U.S. patent application number 13/451713 was filed with the patent office on 2012-11-22 for synthetic dry adhesives.
Invention is credited to Mark R. Cutkosky, Paul S. Day, Eric V. Eason.
Application Number | 20120295068 13/451713 |
Document ID | / |
Family ID | 47175123 |
Filed Date | 2012-11-22 |
United States Patent
Application |
20120295068 |
Kind Code |
A1 |
Cutkosky; Mark R. ; et
al. |
November 22, 2012 |
Synthetic Dry Adhesives
Abstract
A method of forming synthetic dry adhesives is provided that
includes using a wedge-shaped tool to form mold cavities in a mold,
filling the mold cavities with an elastomeric adhesive, removing
the elastomeric adhesive from the mold, where a tapered lamellar
ridge extends from a surface of the elastomeric adhesive, treating
a tip of the extending ridge with a film of uncured elastomeric
material, and curing the film of uncured material while the
extending ridge is pressed against a substrate surface having a
smoothness or texture. The synthetic dry adhesive comprises a
close-packed array of tapered lamellar ridges, where the centerline
of a ridge is angled relative to a direction normal to the
synthetic dry adhesive and the cross section includes an internal
taper. The tapered ridge bends when it contacts a surface,
whereupon the radius of curvature of the ridge increases
monotonically with increasing shear load.
Inventors: |
Cutkosky; Mark R.; (Palo
Alto, CA) ; Day; Paul S.; (San Mateo, CA) ;
Eason; Eric V.; (Boulder, CO) |
Family ID: |
47175123 |
Appl. No.: |
13/451713 |
Filed: |
April 20, 2012 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
61517496 |
Apr 20, 2011 |
|
|
|
Current U.S.
Class: |
428/167 ;
427/207.1 |
Current CPC
Class: |
B29C 33/52 20130101;
B29C 39/006 20130101; B29K 2083/00 20130101; C09J 183/04 20130101;
C09J 7/00 20130101; B29C 37/0053 20130101; B29C 33/3842 20130101;
B29C 33/424 20130101; B29K 2105/0097 20130101; B29K 2105/0002
20130101; B29K 2995/0077 20130101; C09J 2301/31 20200801; Y10T
428/2457 20150115; B29C 33/3857 20130101; B29K 2891/00
20130101 |
Class at
Publication: |
428/167 ;
427/207.1 |
International
Class: |
C09J 7/00 20060101
C09J007/00; B32B 3/30 20060101 B32B003/30; B05D 5/10 20060101
B05D005/10 |
Goverment Interests
STATEMENT OF GOVERNMENT SPONSORED SUPPORT
[0002] This invention was made with Government support under
contract NIRT 0708367 awarded by National Science Foundation (NSF),
and under contract 1118729-2-TFLAP awarded by DARPA. The Government
has certain rights in this invention.
Claims
1. A method of forming synthetic dry adhesives, comprising: a.
using a wedge-shaped tool to form mold cavities in a mold, wherein
said mold cavities comprise a depth t and a spacing h; b. filling
said mold cavities with an elastomeric adhesive; c. removing said
elastomeric adhesive from said mold, wherein a tapered lamellar
ridge extends from a surface of said elastomeric adhesive; d.
treating a tip of said extending tapered lamellar ridge with a film
of uncured elastomeric material; and e. curing said film of uncured
material while said extending tapered lamellar ridge is pressed
against a substrate surface.
2. The method according to claim 1, wherein said mold comprises a
homogeneous wax composition having a Young's modulus to yield
stress ratio E/Y greater than 100.
3. The method according to claim 1, wherein said wedge-shaped tool
comprises at least a primary bevel.
4. The method according to claim 1, wherein said wedge-shaped tool
comprises a primary bevel, a secondary bevel and a tertiary
bevel.
5. The method according to claim 1, wherein said wedge-shaped tool
comprises a lubricated surface.
6. The method according to claim 1, wherein said wedge-shaped tool
is moved along a 2-dimensional or 3-dimensional trajectory into
said mold until a tip of said wedge-shaped tool reaches said depth
t below a top surface of said mold.
7. The method according to claim 1, wherein a trajectory of said
tool is controlled to move displaced mold material in a desired
direction, wherein said mold cavities are desirably spaced and a
shape of said cavities is controlled.
8. The method according to claim 1, wherein a centerline of said
wedge-shaped tool is set at an angle .lamda. with respect to a top
surface of said mold, wherein a trajectory of said tool is at an
intermediate angle .theta. with respect to a top surface of said
mold, wherein said angle .theta. is in a range of
0<.theta.<.lamda..
9. The method according to claim 1, wherein said elastomeric
adhesive comprises an elastomer selected from the group consisting
of silicones, polyurethanes, and polypropylene.
