Image-related device having image-medium receiving tray, and a tray for same, and a method for designing such tray

An image-related device has an image-medium receiving tray. The tray is designed by a method that enables the tray to control the contouring of sheets of image medium during reception. The tray has a planar surface and a curved surface. The curved surface is designed by selecting a series of transverse and longitudinal curves to define a curved surface that is generally concave in the transverse direction while also sloping upward in the longitudinal direction. The combined concave and sloped shape of the curved surface causes the leading-edge region of the image medium to transversely curl and thereby obtain sufficient rigidity to extend beyond the front end of the tray. In addition, the curved surface--operating in conjunction with the kickout mechanism of the device--interacts with sheets of medium in a way that causes the sheets to land on top of each other instead of sliding against each other, thereby reducing the possibility of smearing while at the same time producing a neat, evenly stacked pile of media.

FIELD OF THE INVENTION 
This invention relates generally to the way sheets of image medium are 
collected and to apparatus that controls the collection of sheets; and 
more specifically to an image-related device having an image-medium 
receiving tray, and to a tray for receiving image medium, and to a method 
for designing a tray that controls the contouring of sheets during 
reception. 
Throughout this document the term image medium refers to a medium such as 
paper or transparency that either carries an image, i.e. an image-bearing 
medium, or is capable of having an image formed on it, i.e. printing 
medium. Similarly the term image-related device is hereby defined as 
encompassing both (1) a device that forms an image on image medium--such 
as a printer, copier, or a facsimile (FAX) machine in the receiving 
mode--and (2) a device that senses an image on an image-bearing medium and 
produces a corresponding electrical signal--such as a scanner or a FAX 
machine in the sending mode. Thus "image-related device" for present 
purposes is essentially synonymous with "hard-copy apparatus". 
BACKGROUND OF THE INVENTION 
The functionality of an image-related device is greatly enhanced when it is 
able to consistently provide the user with neat and usable output. The 
image-medium receiving tray of a device plays a crucial role in providing 
such enhancement. 
An effective tray must be able to collect media of different sizes and 
types and do so in a manner that does not disturb, e.g. smear, the image. 
To be even more effective a tray should evenly stack the medium it 
collects. 
To be all of the above, a tray must be designed with consideration given to 
the operating parameters of the associated image-related device. For 
example, the type of device determines the type and size of medium that 
the tray must handle--thereby affecting the size of the tray. 
The device also defines the speed and angle at which the tray receives the 
medium--thereby also affecting the size, the angle at which the tray 
interfaces with the device, and possibly the shape of the tray. Current 
techniques of tray design are discussed below within the context of 
several design considerations. 
(a) Size of image medium--Most devices process image medium of different 
sizes; accordingly the tray must be able to accommodate the same variety 
of sizes. To fulfill this requirement many devices simply use a large tray 
to handle the largest possible medium that the device can output. 
It is desirable, however, that the device and tray be both compact and 
economical. These characteristics are preferably obtained by reducing the 
overall size of the tray and accommodating larger medium in other ways. 
When the leading-edge portion of a sheet of medium curls downward relative 
to the trailing-edge portion of the medium--a phenomenon familiarly known 
as "flopping"--the system may lose control of the medium. In particular 
with a short tray, large medium flops over the front end of the tray 
(i.e., the end farthest from other components of the image-related device) 
and may completely slide over and off the front end of the tray. 
One mechanism for accommodating large medium and preventing flopping is a 
multipiece tray. A multipiece tray includes a main tray and an extension 
tray--mechanically attached to the main tray and usually stowed beneath or 
within the main tray. The extension tray is extended to create, in 
combination with the main tray, a tray large enough to collect large 
medium. 
Though adequate to accommodate large medium and prevent flopping, a 
multipiece tray is undesirable for several reasons. First, repeated 
extension and retraction of the extension tray and the stress it places on 
the mechanism joining the trays results in a device which is susceptible 
to breakage. Second, multipiece trays are a significant inconvenience to 
the user, who must repeatedly extend and retract the extension tray to 
accommodate various media. 
Third, an extension tray and the associated mechanical attachments increase 
the amount of material required to produce the tray and thereby increase 
overall cost. Finally, when extended the extension tray creates a 
discontinuous and rough surface over which sheets of medium must slide. 
This discontinuity often causes sheets to slide erratically, resulting in 
an uneven stack of medium. 
A second technique to accommodate larger medium is to transversely curl the 
medium along its entire length. This is usually implemented through use of 
a cylindrical-surface tray. Such a tray forces the medium to transversely 
curl--thereby giving rigidity to the medium. With this rigidity the medium 
can extend over the front end of the tray without flopping. A beneficial 
feature of this technique is that it operates relatively independently of 
the size of the tray. Though somewhat appealing, this technique is 
undesirable under certain operating conditions as explained below. 
(b) Type of image processing--Another operating parameter to be considered 
when designing a tray is the type of image processing the device performs. 
An effective tray must collect and stack image medium in a manner that 
does not disturb the image just processed by the device. For example, in a 
liquid-ink device a sheet having wet ink is likely to smear when a 
subsequent sheet contacts it. One method of avoiding image disturbance in 
such a context is taught in U.S. Pat. No. 5,299,875 of Hock et al. 
In Hock et al. a set of wing deflectors positioned near the exit slot of a 
portable inkjet printer imparts a W-shaped bow on the leading-edge portion 
of an emerging sheet. This bow imparts rigidity to the leading-edge 
portion--which allows it to extend over and above the output platform of 
the printer and the trailing edge of any already-dropped sheet or sheets 
at rest on the platform. 
