another advantage of an aspect of the present
invention is that the ink does not coalesce on print
media that have a low absorption rate.
Another advantage of an aspect of the present
invention is that the print quality on plain paper is
improved, because the paper flatness is better
controlled, due to minimization of paper cockle.
Another advantage of an aspect of the present
invention is that the plain paper output has improved
quality due to the absence of paper cockle.
Another advantage of an aspect of the present
invention is that the printed medium can be handled
immediately after printing because the ink is already
CA 02471970 2004-07-09
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dry.
Yet another advantage of an aspect of the present
invention is that no special coating or preparation of
the print medium is required.
A further advantage of an aspect of the present
invention is that the inventive system will operate over
a wide temperature range, thus making its use appropriate
for a wide variety of print media.
Another advantage of an aspect of the present
invention is that it maintains the relatively low cost to
manufacture associated with thermal ink-jet printers.
These and other advantages of the present invention
will become clear to those skilled in the art in view of
the description of the best presently known modes of
s5 carrying out the invention and the industrial
applicability of the preferred embodiments as described
herein and as illustrated in the several figures of the
drawing.
BRIEF DESCRIPTION OF THF~ D~WINGS
FIG. 1 is a perspective view of an improved thermal
ink-jet printer according to the present invention;
FIG. 2 is a perspective view of the pen assembly of
the present invention;
FIG. 3 is a diagrammatic example of a possible
pattern produced by a single pass of a print pen;
FIG. 4 is a cross sectional side elevational view of
the improved thermal ink-jet printer according to the
present invention; and
FIG. 5 is a bottom plan view of a platen heater
assembly according to the present invention.
CA 02471970 2004-07-09
The present invention is directed to ink-jet
printers, and is independent of the means of ejecting a
5 droplet of ink. Any ink-jet printer, such as
piezoelectric, thermal, or others, is within the scope of
the invention. The embodiments described herein are with
reference to thermal ink-jet printers; however, the
invention is not limited thereto.
10 The best presently known mode for carrying out the
invention is a thermal ink-jet printer constructed such
that the paper or other media to be printed is heated,
and such that the color bands to be printed in each swath
of the printer head are physically separated. The
predominant expected usage of the inventive printer is as
a means of producing high quality color computer output
hardcopy.
The thermal ink-jet printer of the presently
preferred embodiment of the present invention is
illustrated in a perspective view in FIG. 1 and is
designated therein by the general reference character 10.
In many of its substantial components, the printer l0
does not differ significantly from conventional thermal
ink-jet printers. The conventional elements of printer
to include a printer body 12, a paper feed mechanism 14
for advancing the paper 16, and a pen traversing
mechanism 18. The paper feed mechanism may be of the
commonly used mechanisms, such as tractor, friction, or
other drive means.
3o The inventive printer 10 also includes a pen 20.
The detail of the pen assembly 20 is depicted in FIG. 2.
The pen 20 has attached thereon a nozzle plate 22 having,
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in the best presently known embodiment of the invention,
twenty-four nozzles 24 which nozzles 24 are apertures in
the nozzle plate 22 of about 50um in diameter. The size
of the nozzles 24 is selected to provide an ink drop
volume of approximately 115 picoliters plus or minus 10
picoliters, as this volume has been found by the
inventors to be most effective, given the other aspects
of the inventive printer lo, as described herein.
The nozzles 24 are arranged in a staggered column,
l0 as depicted in FIG. 2, in order to allow closer vertical
spacing of the nozzles 24. This arrangement of nozzles
is not unique to the present invention, nor is the
present invention dependent upon this particular
arrangement. Since data controlling ink ejection from
the nozzles is manipulated to time ink ejection to
simulate a single row column of nozzles 24 an
understanding of the present invention might be aided by
thinking of the nozzles 24 as being arranged in a single
row column, as will be discussed hereinafter. To
illustrate the relationship of FIG. 1 to FIG. 2, the
column of nozzles 24 is situated parallel to the
direction of travel 26 of the paper 16 and perpendicular
to the plane of movement 28 of the pen 20 itself. The
arrangement of, nozzles 24 on the pen nozzle plate 22 can
be seen in FIG. 2. The nozzles 24 are grouped into four
sets of six each. Each set is supplied by a different
portion of an ink reservoir (not shown). In the
commercial embodiment, as many as twelve or more nozzles
per color may be employed.