10. The method according to claim 1, wherein treating a tip of said
extending tapered lamellar ridge with a film of uncured elastomeric
material comprises said uncured elastomeric material disposed on
one or both sides of said lamellar ridge.
11. The method according to claim 1, wherein said substrate surface
comprises a smooth or textured surface, wherein said surface is
disposed to transfer a desired smoothness or desired texture to a
film of said uncured elastomeric material as said uncured
elastomeric material cures.
12. The method according to claim 1, wherein a siping step is used
when said adhesive is de-molded, wherein said siping step comprises
a cut perpendicular to said extending tapered lamellar ridge at a
desired frequency to improve adhesion on textured surfaces having
micro-scale roughness, wherein independent adhesive sections of
said extending tapered lamellar ridge conform to said textured
surface.
13. A synthetic dry adhesive, comprising: a. a close-packed array
of elastomeric adhesive wedge-shaped lamellar ridges, wherein a
cross section of said close-packed array comprises a base of a
leading edge of one said lamellar ridge contacting a base of a
trailing edge of an adjacent said lamellar ridge, wherein said
lamellar ridge comprises an internal taper spanning from a base of
said lamellar ridge to a pointed tip of said lamellar ridge,
wherein a centerline of said lamellar ridge is angled relative to a
direction normal to said synthetic dry adhesive; and b. a secondary
elastomeric adhesive layer disposed on one or both sides of said
wedge-shaped lamellar ridge, wherein said secondary layer comprises
a textured or flat surface.
14. The synthetic dry adhesive of claim 13, wherein said
wedge-shaped lamellar ridge bends into a curve when it contacts a
surface, whereupon the radius of curvature of said wedge-shaped
lamellar ridge increases monotonically with increasing shear
load.
15. The synthetic dry adhesive of claim 13, wherein the tip-to-tip
spacing between adjacent said lamellar ridges is as low as 6
.mu.m.
16. The synthetic dry adhesive of claim 13, wherein said angle of
said centerline of said lamellar ridge is up to 50 degrees relative
to said normal direction.
17. The synthetic dry adhesive of claim 13, wherein both sides of
said lamellar ridge is angled relative to said normal
direction.
18. The method according to claim 13, wherein said elastomeric
adhesive comprises an elastomer selected from the group consisting
of silicones, polyurethanes, and polypropylene.
19. The synthetic dry adhesive of claim 13, wherein said tip of
said wedge-shaped lamellar ridge comprises a film of cured
elastomeric material having a desired smoothness or texture on one
or both sides of said wedge-shaped lamellar ridge.
20. The synthetic dry adhesive of claim 14, wherein said lamellar
ridge comprises siping, wherein said siping is disposed across said
wedge-shape lamellar ridge.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority from U.S. Provisional
Patent Application 61/517,496 filed Apr. 20, 2011, which is
incorporated herein by reference.
FIELD OF THE INVENTION
[0003] This invention relates to synthetic dry adhesives and
methods of making thereof.
BACKGROUND OF THE INVENTION
[0004] Impressive advancements have been made in the field of
gecko-inspired synthetic dry adhesives. A large range of
manufacturing methods for these adhesives has been reported in the
literature. However, the use of such adhesives in applications such
as climbing has been much more limited, with just a few examples
reported. It has generally been found that the adhesion levels
generated in real-world climbing applications are significantly
lower than those obtained using small samples in bench-top
experiments.
[0005] One reason for this disparity is that, in addition to
conforming to surfaces and generating useful levels of adhesion,
the adhesives have additional requirements when used for climbing.
The first of these requirements is controllability, i.e., the
adhesives should not be sticky in the default state and adhere only
when it is desirable. In any other case, energy will be wasted as
it is expended in attaching and detaching the adhesive for each
step. Controllability can be achieved by using switchable
structures or by creating directional adhesive features whose
adhesion generation is a function of applied shear load.
[0006] The second requirement is durability. The adhesives must
undergo thousands of attach/detach cycles without significant loss
of adhesive properties and, ideally, should resist fouling and be
easy to clean. Durability is also correlated with controllability:
gentle attach/detach cycles reduce mechanical wear and promote long
life.
[0007] Micro-wedges are an example of a synthetic dry adhesive that
has been successfully applied to climbing robots. Micro-wedges are
simple, controllable, and durable structures that have enabled
robots weighing 1 kg and more to climb on glass, plastic, wood
paneling, painted metal, and similar surfaces. When unloaded, as
shown in an oblique perspective view in FIG. 1a, they present a
very small real area of contact with a surface and generate
negligible adhesion. However, when loaded in a preferred shear
direction, as shown in FIG. 1b, they bend, creating a larger
contact area and generating adhesion that is proportional to the
shear load. The micro-wedges' asymmetric taper ensures that the
radius of curvature of the feature at the proximal edge of the
contact patch increases with increasing shear load, allowing the
tapered features to outperform features of constant cross-section
at high shear loads. Furthermore, they may be easily cleaned using
a piece of sticky tape.