As the sheet continues to emerge, however, and the leading-edge portion of 
the sheet moves farther from the deflectors it begins to lose rigidity. 
When the trailing edge of the sheet exits the printer, the leading-edge 
portion completely loses rigidity and flops onto the already-dropped 
sheet--making initial contact toward the leading edge of the sheet. The 
trailing-edge portion, still bowed by the deflectors, remains at rest on 
top of the deflectors--separate from the already-dropped sheet. 
When a subsequent emerging sheet contacts the bowed trailing edge of the 
previously exited (but not yet completely dropped) sheet it pushes the 
trailing edge forward past the deflectors. The trailing-edge portion loses 
its rigidity and falls onto the trailing-edge portion of the 
already-dropped sheet. 
In limiting the initial contact between the sheets to their leading-edge 
portions, this device reduces the possibility of smearing since the 
leading-edge portion of the already-dropped sheet is driest. Also, in 
keeping the trailing-edge portions of printed sheets separate until a 
subsequent sheet begins to emerge, this device allows more time for the 
trailing-edge portion of the already-dropped sheet to dry before another 
sheet lands on top of it. 
While generally effective in preventing smearing this technique is somewhat 
undesirable because it curls the medium immediately upon exiting the 
device--thereby curling the medium while the ink is wettest. Because the 
medium is curled while the ink is drying, the medium is likely to have a 
residual curl. 
In addition, while Hock et al. teach a relevant principle, their 
implementation of the principle is in a portable ink-jet printer which 
does not use a tray to collect its output; it merely drops its output onto 
a table. Such operation is outside the field of the present invention as 
defined above, and undesirable in a printer intended for essentially fixed 
installation--as table space is assumed to be at a premium, and a printer 
is commonly positioned with its tray extending over the table edge (except 
when not in use and stowed within the printer). 
(c) Stacking of image medium--A common problem associated with trays is 
uneven stacking of sheets of image medium. This problem occurs when sheets 
ejected from a device slide in a disorderly fashion on the tray surface 
and particularly on previously deposited sheets. 
The result is a pile of misaligned or sometimes even scattered sheets. The 
user has no option but to manually even the edges of the medium. 
A factor contributing to uneven stacking is the manner in which the tray 
receives the medium from the device. Some typical devices have their trays 
positioned so that the leading edge of each sheet of medium slides from 
the back of the tray (i.e., the end closest to other components of the 
image-related device) toward the front. While sliding, the medium 
encounters resistance and discontinuities in the tray surface or 
resistance from previously deposited medium. This resistance sometimes 
causes the medium to move erratically. 
A common technique to achieve even stacking is to add stops at the front 
end or along the sides of the tray, or both. As with the multipiece tray 
design previously mentioned, such mechanical additions to the tray are 
inconvenient, costly, and susceptible to breakage. 
Another mechanism for even stacking in inkjet devices uses a pair of 
longitudinally extending wings driven by an electromechanical assembly. 
The wings initially hold a newly printed sheet spaced above a previously 
printed sheet. After printing is complete, the wings move apart, allowing 
the printed sheet to drop onto the previously printed sheet. 
Therefore the sheets fall into an orderly stack. Though quite effective in 
stacking medium, this mechanism may be relatively more costly. 
(d) Summary of related techniques--As previously stated, common techniques 
for designing effective trays generally include the use of a simple planar 
surface with various mechanical additions such as extensions and stops. 
More sophisticated designs have used cylindrical surfaces to control the 
shape of the medium or electromechanical wings to control the placement of 
medium. 
These techniques, while providing trays that enhance device functionality, 
create problems in other areas. For example, transverse curling of wet 
medium--either by deflectors or by a cylindrical surface--causes the 
medium to have a residual curve. The use of a multipiece tray creates 
surface discontinuities which may cause uneven stacking of medium. A final 
problem is that the trays produced by some of these techniques--with their 
extensions and stops or electromechanical wings--are economically 
inefficient. 
(e) Previously unrelated techniques--In a field not previously associated 
with the interaction between trays and solid but very flexible image 
media, it is known to use B-spline curves to design surfaces. Such surface 
design is common in the automotive and aerospace industries, where the 
interaction between surfaces and fluids is closely scrutinized to optimize 
machine performance and efficiency. Such techniques are also common in the 
field of industrial design, where they are used in shaping common 
household products to help find aesthetically pleasing forms. 
As previously stated, the B-spline surface design technique has not been 
previously associated with, or suggested for use in, the functional design 
of image-medium receiving trays. 
(f) Conclusion--Thus important aspects of the technology used in the field 
of the invention remain amenable to useful refinement. 
SUMMARY OF THE DISCLOSURE 
The present invention introduces such refinement. In its preferred 
embodiments, the present invention has several aspects or facets that can 
be used independently, although they are preferably employed together to 
optimize their benefits. 
In preferred embodiments of a first facet or aspect, the invention is an 
image-medium receiving tray for collecting and stacking sheets of image 
medium from an image-related device. The image-related device includes at 
least one of a printer, copier, scanner or FAX machine. 
The image-medium receiving tray includes a curved surface having a 
longitudinal central region, two side regions, and a boundary. The side 
regions substantially smoothly curve upward from the central region in the 
lateral direction and upward from the boundary in the longitudinal 
direction. The substantially smoothly curved surface may have relatively 
small or minor surface disruptions, such as cavities or through-holes, 
that do not affect the behavior of the sheets. 
The tray also includes some means for linking the curved surface to the 
image-related device. For purposes of generality and breadth in expressing 
the invention these means will be called simply "the linking means". 