The preferred embodiment of the present invention
has a first group of nozzles for cyan ink 32, a second
group of nozzles for magenta ink 34, a third group of
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nozzles for yellow ink 36, and a fourth group of nozzles
for black ink 38. The distance span 40 between centers
of any two adjacent nozzles 24 of the same group is
approximately 0.085 mm to reflect a conventional
resolution of 300 dots per inch (DPI). Other resolutions
would cause a corresponding change in the distance space.
This center to center distance span 40 is also referred
to as one index length. A group separation span 42 is
the distance between adjacent nozzles 24 of different
color groups 32, 34, 36 and 38 and is approximately 0.170
mm (for 300 DPI), or approximately two index lengths.
Each swath of the pen 20 across the paper 16 moves the
nozzles 24 of each of the color groups 32, 34, 36 and 38
across a band of paper six index lengths wide. At each
location across the paper 16, each of the nozzles 24 may
be directed by the controlling microprocessor (not shown)
to fire a droplet of ink onto .the paper 16. The paper 16
is then advanced six index lengths before the pen 20
makes its next swath.
Data offset is the number of index lengths by which
any nozzle 24 follows the corresponding nozzle 24 in the
preceding color band. The data offset will normally be
the number of nozzles of a given color band plus the
nozzle equivalent of the group separation span. An
example of data offset in the preferred embodiment of the
present invention is the number of index positions the
paper 16 must be advanced before a first magenta ink
nozzle 44 is over the same position on the paper 16 as
was a first yellow ink nozzle 46 during a last previous
pass of the pen 20. The preferred embodiment of the
invention described herein uses a data offset of six
index lines. Data offset is used in prior art printer
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designs. However, heretofore data offset in such
applications has been equal to an actual number of
nozzles 24 used per color of ink. As can be appreciated
from the description herein, the adjustment to the data
offset number is necessary to accommodate the unique
placement of nozzles 24 described herein, and the
associated method of printing.
To further represent the pattern of printing which
is an aspect of the present invention, FIG. 3 illustrates
in diagrammatic form a portion of the medium 16 as it
might appear after a single pass of the pen 20. As can
be appreciated by one skilled in the art, the single pass
illustrated by FIG. 3 is not one of a first three passes,
or a final three passes that would be accomplished to
produce an overall image. This is because at the
beginning and end of any such complete process it is
necessary to make passes using only a portion of the
available nozzle groups 32, 34, 36 and 38 in order that
all of the medium 16 might be printed with all available
colors.
In the example illustrated in FIG. 3, a yellow band
48 has been printed by the first nozzle group 32, a
magenta band 50 has been printed by the second nozzle
group 34, a cyan band 52 has been printed by the third
nozzle group 36, and a black band 54 has been printed by
the fourth nozzle group 38. Of course, one skilled in
the art will recognize that it would be unlikely that it
would be desired to print all possible locations on the
medium 16 with all available colors. However, since in
order to produce any possible desired image it is
necessary to have the capability of doing so, this
extreme example best illustrates and explains the present
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invention.
As is shown in FIG. 3, a group separation span 42
separates the color bands 48, 50, 52 and 54 from each
other on the single pass shown in the drawing. This
prevents different color inks from bleeding together as
they are printed, and allows for a drying time (the time
between consecutive passes of the pen 20) to occur before
there is any possibility of different color inks being
printed on the same or adjacent locations on the medium
to 16. After the pattern shown in the drawing is
accomplished, the medium 16 is advanced by a color band
width 56 in the paper travel direction 26 (which span is,
in the case of the best presently preferred embodiment of
the invention as described herein, six index lengths).