[0008] In previous work, micro-wedges were manufactured by casting
a polydimethylsiloxane (PDMS) silicone elastomer into molds created
through a photolithographic process in which SU-8.RTM. photoresist
(MicroChem Corp.) was subjected to two exposures, one angled, one
vertical, through contact masks. The necessity of a thick
photo-resist layer combined with the requirement for high precision
alignment of exposures resulted in a time consuming, expensive mold
fabrication process with relatively low yield.
[0009] What is needed is a method of fabricating controllable and
durable synthetic dry adhesives that does not use an expensive
photolithographic process, and which provides synthetic dry
adhesives with performance in climbing and other applications that
is comparable to or better than the micro-wedges used in previous
work.
SUMMARY OF THE INVENTION
[0010] To address the needs in the art, a method of forming
synthetic dry adhesives is provided, which according to one
embodiment includes using a wedge-shaped tool to form mold cavities
in a mold, where the mold cavities comprise a depth t and a spacing
h, filling the mold cavities with an elastomeric adhesive, removing
the elastomeric adhesive from the mold, where a tapered lamellar
ridge extends from a surface of the elastomeric adhesive, treating
a tip of the extending tapered lamellar ridge with a film of
uncured elastomeric material, and curing the film of uncured
material while the extending tapered lamellar ridge is pressed
against a substrate surface.
[0011] According to one aspect of the invention, the mold includes
a homogeneous wax composition having a Young's modulus to yield
stress ratio E/Y greater than 100.
[0012] In another aspect of the invention, the wedge-shaped tool
comprises at least a primary bevel, or includes a primary bevel, a
secondary bevel and a tertiary bevel. In one aspect the
wedge-shaped tool includes a lubricated surface.
[0013] According to one aspect of the invention, the wedge-shaped
tool is moved along a 2-dimensional or 3-dimensional trajectory
into the mold until a tip of the wedge-shaped tool reaches the
depth t below a top surface of the mold.
[0014] In a further aspect of the invention, a trajectory of the
tool is controlled to move displaced mold material in a desired
direction, where the mold cavities are desirably spaced and a shape
of the cavities is controlled.
[0015] In yet another aspect of the invention, a centerline of the
wedge-shaped tool is set at an angle .lamda. with respect to a top
surface of the mold, where a trajectory of the tool is at an
intermediate angle .theta. with respect to a top surface of the
mold, where the angle .theta. is in a range of
0<.theta.<.lamda..
[0016] According to another aspect of the invention, the
elastomeric adhesive is an elastomer that can include silicones,
polyurethanes, or polypropylene.
[0017] In a further aspect of the invention, a tip of the extending
tapered lamellar ridge is treated with a film of uncured
elastomeric material, where the uncured elastomeric material is
disposed on one or both sides of the lamellar ridge.
[0018] According to another aspect of the invention, the substrate
surface includes a smooth or textured surface, where the surface is
disposed to transfer a desired smoothness or desired texture to a
film of the uncured elastomeric material as the uncured elastomeric
material cures.
[0019] In a further aspect of the invention, a siping step is used
when the adhesive is de-molded, where the siping step includes a
cut perpendicular to the tapered lamellar ridge at a desired
frequency to improve adhesion on textured surfaces having
micro-scale roughness, where independent adhesive sections of the
extending tapered lamellar ridge conform to the textured
surface.
[0020] According to another embodiment, a synthetic dry adhesive is
provided that includes a close-packed array of elastomeric adhesive
wedge-shaped lamellar ridges where a cross-section of the
close-packed array includes a base of a leading edge of one
lamellar ridge contacting a base of a trailing edge of an adjacent
lamellar ridge, where the lamellar ridge comprises an internal
taper spanning from a base of the lamellar ridge to a pointed tip
of the lamellar ridge, where a centerline of the lamellar ridge is
angled relative to a direction normal to the synthetic dry
adhesive, and a secondary elastomeric adhesive layer disposed on
one or both sides of the tip of the wedge-shaped lamellar ridge,
where the secondary layer comprises a textured or flat surface.
[0021] According to one aspect of the current embodiment, the
wedge-shaped lamellar ridge bends into a curve when it contacts a
surface, whereupon the radius of curvature of the wedge-shaped
lamellar ridge increases monotonically with increasing shear
load.
[0022] In another aspect of the current embodiment, the tip-to-tip
spacing h between adjacent lamellar ridges is as low as 6
.mu.m.