The foregoing may constitute a description or definition of the first facet 
of the invention in its broadest or most general form. Even in this 
general form, however, it can be seen that this aspect of the invention 
significantly mitigates the difficulties left unresolved in the art. 
In particular, the combined transverse and longitudinal curves of the 
surface ensure that the leading-edge portion of the image medium is 
transversely curled to provide sufficient rigidity to extend beyond the 
front end of the tray. In addition, the curved surface interacts with 
sheets of medium in a way that causes the sheets to land on top of each 
other instead of sliding against each other and thereby reduces the 
possibility of smearing--a particularly beneficial feature when the tray 
is used in conjunction with a liquid-ink device. Also, the controlled 
interaction between the curved surface and the sheets results in a neat, 
evenly stacked pile of media. 
For these benefit to be fully realized the tray preferably operates in 
conjunction with other elements of the device so that the leading-edge 
portion of an exiting sheet reaches the elevated region of the curved 
surface before the trailing edge reaches the lower region of the curved 
surface. These "other elements" are detailed later in this document. 
An already-exited sheet, at rest on the tray, has a leading-edge portion on 
the elevated region of the curved surface and a trailing-edge portion on 
the lower region of the curved surface. As a sheet emerges from the device 
it extends over and above the trailing-edge portion of the already-exited 
sheet and makes initial contact with the leading-edge portion of the 
already-exited sheet. 
The trailing-edge portion of the just-exited sheet then lands, most 
typically floating down gently, on the trailing-edge portion of the 
already-exited sheet. Thus the just-exited sheet comes to rest on top of 
the already-exited sheet without sliding along the sheet--thereby reducing 
the possibility of smearing while at the same time resulting in a even 
stack of sheets. 
In Hock et al., as previously described, a similar concept is used to 
prevent smearing. That concept, however, is employed in a device 
structurally very distinct from our tray--and, as will be seen shortly, 
the compound curves of the present invention impart benefits far beyond 
those of the Hock system. 
Although this aspect of the invention in its broad form thus represents a 
significant advance in the art, it is preferably practiced in conjunction 
with certain other features or characteristics that further enhance 
enjoyment of overall benefits. 
For example, it is preferred that the linking means include a generally 
planar surface having a boundary and naturally some mechanical device to 
couple the tray with the image-related device. It is also desirable that 
the planar surface and the curved surface substantially smoothly blend 
together at their respective boundaries. By "blend" we mean a continuous 
transition between the planar and shaped surfaces. 
It is also preferred that the combined longitudinal length of the curved 
surface and the planar surface be shorter than letter-size paper and that 
the curved surface and the planar surface be for supporting sheets of 
image medium. It is further desirable that the image-medium receiving tray 
comprise no other means for supporting such sheets. 
It is further preferred that the lateral widths of the planar surface and 
curved surface be narrower than letter-size paper. By "letter-size paper" 
we mean paper having dimensions about 22 by 28 cm (81/2 by 11 inches). 
These small dimensions are possible because of the gently curved surface of 
the tray which imparts rigidity on the medium so that it can extend beyond 
the front end of the tray, i.e., the end remote from the device. 
Remarkably, our letter-size tray is able to support legal-size medium, 
having dimensions of about 22 by 36 cm (81/2 by 14 inches)--without 
flopping and also without residual curl. 
It is yet further preferred that the image-medium receiving tray have no 
longitudinal image-medium stop. It is still further preferred that the 
planar surface have a maximum width and that the curved surface further 
comprise two corners substantially smoothly curving upward from their 
respective side regions in a lateral direction, and extending laterally 
beyond the maximum width of the planar surface. 
In preferred embodiments of a second independent aspect or facet, the 
invention is an image-medium receiving tray for collecting and stacking 
sheets of image medium from an image-related device that comprises at 
least one of a printer, copier, scanner or FAX machine. The image-medium 
receiving tray includes a curved surface defined substantially by the 
following equations in conjunction with Table 1: 
##EQU1## 
where: V.sub.i,j are the coordinates of the control vertices; 
##EQU2## 
w.sub.i,j being a weight function; 
##EQU3## 
is the basis function in the u direction, where the first-order basis 
functions are: 
##EQU4## 
and having values of u in accordance with 
EQU T.sub.knot (u) =u.sub.min,u.sub.min , . . . u.sub.min,u.sub.k . . . 
u.sub.M-k-1 ,u.sub.max,u.sub.max . . . u.sub.max ! (Eq. 4) 
where the total number of u values is M=k+n, and the number of u.sub.min 
and u.sub.max is equal to k; 
##EQU5## 
is the basis function in the v direction where the first-order basis 
functions are: 
##EQU6## 
and having values of v in accordance with 
EQU T.sub.knot(v) =v.sub.min,v.sub.min, . . . v.sub.min,v.sub.l, . . . 
v.sub.M-l -1,v.sub.max,v.sub.max, . . . v.sub.max ! (Eq. 6) 
where the total number of v values is M=l +m, and the number of v.sub.min 
and v.sub.max is equal to l; 
n is the number of control vertices in the u direction; 
m is the number of control vertices in the v direction; 
k is the order of the basis function in the u direction which is equal to 
the order of the B-spline in the u direction; 
l is the order of the basis function in the v direction which is equal to 
the order of the B-spline in the v direction. 
(In the computer-generated Table 1, the letter "D" indicates that the full 
data are being maintained to "double precision", the numbers actually 
tabulated here being only the first twelve digits. The following algebraic 
sign and final two digits represent the power of ten; thus the tabulation 
is essentially in scientific notation.) 
The tray also includes means for linking the curved surface and 
image-related device--again, the "linking means". 