It is evident that, following such advance, the second
nozzle group 34 will not be directly over the yellow band
48. Instead, only four of the six nozzles 24 of the
second nozzle group 34 will be over the yellow band 48,
with the remaining two nozzles 24 of the second nozzle
group 34 being aligned over the group separation span 42
separating the yellow band 48 from the magenta band 50.
After this described advance, the pen 20 is ready to
begin another pass. The example illustrated by FIG. 3
further illustrates the need for the modification to the
data index number heretofore discussed.
Referring now to FIG. 4, wherein is shown a cross-
sectional side elevational view of the printer 10, the
preferred embodiment of the present invention includes a
base plate 58 that, in many respects is not unlike the
base plate of conventional printers. However, the base
plate 58 of the inventive printer includes an aperture 60
wherein is affixed a vacuum fan 62 and a vacuum fan motor
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64. The vacuum fan 62 is positioned so as to draw air
out of a hollow center cavity 66 of the printer 10, thus
creating a partial vacuum within the center cavity 66.
The inventors have found that a vacuum approximately
5 equal to 8 inches of water will work best with the other
aspects of the inventive printer 10, as described herein.
The printer 10 of the preferred embodiment of the
present invention also includes a platen heater assembly
68 which is depicted in a cut away plan view in FIG. 5
10 and can also be seen in an elevational cross sectional
view in FIG. 4, and in the perspective view of FIG. 1.
In one embodiment, the platen heater assembly 68
comprises a low heat capacity heater plate, or platen, 70
to which is affixed a thin foil heater 72. Those skilled
15 in the art will appreciate that other heating means, such
as a heater rod, lamp, or similar means may be employed
in place of the thin foil heater 72, and the heater plate
(or platen) 72 may be flat or curved or partly flat and
partly curved.
A plurality of holes 74 is provided in the heater
plate 70 positioned such that the paper is pulled onto
the heater plate 70 by the vacuum of the hollow center
cavity 66. A conventional paper shim 76 is provided to
mechanically press the paper 16 against the heater plate
70. This also helps to promote effective heat conduction
from the heater plate 70 to the paper 16.
In the preferred embodiment of the invention, the
heater plate 7o is made from a low heat capacity metal to
give the system fast thermal response without requiring
large energy input. With the fast thermal response, the
temperature of the platen heater can be modulated to
match print density on the same plot, thus, optimizing
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energy consumption without slowing down the print speed.
The low heat capacity platen heater also cools down
quickly, thus preventing burns if the user needs to gain
access to the print area (such as to clear a paper jam).
The exposed surface 78 of the heater plate 70 is
designed for low emissivity so as to minimize heat
transfer by radiation to the pen 20. The thin foil
heater 72 is of a conventional nichrome etched foil type,
comprising foil traces 82, which are created by the
conventional process of acid etching a nichrome film that
has been bonded to a 5.08 mm thick film substratum. The
foil heater 72 is coated on its trace side 84 with a
layer approximately 2.54 mm thick of a high temperature
thermoplastic adhesive (not shown). This adhesive bonds
the thin foil heater 72 to the heater plate 70 and
promotes heat conduction from the heater 72 to the heater
plate 70. The heater nichrome foil traces 82 are
terminated on the film substratum at a pair of heater
wires 86 that connect the heater 68 to the heater control
circuitry 88 (FIG. 4). The heater control circuitry 88
is a typical heat regulating circuit which allows for
adjustment and control of the heat output of the heater
68. Different papers 16 or other print media may need
different temperature adjustments for optimal operation
of the printer 10. Further, temperature adjustment may
be necessary because of differing heat tolerances of
alternative media. The inventors have found that the
inventive printer 10, using ordinary bond paper and the
low viscosity inks with which the printer 10 is designed
to best operate, best accomplishes its combined purposes
with a platen temperature of about 120°C plus or minus
20°C.
CA 02471970 2004-07-09
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In the presently preferred embodiment of the
invention 10, the heater plate 70 extends under the
medium 16 such that heating of any given area of the
medium Z6 occurs prior to, during, and after printing
actually occurs on that given area. This improves
performance of the printer 10 by preheating the medium 16
such that solvents in the ink are quickly volatilized
upon contact with the medium, and further by continuing
to heat the medium after printing has occurred so as to
drive off any remaining solvents and to rapidly fix the
ink onto the position where it is deposited.