[0023] In a further aspect of the current embodiment, the angle of
the centerline of the tapered ridge is up to 50 degrees relative to
the normal direction.
[0024] In one aspect of the current embodiment, both sides of the
tapered ridge are angled relative to the normal direction.
[0025] According to another aspect of the current embodiment, the
elastomeric adhesive is an elastomer that includes silicones,
polyurethanes, and polypropylene.
[0026] In yet another aspect of the current embodiment, the tip of
the wedge-shaped lamellar ridge includes a film of cured
elastomeric material having a desired smoothness or texture on one
or both sides of the wedge-shaped lamellar ridge.
[0027] According to a further aspect of the current embodiment, the
lamellar ridge includes siping, where the siping is disposed across
the wedge-shaped lamellar ridge.
BRIEF DESCRIPTION OF THE DRAWINGS
[0028] FIGS. 1a-1b show prior art SEM micrographs of PDMS
directional adhesive features: (a) perspective view of unloaded
micro-wedges from a photolithographic mold, (b) planar view of
micro-wedges under shear loading
[0029] FIG. 2a-2c show cross-section views of wedge-shaped lamellar
ridges having cured elastomeric material with a desired smoothness
or texture on one or both sides of the wedge-shaped lamellar ridge,
according to some embodiments of the current invention.
[0030] FIG. 3a-3b show diagrams of the geometry and the parameters
of the micro-machining process for a single cavity, where "Traj."
is the tool trajectory; "S.P." is the shear plane, according to one
embodiment of the invention.
[0031] FIG. 4a-4e show a diagram of the steps for treating the tips
of the extending tapered lamellar ridges with a film of elastomeric
material, according to one embodiment of the invention.
[0032] FIG. 5a-5b show perspective drawings of post-treated
wedge-shaped lamellar ridges before and after a siping step,
according to one embodiment of the invention.
[0033] FIG. 6 show cross-section views of a microtome blade having
three different beveled sections the wedge-shaped tool bevels,
according to one embodiment of the invention.
[0034] FIG. 7a-7b a micrograph of a single mold cavity created in
cutting force tests showing triangular built-up region, and
measured shear stress with values of shear yield stress k for
comparison (T, S, and C correspond to trajectories parallel to the
tertiary bevel, secondary bevel, and centerline of the tool),
according to one embodiment of the invention.
[0035] FIGS. 8a-8d show micrographs of the effect of trajectory
angle on mold cavity shape. For some trajectories (a-b), a
continuous chip of built-up material is formed after the final
cavity, according to one embodiment of the invention.
[0036] FIG. 9 shows geometric data taken from characterization
experiment micrographs (FIGS. 8a-8d), according to one embodiment
of the invention.
[0037] FIG. 10 shows a graph of a comparison of the limit curves
for macroscopic arrays of adhesive features produced with
micro-machined molds and photolithographic molds, according to one
embodiment of the invention.
DETAILED DESCRIPTION
[0038] Directional dry adhesives are inspired by animals such as
geckos and are a particularly useful technology for climbing
applications. Previously, they have generally been manufactured
using photolithographic processes. The current invention provides a
micro-machining process that makes cuts in a soft material using a
sharp, lubricated tool to create closely spaced negative cavities
of a desired shape. The machined material becomes a mold into which
an elastomer is cast to create the directional adhesive. The
trajectory of the tool is varied to avoid plastic flow of the mold
material that may adversely affect adjacent cavities. The
relationship between tool trajectory and resulting cavity shape is
established through modeling and process characterization
experiments.
[0039] The micro-machining process of the current invention is much
less expensive than previous photolithographic processes used to
create similar features and allows greater flexibility with respect
to the micro-scale feature geometry, mold size, and mold material.
The micro-machining process produces controllable, directional
adhesives, where the normal adhesion increases with shear loading
in a preferred direction. This is verified by multi-axis force
testing on a flat glass substrate. Upon application of a
post-treatment to improve the smoothness of the engaging surfaces
of the features after casting, the adhesives significantly
outperform comparable directional adhesives made from a
photolithographic mold.
[0040] One embodiment of the current invention includes a mold
created with a micro-machining process that involves making a
pattern of cavities in a mold using a narrow cutting tool.
Machining processes have been used previously to create stamps for
soft lithography and synthetic adhesive structures using
nano-indenters and AFM tips, but neither fabrication nor testing of
macroscopic adhesive arrays (.about.1 cm.sup.2) has been
demonstrated, the aspect ratio of the resulting features has been
low, and the features have not been closely spaced. This in turn
leads to unused space between features, decreased real area of
contact, and decreased adhesive performance.
[0041] The current invention provides a micro-machining process
that is a hybrid of orthogonal machining and wedge indenting.