TABLE 1 
__________________________________________________________________________ 
Curved Surface Definition 
__________________________________________________________________________ 
Surface type: open, nonperiodic, rational B-spline in both u and v 
directions 
Order of B-spline: 
u direction: k=5 
v direction: l=4 
Numbers of control vertices: 
u direction: n=13 
v direction: m=12 
Knot vector, T.sub.knot(u), in u direction: 
-1.10045330958D+01, 
-1.10045330958D+01, 
-1.10045330958D+01, 
-1.10045330958D+01, 
-1.10045330958D+01, 
1.04593460712D+00, 
1.04593460712D+00, 
1.04593460712D+00, 
1.04593460712D+00, 
1.10045294954D+02, 
1.10045294954D+02, 
1.10045294954D+02, 
1.10045294954D+02, 
1.21049828049D+02, 
1.21049828049D+02, 
1.21049828049D+02, 
1.21049828049D+02, 
1.21049828049D+02! 
Knot vector, T.sub.knot(v), in v direction: 
-1.36399472686D+01, 
-1.36399472686D+01, 
-1.36399472686D+01, 
-1.36399472686D+01, 
1.D+00, 1.D+00, 
1.D+00, 2.1D+01, 2.1D+01, 
1.4225070206D+02, 
1.4225070206D+02, 
1.4225070206D+02, 
1.56422579271D+02, 
1.56422579271D+02, 
1.56422579271D+02, 
1.56422579271D+02! 
w.sub.i,j = 1.0 for all control vertices 
x, y, z coordinates of control vertices, V.sub.i,j in the u and v 
directions: 
i,j x-axis y-axis z-axis 
0,0 -1.12349933671D+01 
-1.38626377081D+01 
5.56521174617D-02 
1,0 -8.62036451534D+00 
-1.38626377034D+01 
5.56521174428D-02 
2,0 -5.88294348505D+00 
-1.38626376985D+01 
5.56521174231D-02 
3,0 -3.01299212726D+00 
-1.38626376933D+01 
5.56521174024D-02 
4,0 0.D+00 -1.38626376879D+01 
5.56521173807D-02 
5,0 2.72532338742D+01 
-1.3862637639D+01 
5.56521171841D-02 
6,0 5.45087993677D+01 
-1.38626222758D+01 
8.1516786184D-02 
7,0 8.17595984574D+01 
-1.38625736943D+01 
1.34412485333D-01 
8,0 1.08999360346D+02 
-1.38624620928D+01 
2.10814121479D-01 
9,0 1.11749476129D+02 
-1.38624508255D+01 
2.18527600997D-01 
10,0 1.14382330974D+02 
-1.38624400379D+01 
2.25912544189D-01 
11,0 1.16906547814D+02 
-1.38624296946D+01 
2.32993110393D-01 
12,0 1.19330115481D+02 
-1.3862419763D+01 
2.39791682357D-01 
0,1 -1.12345873692D+01 
-9.51065047897D+00 
3.81808893808D-02 
1,1 -8.62004432704D+00 
-9.51065047734D+00 
3.81808893742D-02 
2,1 -5.88271903114D+00 
-9.51065047564D+00 
3.81808893674D-02 
3,1 -3.01297411961D+00 
-9.51065047385D+00 
3.81808893602D-02 
4,1 0.D+00 -9.51065047198D+00 
3.81808893527D-02 
5,1 2.72521664668D+01 
-9.510650455D+00 
3.81808892845D-02 
6,1 5.450593122D+01 
-9.51064512881D+00 
5.59106840217D-02 
7,1 8.17564286983D+01 
-9.51062828629D+00 
9.21699114385D-02 
8,1 1.08999360346D+02 
-9.5105895956D+00 
1.44542550467D-01 
9,1 1.11749796147D+02 
-9.5105856894D+00 
1.49830071767D-01 
10,1 1.14382940319D+02 
-9.51058194948D+00 
1.54892370391D-01 
11,1 1.16907418053D+02 
-9.51057836362D+00 
1.59746008376D-01 
12,1 1.19331220272D+02 
-9.51057492049D+00 
1.64406329848D-01 
0,2 -1.12341580969D+01 
-4.90918015587D+00 
1.97081013669D-02 
1,2 -8.61970578355D+00 
-4.90918015587D+00 
1.97081013669D-02 
2,2 -5.88248171012D+00 
-4.90918015587D+00 
1.97081013669D-02 
3,2 -3.01274934702D+00 
-4.90918015587D+00 
1.97081013669D-02 
4,2 0.D+00 -4.90918015587D+00 
1.97081013669D-02 
5,2 2.72510378689D+01 
-4.90918015587D+00 
1.97081013669D-02 
6,2 5.45028986487D+01 
-4.90918015587D+00 
2.88366488847D-02 
7,2 8.17530772127D+01 
-4.90918015587D+00 
4.75055155311D-02 
8,2 1.08999360346D+02 
-4.90918015587D+00 
7.44709588388D-02 
9,2 1.11750134512D+02 
-4.90918015587D+00 
7.71933795244D-02 
10,2 1.14383584539D+02 
-4.90918015587D+00 
7.97998313351D-02 
11,2 1.16908338007D+02 
-4.90918015587D+00 
8.22988421901D-02 
12,2 1.19332388057D+02 
-4.90918015587D+00 
8.4698312897D-02 
0,3 -1.12337025098D+01 
-2.56340649229D-02 
1.02908817787D-04 
1,3 -8.61934648693D+00 
-2.56340649229D-02 
1.02908817787D-04 
2,3 -5.88222984104D+00 
-2.56340649229D-02 
1.02908817787D-04 
3,3 -3.01261692572D+00 
-2.56340649229D-02 
1.02908817787D-04 
4,3 0.D+00 -2.56340649229D-02 
1.02908817787D-04 
5,3 2.72498400866D+01 
-2.56340649229D-02 
1.02908817787D-04 
6,3 5.44996801732D+01 
-2.56340649229D-02 
1.02908817787D-04 
7,3 8.17495202598D+01 
-2.56340649229D-02 
1.02908817787D-04 
8,3 1.08999360346D+02 
-2.56340649229D-02 
1.02908817787D-04 
9,3 1.1175049362D+02 
-2.56340649229D-02 
1.02908817787D-04 
10,3 1.14384268193D+02 
-2.56340649229D-02 
1.02908817787D-04 
11,3 1.16909314186D+02 
-2.56340649229D-02 
1.02908817787D-04 
12,3 1.19333627094D+02 
-2.56340649229D-02 
1.02908817787D-04 
0,4 -1.12330801207D+01 
6.64590101828D+00 
-2.66802375822D-02 
1,4 -8.61885564277D+00 
6.64590101828D+00 
-2.66802375822D-02 
2,4 -5.88188575636D+00 
6.64590101828D+00 
-2.66802375822D-02 
3,4 -3.01243602166D+00 
6.64590101828D+00 
-2.66802375822D-02 
4,4 0.D+00 6.64590101828D+00 
-2.66802375822D-02 
5,4 2.72482037661D+01 
6.64590101828D+00 
-2.66802375822D-02 
6,4 5.4495283333D+01 