As is shown above, in great part the printer 10
according to the present invention closely resembles
prior art conventional printers in many of its
components. The substantial differences exist in the
inclusion of (a) a means of heating the print media, (b)
a means of holding the print media against the heater,
and (c) a means of separating simultaneously printed
bands of different colors; collectively, the means of
this invention provide improved definition of dot shape,
reduction of color bleed, reduction of drop coalescence
on low absorption media, and reduction of paper cockling
and wrinkling. No significant changes of materials are
envisioned nor are any special construction techniques
required.
Various modifications may be made to the invention
without altering its value or scope. For example, while
the present invention is described in terms of a printer
for producing multicolored images, the principles and
unique features of the invention, with the exception of
the irregularly spaced nozzles, axe equally applicable to
mono-color printing devices. Further, while it is
CA 02471970 2004-07-09
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expected that the various unique parts of the inventive
printer will be utilized together as a system to maximize
the beneficial effect of each of them, some benefit could
be gained by utilizing the unique features of the present
invention individually.
Another possible modification that could be made to
the present invention would be to remove the ink
reservoirs) from the pen assembly and to connect them
thereto by means of tubing to transfer the inks from the
l0 reservoirs) to the pen.
Another possible modification that could be made
would be to change the number of columns of ink-jet
nozzles incorporated. The number of columns could be
increased as a way of increasing printing speeds by means
of reducing the number of individual positions of the pen
at which the ink-jets are required to fire. This idea
could be extended to the point that there could be
sufficient columns of nozzles to extend all the way
across the print medium, and thus an entire swath could
be printed at one instance of nozzle firing.
The printer could also be constructed using any
number of nozzle groups for any number of different
colored inks. Also, any number of nozzles per ink color
group could be used, and any spacing between color groups
that is an even multiple of the index length could be
used with appropriate changes to the data index.
Integer nozzle spacing may be provided between
nozzles of any given color band to prohibit intra-band
bleeding. The paper advance and the data stream would
then be appropriately modified to accomplish this, as set
forth in the teachings of this invention.
All of the above are only some of the examples of
CA 02471970 2004-07-09
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available embodiments of the present invention. Those
skilled in the art will readily observe that numerous
other modifications and alterations may be made without
departing from the spirit and scope of the invention.
Accordingly, the above disclosure is not intended as
limiting and the appended claims are to be interpreted as
encompassing the entire scope of the invention.
Ink-jet printers are likely to find increased usage
as the technology is advanced. They can operate at
higher speeds than can printers with mechanical print
mechanisms. They are more adaptable to extended
continuous usage since they have no moving parts in the
print head. And because they do not physically impact
the print medium, they can be used on delicate or even
irregularly shaped media. The predominant current usage
of the embodiment of the present invention is in
producing computer data printing for applications such as
letter correspondence and desk top publishing.
The ink-jet printer of the present invention may be
utilized in many applications wherein conventional
printers are used. Because it can print faster than
prior art printers in the same potential price range with
comparable print quality, a single printer of the present
invention may be used to replace several prior art
printers in multi-user computer network systems.
Since the unique properties of the ink-jet printing
system of the present invention are all compatible with a
wide variety of print media and since the print media
needs no special coating or preparation, it is further
CA 02471970 2004-07-09
expected that the inventive printer will be used in a
variety of specialized industrial applications such as
producing drafts of drawings for electrical and
mechanical engineers.
5 Since the improved ink-jet printers of the present
invention may be readily constructed and are entirely
compatible with present conventional computers and
computer interface devices, it is expected that they will
be accepted in the industry as substitutes for
10 conventional printers. The improved print quality,
increased speed, and improved reliability of the
inventive printers will make them desirable as
substitutes and in new installations. For these and
other reasons, it is expected that the utility and
15 industrial applicability of the invention will be both
significant in scope and long-lasting in duration.