According to one embodiment, a sharp wedge-shaped tool is moved
along an oblique trajectory into a soft mold surface, producing
wedge-shaped cavities of depth on the order of up to 500 .mu.m and
of any desired width, for example. By controlling the tool geometry
and trajectory and repeating this operation in a pattern across the
mold surface, it is possible to obtain a dense packing of sharp,
wedge-shaped cavities. As an example, casting PDMS into these
cavities produces micro-wedge lamellar features as seen in FIG. 5a.
In comparison to photolithography, the method presented here is
cheaper, faster, and affords greater freedom to control the cavity
geometry, which governs adhesive performance.
[0042] The main motivation of the current invention is the need for
a practical adhesive for climbing. The new micro-machined features,
upon application of a post-treatment process according to another
embodiment (see FIGS. 2a-2c and FIGS. 4a-4e), perform significantly
better than photolithographic micro-wedges in adhesive tests, where
the post-treatment process includes treating a tip of the extending
tapered features with a film of uncured elastomeric material
disposed on one or both sides of the features, and a treatment
transfer substrate is disposed to transfer a desired smoothness or
desired texture to the uncured film as it cures. The improvement is
partly a result of having greater freedom to control the wedge
taper and angle of inclination. Arrays of the new features have
been produced and tested, with maximum normal adhesion of 38 kPa
attained at a shear stress of 49 kPa for an array of area 1.21
cm.sup.2.
[0043] In addition, the micro-machined features formed by the
method of the current invention retain the controllability and
durability of photolithographic micro-wedges.
[0044] In order to better understand the mechanics involved, a
micro-machining process may be described using numerical
finite-element modeling or semi-analytic theoretical models.
Theoretical models are mostly applied to ideal rigid-plastic
materials and are not as likely to accurately predict the forces
and deformations. Conversely, state of the art numerical models can
account for realistic material behavior and friction effects.
However, the material properties and tribological behavior of the
wax mold material used here have not been sufficiently well
characterized to justify a numerical model. Moreover, it is not
required to produce a numerical prediction of the cutting forces in
terms of the cutting parameters (e.g. cutting depth, speed,
friction, tool angle, or tip radius) as the forces are, in any
case, quite low.
[0045] Instead, it is useful to understand how the cutting
parameters and tool geometry affect the deformation behavior. In
particular, it is desirable to produce a tightly packed array of
cavities in order to obtain a high density of adhesive features.
Accordingly, an important question is whether displaced material is
moved mainly in the forward direction (towards the unmachined part
of the mold) or the rearward (tending to close up the previously
made cavity). Semi-analytic theoretical models can provide this
insight without recourse to running numerous simulations, which may
be poorly convergent or sensitive to boundary conditions and may
require frequent re-meshing due to the large deformations
involved.
[0046] If the cutting depth t and the tool cross-section are
constant along the width of the cavity (into or out of the page in
FIGS. 3a-3b), and if t is much smaller than the width of the
cavity, then the stressed material is confined to a long, narrow
prismatic region. In the experiments described here, t.ltoreq.100
.mu.m and the cavity width is greater than 10 mm, so it is
reasonable to assume that the material is in a state of plane
strain.
[0047] The process bears resemblance to two classical problems from
plane-strain plasticity theory: oblique wedge indenting, in which a
rigid wedge-shaped tool penetrates the work surface, and orthogonal
machining, in which the tool removes a thin strip of material by
moving parallel to the work surface. The process according to the
current invention is a generalization of the two processes: the
tool is wedge-shaped with internal angle 2.beta., the centerline of
the tool is set at an angle .lamda. with respect to the work
surface, and the direction of motion of the tool is neither
parallel to the centerline (as in wedge indenting) nor to the work
surface (as in orthogonal machining), but instead is set at an
intermediate angle 0<.theta.<.lamda., as shown in FIGS.
3a-3b.
[0048] To model this process analytically, it is assumed that the
work material is perfectly rigid-plastic. While most plasticity
studies have been concerned with the plastic behavior of metals,
wax has also been used as a work material, and waxes can be closer
to rigid-plastic than metals. The wax used in this example has been
found through axial compression testing to have a low shear yield
strength (approximately 2 MPa) and little work hardening; however,
it does exhibit some elastic recovery, which can affect the forces
and cavity geometry during micro-machining.
[0049] Given these assumptions, it is feasible to adapt an existing
semi-analytic model to the present situation to obtain an estimate
of the flow of material on both sides of the tool and the expected
buildup region adjacent to the cavity.