6.64590101828D+00 
-3.91509758304D-02 
7,4 8.17446610171D+01 
6.64590101828D+00 
-6.46549838761D-02 
8,4 1.08999360346D+02 
6.64590101828D+00 
-1.01493153868D-01 
9,4 1.11750984208D+02 
6.64590101828D+00 
-1.05212321206D-01 
10,4 1.14385201127D+02 
6.64590101828D+00 
-1.08772798227D-01 
11,4 1.16910644774D+02 
6.64590101828D+00 
-1.12186254425D-01 
12,4 1.19335313929D+02 
6.64590101828D+00 
-1.15463501165D-01 
0,5 -1.12324577316D+01 
1.33174361015D+01 
-5.34633839821D-02 
1,5 -8.61836479862D+00 
1.33174361015D+01 
-5.34633839821D-02 
2,5 -5.88154167167D+00 
1.33174361015D+01 
-5.34633839821D-02 
3,5 -3.01225511759D+00 
1.33174361015D+01 
-5.34633839821D-02 
4,5 0.D+00 1.33174361015D+01 
-5.34633839821D-02 
5,5 2.72465674456D+01 
1.33174361015D+01 
-5.34633839821D-02 
6,5 5.44908864928D+01 
1.33174361015D+01 
-7.84048604786D-02 
7,5 8.17398017743D+01 
1.33174361015D+01 
-1.2941287657D-01 
8,5 1.08999360346D+02 
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-2.24475199474D-01 
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10,11 
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1.16476937998D+02 
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12,11 
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3.4358300159D+01 
__________________________________________________________________________ 
The foregoing may constitute a description or definition of the second 
facet of the invention in its broadest or most general form. Even in this 
general form, however, it can be seen that this aspect of the invention 
too significantly mitigates the difficulties left unresolved in the art. 
In particular these equations, with their specified coefficients, define a 
highly optimized curved surface for controlling the behavior of sheets of 
image medium. These equations and coefficients represent the best 
implementation of the invention found so far. 
Of course a reasonable range of tolerances for the coefficients is to be 
accepted without significantly altering the overall functionality of the 
tray, and therefore is encompassed within the term "substantially" above. 
A tray as so defined is accordingly within the scope of the corresponding 
appended claims. 
In preferred embodiments of a third aspect, the invention is an 
image-related device for handling sheets of image medium and for 
incrementally scanning images thereon or forming images thereon, or both. 
The device includes some means for processing an image on each sheet, 
which again for purposes of generality will be called simply the 
"image-processing means". 
The invention also includes some means for sequentially supplying multiple 
sheets to the image-processing means. We call these means the "supplying 
means". The device further includes a kickout mechanism for removing 
sheets from the image-processing means. 
Also included is an image-medium receiving tray for receiving sheets from 
the kickout mechanism and collecting and stacking the sheets. The tray 
includes means for transversely curling a leading-edge portion of each 
sheet, and means for flattening a trailing-edge portion of each sheet. We 
call these means the "curling means" and "flattening means" respectively. 
The foregoing may constitute a description or definition of the third facet 
of the invention in its broadest or most general form. Even in this 
general form, however, it can be seen that this aspect of the invention 
too significantly mitigates the difficulties left unresolved in the art. 
In particular, the image-medium receiving tray acts in concert with the 
other elements of the image-related device to form a functionally enhanced 
device that collects and stacks its final output in a manner that does not 
disturb the image on the medium. In addition, the device collects an 
evenly stacked pile of medium. 
Although this third aspect of the invention in its broad form thus 
represents a significant advance in the art, it is preferably practiced in 
conjunction with certain other features or characteristics that further 
enhance enjoyment of overall benefits. 
For example, it is preferred that the image-processing means comprise 
wet-process means for forming images on each such sheet by aggregation of 
liquid ink. It is also preferred that the image-medium receiving tray be 
positioned and oriented relative to the kickout mechanism so that the 
curling means intercept the leading-edge portion of each sheet first and 
thereafter the flattening means receive the trailing-edge portion of each 
sheet. 
As previously mentioned, this feature of the leading-edge portion of the 
medium reaching the curling means first is particularly powerful in 
printing machines that use liquid ink. For this feature to be realized it 
is important that the kickout mechanism of the device cooperate with the 
tray. 