[0050] For a perfect rigid-plastic material, the interior shape of
the cavity will be identical to the swept volume of the tool as it
moves along its trajectory, which means that any trajectory angle
.theta. can be chosen from the range
.lamda.-.beta.<.theta.<.lamda.+.beta. without affecting the
shape of the cavity. However, the extent of plastic deformation and
the amount of buildup occurring on the leading and trailing faces
of the tool will vary with .theta.. If material is displaced on
both sides of the tool, and the mold cavities are spaced closely,
this flow will result in partial collapse of the previously formed
cavity.
[0051] In order to minimize this effect, the trajectory angle may
instead be chosen to lie outside this range:
.theta.=.lamda.-.beta.-.epsilon., where .epsilon.>0 is a relief
angle. This increases the angular width of the cavities by the
angle .epsilon.. This geometry can be seen in FIGS. 3a-3b. The
benefit of the relief angle is that the trailing side of the tool
should no longer make contact with the wall of the cavity. As a
result, assuming that the tip of the tool is sufficiently sharp,
the zone of plastic deformation is limited to the leading side of
the tool only, and material on the trailing side remains rigid
throughout the process, theoretically preventing partial collapse
of the previous cavity. In one aspect of the invention, the angle
of the centerline of the resulting adhesive feature produced by
this process is up to 50 degrees relative to the normal
direction.
[0052] Two possibilities are predicted for the plastic deformation
on the leading side of the tool.
[0053] In the first case, the plastic region covers the entire area
of displaced material, and it is possible to construct a slip-line
field throughout this region. In the second case, the plastic
region is restricted to a single shear plane, and elsewhere the
material is rigid.
This second case occurs if the trajectory angle is lower than a
critical value:
2 tan .theta.<+[1+tan(.alpha.+.theta.)].sup.2 (1)
[0054] However, this equation is always satisfied if the rake angle
.alpha. is positive, as in the present case. Therefore, the model
predicts that a single shear plane solution is appropriate on the
leading face of the tool. The model also provides a prediction of
the shear plane angle .phi. based on an energy-minimization
argument, but since the model does not include friction this
prediction is not expected to be accurate. Furthermore, there is
doubt about the theoretical and experimental validity of this
argument.
[0055] Despite the lack of a trustworthy prediction of the shear
plane angle .phi., the model can be used to make a testable
prediction about the cutting forces if .phi. can be measured
experimentally. Let the net force applied by the machine to the
tool be denoted by
F=F.sub.x{circumflex over (x)}+F.sub.yy (2)
and let the total force on the shear plane be denoted by
f=f.sub.ss+f.sub.n{circumflex over (n)} (3)
as shown in FIGS. 3a-3b. In accordance with the model, it is
assumed that the displaced material is limited to a triangular
built-up region also shown in FIGS. 3a-3b. As long as there is no
contact on the trailing side of the tool, these forces are equal:
F=f, and therefore:
f.sub.s=F.sub.x({circumflex over (x)}s)+F.sub.y(ys)=F.sub.x cos
.phi.+F.sub.y sin .phi. (4)
[0056] This relationship does not require any assumptions about the
shear plane angle .phi. or the friction at the leading side of the
tool. Finally, according to the theory of perfect rigid-plastic
materials in plane strain, the shear stress along the shear plane
is constant and equal to the shear yield stress k:
f.sub.s/A=k (5)
where A is the area of the shear plane.
[0057] Although the semi-analytic model cannot be expected to
produce a complete prediction of the cutting forces with high
accuracy, it produces a useful prediction about the deformation
mode of the material (the existence of a shear plane), and it is
also useful for understanding relationships among .lamda., .beta.,
.theta., and .phi.. This leads to the expectation that most of the
displaced material will be pushed forward if the trajectory angle,
.theta., is sufficiently small compared to the angle of the
trailing face of the tool, .lamda.-.beta.. In this situation, the
model does produce a testable prediction about the cutting forces
(Eqs. 4 and 5).
[0058] The mold fabrication method of the current invention relies
on a few key components to be effective. Most important is the
wedge-shaped tool, whose shape strongly influences the shape of the
resulting mold cavities. The tool used in this example is a
PTFE-coated steel disposable microtome blade (Delaware Diamond
Knives D554X). This tool has a fine surface finish, with blade
roughness on length scales <<1 .mu.m, an internal angle of
2.beta..apprxeq.24.degree., and an edge radius of less than 0.9
.mu.m.
[0059] The material used for the mold must also be selected for
desirable properties. An ideal material for machining would have a
homogeneous composition, a relatively low yield strength, and
perfect rigid-plastic behavior to minimize elastic recovery of the
machined region. Rigid-plastic behavior is most likely to occur in
micro-machining processes of the current invention if the included
angle of the tool is acute and the ratio of Young's modulus to
yield stress E/Y is large. According to one aspect, the mold
includes a material composition having a Young's modulus to yield
stress ratio E/Y greater than 100.
[0060] In one embodiment, a soft, rolled sheet wax (Kindt-Collins
Master.RTM. Regular Sheet Wax) is used, having a ratio of Young's
modulus to yield stress of approximately E/Y.apprxeq.110-160. For
this value of E/Y with a tool angle of 24.degree., the deformation
behavior is not dominated by elastic effects and rigid-plastic
behavior may be possible.
[0061] Adhesive wear at the tool-mold interface is undesirable and
could lead to a poor surface finish. However, this is mitigated by
lubricating the interface, according to one embodiment. In addition
a post-treating process has been devised to refinish the surfaces
entirely. For these reasons the tribological properties of the mold
material are not a major concern for material selection.
[0062] The micro-machining process according to one embodiment of
the invention, may be performed on a standard CNC milling machine
or other machine with positioning control in at least two axes and
sufficient accuracy. In the current example of the invention,
adhesives have been produced using a tabletop CNC milling machine
with 1 .mu.m precision (Levil WL400), a larger CNC milling machine
with 2.5 .mu.m precision (Haas VF-0E), and a motorized stage with
an estimated accuracy of .+-.1 .mu.m (Velmex MAXY4009C-S4 and
Newport GTS30V).
[0063] Ultimately, the dimensions of an adhesive patch are
constrained only by the width of the microtome blade and the length
of the workspace of the machine. With the equipment described
above, it is possible to make a single uninterrupted patch of
adhesive as large as 76 mm wide by 762 mm long or longer.
[0064] First, the wax is melted and cast into a block to improve
the consistency of its plastic behavior and to obtain a desirable
form factor for fixturing, and then it is cooled to room
temperature. The mold surface is milled and planed to ensure it is
flat and parallel to the machine ways. Next, the surface is cleaned
and the micro-machining tool is mounted to the machine head. The
blade is fixed so that its centerline is tilted by a constant angle
of .lamda.=60.degree. with respect to the horizontal surface of the
wax (see FIGS. 3a-3b). The tip of the blade is then aligned to the
wax surface.
[0065] The tool is moved by the machine along a specified 2-D or
3-D trajectory into the wax until its tip reaches a desired depth t
in the negative y-direction (see FIGS. 3a-3b). At this point the
tool is retracted above the surface and then advanced a set
distance in the positive x-direction to create a space between
cuts. The cycle then repeats.
[0066] The tool trajectory may be chosen from a large space of
possible paths. Varying the trajectory provides freedom to control
the completed cavity shape and the plastic flow of the mold
material.
[0067] Without lubrication, adhesive wear occurs between the tool
and the mold material. SEM examination of the features cast from
these molds indicates significant surface roughness on critical
areas such as the engaging faces that will ultimately generate
adhesion. To address this issue, a lubricant may be added to the
process to inhibit material transfer from the wax mold to the tool.
Several fluids were tested, including various mixtures of water and
surfactants in the form of liquid dish soaps. Surface roughness was
measured by capturing stereoscopic SEM images and generating 3D
topographical plots using the Alicona Imaging MeX software package.
Average roughness data were taken across line profiles over the
engaging surfaces of the features. The best surface finish,
corresponding to an RMS roughness of approximately 39 nm, was
obtained with a 10:2 concentration of Ajax liquid dish soap
(Colgate-Palmolive) to water.
[0068] The completed mold is cleaned with solvents and water to
remove all traces of lubricant. A PDMS silicone elastomer (Dow
Corning Sylgard.RTM. 170) is vacuum de-gassed and poured into the
mold. Other materials can include elastomers such as silicones,
polyurethanes, or polypropylene. For samples for adhesion force
testing, a 300 .mu.m thick backing layer of PDMS is desired. This
can be achieved by spinning the mold at 160 RPM for 30 seconds, or
alternatively a two-part mold may be created by placing a flat
sheet of glass upon 300 .mu.m supports, which rest on the wax mold
surface. For climbing applications, the sheet of glass may be
replaced by a rigid tile made of glass fiber or aluminum. The tile
is treated with a primer (Dow Corning PR-1200), which allows the
PDMS to bond directly to the tile. In any case, the casting is then
allowed to cure at room temperature for 24 hours (heat acceleration
is also possible). Once removed from the mold, the elastomeric
adhesive is ready for use. The mold may become damaged as the
castings are de-molded, in which case the mold may be resurfaced
and micromachined again before its next use.
[0069] While the addition of lubrication to the micro-machining
process improves the surface finish of the molds and molded
features, there is still some remaining roughness that can affect
the performance of the adhesives by reducing the real area of
contact between the adhesive and the substrate. In order to further
reduce this roughness, a post-treatment is employed after casting.