By "kickout mechanism" we mean those mechanisms located within the device 
which drive sheets of medium toward the tray at a specified angle and 
velocity. Such mechanisms typically include a set of engaging motorized 
rollers or wheels. The angle and velocity of the exiting medium are set so 
that the leading-edge portion of the medium reaches the curling means 
before the trailing edge reaches the flattening means. 
In preferred embodiments of a fourth aspect or facet, the invention is a 
method for designing an image-medium receiving tray that will control the 
contouring and reception of image-medium sheets from an image-related 
device. The design method includes the step of establishing a set of 
transverse curves and a set of longitudinal matchline curves to generally 
define a part of the tray surface. 
In this method, the transverse curves and longitudinal matchline curves are 
at least quadratic B-splines. The method also includes the step of 
interconnecting adjacent ones of the transverse curves along paths of the 
longitudinal matchline curves to further define the part of the tray 
surface. 
The foregoing may constitute a description or definition of the fourth 
facet of the invention in its broadest or most general form. Even in this 
general form, however, it can be seen that this aspect of the invention 
too significantly mitigates the difficulties left unresolved in the art. 
In particular, the design method uses B-spline curves to define the tray 
surface so that the interaction between the image medium and the surface 
may be more precisely defined and the behavior of the medium better 
controlled. This method extends the use of known design 
techniques--commonly associated with the field of fluid mechanics--into an 
area of solid-but-very-flexible-medium mechanics, with which such 
techniques have not been previously associated. 
Although this fourth aspect of the invention in its broad form thus 
represents a significant advance in the art, it is preferably practiced in 
conjunction with certain other features or characteristics that further 
enhance enjoyment of overall benefits. 
For example, it is preferred that the transverse curves and longitudinal 
matchline curves be adjusted to further define the part of the surface as 
curved, for curling a leading-edge portion of each sheet to give the 
leading-edge portion sufficient rigidity for extending beyond the front 
end of the tray (i.e., the end farthest from the other components of the 
image-related device). At the same time it is preferred that the 
transverse curves and longitudinal matchline curves be adjusted to 
restrain both the tightness and longitudinal extent of the curling so that 
the image medium is not strongly curled where it is wettest, and so tends 
not to retain a residual curl. This adjustment is particularly relevant 
for a tray that is to be used with an image-related device that operates 
using a wet process. 
It is also desirable that a generally planar part of the tray surface be 
defined for flattening a trailing-edge portion of each sheet. It is 
further preferred that the transverse curves and longitudinal matchline 
curves be further adjusted so that for a specified initial height and 
velocity of the sheet, the curved surface intercepts the leading-edge 
portion of the sheet first and thereafter the planar surface receives the 
trailing-edge portion of the sheet.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Preferred embodiments of our invention provide an image-related device 
which includes a one-piece image-medium receiving tray (FIG. 1), and a 
tray for such a device. The tray interacts with sheets of medium from the 
other components of the device, in a way that allows the device to collect 
and neatly stack the sheets without disturbing the images on the sheets. 
As previously mentioned, for the device to function in this manner certain 
elements of the device must cooperate--specifically the kickout mechanism 
and the tray. In addition, the operating parameters (e.g. image-medium 
size and image processing type) of the associated device must be taken 
into account when designing the tray. 
Following is a physical description of a preferred embodiment of our 
image-related device and tray. 
Physical Description 
Although the tray 11 (FIG. 1) is smooth and continuous, for design and 
descriptive purposes it is divided into a planar surface 12 at the back 
(i.e., again, the end closest to the other components of the image-related 
device) and a three-dimensionally curved surface 13 at the front. As 
stated previously, the smooth and continuous curved and planar surfaces 
may have relatively small or minor surface disruptions such as cavities or 
throughholes that do not significantly affect the functionality of the 
tray. 
The curved surface 13 (FIG. 2) is further conceptually divided, having two 
side regions 21 separated by a longitudinal central region 22. Extending 
each side region outward 21 is a corner 23. These corners 23 extend the 
curved surface 13 laterally beyond the longitudinal edges 27 of the planar 
surface 12. 
The curved surface also includes a back boundary 24 and a front end 43. 
Located at the front end 43 is a handle 44 for gripping the tray 11 during 
installation and removal from--and stowing within--the main chassis of the 
image-related device. 
The planar surface 12 has a front boundary 25, which smoothly blends with 
the back boundary 24 of the curved surface 13. The boundaries 24, 25, are 
aids to assist in describing the shape of the tray surface. The tray 11 is 
all one piece, and the boundaries 24, 25 between the smoothly blended 
planar surface 12 and subtly curved surface 13 cannot be perceived by the 
unaided eye or touch. The planar surface 12 also has a curved planar end 
26. 
The curved surface 13 (FIGS. 5 and 6) is very generally concave in the 
transverse direction with its sides 21 curving upward from the central 
region 22 in a lateral direction. The corners 23 extend the side regions 
21 outward to left and right, and continue the same general curved shape. 
While concave transversely, the curved surface 13 (FIG. 3) is also curved 
longitudinally--i.e., the sides 21 curve upward from the boundary 24 in 
the longitudinal direction. The combined concave and upward curves result 
in a curved surface 13 (FIG. 6) that is concave at the far periphery 61 
and gradually slopes downward to the boundary 24. A more-detailed 
description of the curved surface 13 is provided later in this document. 
The underside of the tray 11 (FIGS. 7 and 8) includes a pair of side guides 
74 and a center guide rib 72. Near the end of each guide 74 is a stop 73. 
The side guides 74 and center guide rib 72 provide the means to guide the 
tray 11 in and out of the chassis during stowing. The stops 73 prevent the 
tray 11 from being inadvertently removed from the device chassis while the 
tray 11 is being extended from a stowed position. 
Also on the underside is a pattern of support ribs 71. The arrangement, 
number and dimensions of the ribs 71 are selected to provide strength to 
the tray surface, while at the same time minimizing the amount of plastics 
required to form a tray. 
Except in thickness, the tray 11 (FIG. 1) is smaller than a letter-size 
sheet of paper. As previously stated, this is made possible by the 
combined transverse and longitudinal curves of the curved surface 13. 
These curves impart rigidity to a sheet of medium so that the sheet can 
extend beyond the front end 43 of the tray without flopping--while at the 
same time avoiding adverse effects of strong curvature. Because of this 
feature the tray can be much smaller than the largest medium it is 
expected to handle, contrary to the requirements of many common trays. 
Notably absent from the tray 11 are discrete side guards and a discrete 
longitudinal stop. As will be explained in the functional description 
which follows, the need for such items is eliminated by the manner in 
which our tray interacts with the medium it collects. 
The tray as described above includes these approximate dimensions: 
______________________________________ 
MILLI- 
METERS DIMENSION 
______________________________________ 
175 distance between the planar surface left 
edge 41 (FIG. 2) and the planar surface right edge 28 
182 distance between the left guide outer 
edge 29 and the right guide outer edge 42 
6 distance from the planar surface top 32 
(FIG. 3) to the guide bottom 31 
250 distance from the planar edge 45 
(FIG. 2) to the curved surface extreme point 46 
215 distance between the left corner edge 51 
(FIG. 5) and the right corner edge 52 
170 distance from the planar edge 45 (FIG. 8) 
to the guide end 83 
169 distance between the right guide inner edge 
81 and the left guide inner edge 82. 
______________________________________ 
Specific Physical Description 
The curved surface of the tray is geometrically modeled using B-spline 
curves. A general explanation of these curves and surfaces is available in 
Bartels et al., An Introduction to Splines For Use In Computer Graphics & 
Geometric Modeling (1987). 
We model the curved surface 13 (FIG. 1a) by creating a meshed surface using 
the following curves: a top polynomial curve 14, an intermediate 
polynomial curve 15, a straight line 16, and a set of matchline curves 17. 
The surface is then formed by lofting the top polynomial curve 14, along 
the paths of the set of matchline curves 17, to the intermediate 
polynomial curve 15 and finally to the straight line 16. While we prefer 
lofting to form the tray surface, other known techniques such as 
extrusion, ruling and sweeping are comparably effective and are to be 
understood as within the scope of our invention. 
The selection of curves is determined by the operating parameters of a 
specific image-related device as detailed in the following functional 
description. The curves result in a surface 13 (FIG. 1a) that 
longitudinally curves upward to intercept medium emerging from the device. 
The surface also curves transversely to impart sufficient rigidity to the 
medium so it can extend over the front end 43 of the tray 11 without 
flopping. 
Our selection of longitudinal and transverse curves gives the surface a 
gentleness of curve to restrain the leading-edge portion of the medium 
from curling too much. It is desirable to keep the transverse curve of the 
surface to a minimum to limit the tightness and longitudinal extent of the 
transverse curl of the medium. Likewise, it is desirable to keep the 
longitudinal curve to a minimum to limit the longitudinal curl of the 
medium. 
Minimizing the curves in this way is important for several reasons. First, 
in minimizing the steepness of the surface curves, sheets of print medium 
are better able to conform to the surface of the tray 11. Accordingly, a 
greater number of sheets can be neatly stacked. 
Second, as previously mentioned, in minimizing the extent of the curl in 
the medium we minimize residual curl. This is particularly relevant when 
the tray 11 is part of a liquid-ink image-processing device in which 
drying ink usually leaves a residual curl in those portions of the medium 
that are curled while drying. 
The surface formed by the above-described lofting technique is 
substantially defined by Eqs. 1 through 6, in conjunction with the 
coefficients of Table 1, as previously stated. The nonuniform B-spline 
surface is formed by summing over the products of the basis functions 
N.sub.i,k (u) (Eq. 3) and N.sub.j,l (v) (Eq. 5), where u and v are 
parametric variables in two directions along the surface. 
The values of t are provided by T.sub.knot(u) (Eq. 4) and T.sub.knot(v) 
(Eq. 6). These knot vectors are appropriate for any open nonuniform 
B-spline of order k and degree k-1. Each T.sub.knot begins with a number 
of t.sub.min knots equal to the order, k or l, of the basis function and 
ends with the same number of t.sub.max knots. The resultant series of 
knots are nonuniformily spaced along the parameter t. The total number of 
knots for each T.sub.knot is the summation of the order, k or l, and the 
number of control vertices, n or m, respectively. For our surface the 
number of knots in the u direction is eighteen and sixteen in the v 
direction. 
Listed in Table 1 are values of control vertices, V.sub.i,j, for the u and 
v directions. There are twelve (m=12) groups of thirteen (n=13) rows; each 
row lists the x, y, and z coordinates of a vertex. The x-axis 18 (FIG. 1b) 
is coincident with the boundaries 24, 25 of the curved surface 13 and the 
planar surface 12. Likewise, the y-axis 19 (FIG. 1b) is coincident with 
the longitudinal axis of symmetry 33. The z-axis 34 is normal to the plane 
of the paper. These vertices provide a three-dimensional representation of 
the best implementation of the invention found so far. 
Once the surface is defined a three-dimensional computer model 
advantageously may be formed--for example using a computer-aided design 
(CAD) system. The tray mold, from which one-piece image-receiving trays 
will be cast, is generated by interrogating the model at fine positional 
increments, and passing the results to a numerically controlled machining 
process. 
Functional Description 
An image-related device in accordance with our invention has the following 
operating parameters: 
______________________________________ 
Image processing type - liquid ink 
Medium type - paper, glossy, and transparency 
Largest output - legal-size medium 
Exit velocity - 61/2 to 12 cm (2.6 to 4.7 inches) per second 
leading trailing 
edge edge 
side center side center 
______________________________________ 
Ejection angles 
(in degrees): 
glossy medium 20 0 3 6 
transparency medium 
20 0 3 6 
20-pound legal size 
20 4 5 6 
20-pound letter size 
20 4 10 9 
Ejection height 
(in cm): 
glossy medium 3.2 3.0 4.5 2.5 
transparency medium 
3.2 3.0 4.5 2.5 
20-pound legal size 
5.8 4.8 4.5 3.2 
20-pound letter size 
5.8 4.8 4.5 3.2 
Pinch point - 4.5 cm above planar surface 
______________________________________ 
By "side angle" (first and third columns above) we mean the lateral angle 
which lateral tangents to the longitudinal side regions of the medium, 
near the outboard edges, make with the horizontal--at the exit slot. By 
"central angle" (second and fourth columns) we mean the longitudinal angle 
which the central region of the medium makes relative to the horizontal, 
also at the exit slot. 
By "ejection height" we mean the distance between the tray surface and the 
medium, measured when the medium is almost completely exited from the 
device. The leading edge is measured from the curved surface, while the 
trailing edge is measured from the planar surface at the pinch point. The 
"pinch point" is the point at which the wheels of the kickout mechanism, 
located at the outboard edges of the exit slot, engage to drive sheets of 
medium from the device. 
Based on these parameters our tray is sized and shaped, as previously 
described, and positioned relative to the pinch point of the kickout 
mechanism to collect and stack medium as follows. For a device operating 
at approximately 61/2 cm (2.6 inches) per second the leading-edge portion 
of an emerging sheet extends over and above the planar surface 12 without 
contacting the surface. As the sheet continues to emerge, the leading edge 
approaches the curved surface 13 of the tray--while the trailing-edge 
portion now extends over and above the planar surface 12. 
Before the trailing edge of the sheet is kicked out (i.e., completely 
exited from the kickout mechanism), the tray--with its upward sloping 
curved surface 13--intercepts the leading-edge portion of the sheet. 
Forward motion of the sheet is impeded, and the leading-edge portion 
conforms to the shape of the curved surface 13. The trailing-edge is then 
kicked out and floats down onto the planar surface 12. Thus there is a 
slight time differential of between the leading edge conforming to the 
curved surface and the trailing edge conforming to the planar surface. 
For a device operating at approximately 12 cm (4.7 inches) per second the 
just-described interaction between the tray surface and exiting medium is 
slightly altered. At this increased exit velocity the leading-edge portion 
of the sheet travels above the tray surface for a greater distance before 
being intercepted by the curved surface. As a result the trailing edge is 
typically kicked out before the leading edge contacts the curved surface. 
Thus the time differential between the leading-edge portion and the 
trailing-edge portion landing on the tray is very slight with both 
portions of the sheet landing at approximately the same time. 
At either exit velocity the sheet conforms to the surface of the tray and 
thereby functions as the tray surface with regard to the next ejected 
sheet. The above-described interaction continues for subsequent sheets, 
and the end result is a neat, evenly stacked pile of medium. 
The type of medium also affects the interaction between the tray surface 
and the medium. Plain paper is rigid and travels above the tray surface 
for a greater distance before contacting the curved surface, than does 
transparency, which is more flexible and begins to slope downward when 
emerging from the kickout mechanism. The tendency of transparency to slope 
and thereby contact the curved surface sooner than paper can be seen in 
the ejection height data provided in the list of operating parameters. 
Upon complete exit the leading edge of a sheet of paper is between 4.8 and 
5.8 centimeters above the tray surface. For transparency, the leading edge 
is between 3.0 and 3.2 centimeters above the surface. 
Our device is optimized to collect and stack all required types of medium 
exiting at either 61/2 or 12 cm per second. Of course there is a limit to 
the number of sheets that can be effectively stacked before the curved 
surface begins to lose shape, i.e. flatten out. In practice the device has 
been able to successfully stack one-hundred sheets of legal- or 
letter-size paper, transparency, or glossy. 
As previously mentioned, the above-described interaction between the tray 
surface and the emerging sheets is particularly beneficial in liquid-ink 
devices. The way in which the sheets leave the device and land down onto 
the tray prevents just-exited sheet from sliding along the already-ejected 
sheets and thereby reduces the possibility of smearing. 
Other inherent benefits of the tray based on the interaction between the 
tray surface include the absence of a discrete longitudinal stop. In our 
tray, the curved surface 13 acts in lieu of a stop when it intercepts the 
leading-edge portion of the sheet and impedes the motion of the sheet. In 
addition, due to the downward landing of the sheets there is no need for 
side guards to guide the medium along the length of the tray--as is common 
in devices which output medium in a manner that slides the medium from 
back to front along the tray surface 
The scope of our invention is not limited to an image-related device having 
the above-described operating parameters. Given a different set of 
operating parameters, a person skilled in the art can redefine and 
readjust the curves to design a tray that duplicates the operation of our 
preferred embodiment. 
The foregoing detailed disclosure is intended as merely exemplary, and not 
to limit the scope of the invention--which scope is to be determined by 
reference to the appended claims.