This treatment adds a thin secondary layer of PDMS to the engaging
faces of the molded features. This layer may be smooth or textured
as desired. In the case of a smooth layer, the treatment proceeds
as follows (see FIGS. 4a-4e):
1. Uncured PDMS is diluted to a concentration of 10% toluene by
volume. The diluted mixture is then poured onto a four-inch quartz
wafer and spun at 8000 RPM for 60 seconds to obtain a uniform thin
layer 3-5 .mu.m thick. 2. One half of the wafer is cleaned using
isopropyl alcohol, and the wafer and a cast adhesive sample are
secured to a three axis motorized positioning stage. 3. The sample
is brought into contact with the PDMS-coated half of the wafer.
After applying a normal load so that the features are in contact
with the wafer over approximately one third of their length, the
features are taken out of contact, leaving a thin, wet layer of
PDMS on the tips of the features. 4. After this "inking" procedure,
the features are loaded against the cleaned half of the wafer and
held there in order to flatten this thin, wet layer as it cures. 5.
The cured thin layer binds strongly to the previously cured
features. The post-treatment results in smooth patches of PDMS on
the engaging faces of the features (see FIG. 5).
[0070] For a climbing adhesive, which has been cast directly to a
rigid tile, the post-treatment may be done without the motorized
positioning stage, by simply using an appropriately sized weight.
In this variation of the process, the wafer is placed on a flat
surface, the adhesive is placed on the wafer (with the back of the
tile facing up), and the weight is placed on the tile. The best
post-treatment results have been obtained using weights such that
the average pressure is approximately 7-8 kPa, but this depends on
the shape and stiffness of the features.
[0071] Experiments were performed to test the semi-analytic model
introduced above, to empirically characterize the micro-machining
process, and to measure the adhesive performance of macroscopic
arrays of micro-machined micro-wedges. However, it is first
necessary to look more closely at the geometry of the microtome
blades used here as micro-machining tools.
[0072] According to one aspect of the current embodiment, the
wedge-shaped tool includes a wedge, or at least a primary bevel. As
seen in the embodiment shown in FIG. 6, the shape of the tool is
not simply a primary bevel. Instead, the wedge-shaped tool is
sharpened to a profile with three different beveled sections.
According to one embodiment, the primary bevel begins approximately
1.7 mm from the tip and has an angle of 12.degree. (this section is
above the wax mold at all times). The secondary bevel begins 270
.mu.m from the tip and has an angle of 24.degree., and the tertiary
bevel extends over the final 40 .mu.m of the blade's length and is
34.degree. wide. The tip is too small to be seen at this
magnification, but an upper limit radius of 0.9 .mu.m may be
established.
[0073] In the described machining geometry, the border between the
secondary and tertiary bevels is below the surface of the wax
whenever the blade is inserted more than 40 .mu.m deep. However,
the mold cavities created by the micro-machining process (with a
nominal depth of 100 .mu.m) show little evidence of this border,
and the terminal angle of the features is considerably narrower
than the tertiary blade bevel.
[0074] This implies that there is significant elastic behavior
occurring in the mold material, as the tips of the mold cavities
are narrowing by several degrees when the blade is retracted. This
effect is observed for single cavities as well as arrays of
cavities.
[0075] To test the predictions of the semi-analytic model, the
cutting forces during micro-machining were measured. A wax specimen
of width 1 cm was attached to a six-axis force/torque sensor (ATI
Gamma SI-32-2.5) which was mounted in a CNC milling machine, and a
variety of micro-machining trajectories were used to create
cavities in the wax. The trajectories were linear and differed by
trajectory angle, ranging from .theta.=36.degree. to 60.degree.,
and maximum depth, ranging from t=20 .mu.m to 100 .mu.m. The blade
centerline angle was .lamda.=60.degree. in all cases, an angle
found empirically to produce features with the desired directional
behavior. In this exemplary experiment, the cavities were spaced
far apart (0.5 mm tip-to-tip) so that the interaction between them
was negligible. The blade was wider than the wax specimen so that
its corners were not in contact.
[0076] The resulting force data were analyzed to find the cutting
force F corresponding to the endpoint of each trajectory, the point
in time when the tool was at its maximum cutting depth t for each
cavity. The final cavity shape, preserved by casting PDMS into the
specimen, serves as a record of the shape of the cavity at that
same point in time. As shown in FIG. 7a, these castings clearly
show the triangular shape of the built-up material adjacent to the
leading side of the tool (consistent with the model). By
constructing a line from the tip of the cavity to the front edge of
the built-up region, and taking into account the width of the wax
specimen, it is possible to measure the area of the shear plane A
and the shear plane angle .phi. (FIG. 7a).
[0077] For each cavity, the value of F was projected onto the shear
plane using Eq. 4 to produce an estimate of the shear stress
f.sub.s/A. This assumption is only accurate if there is no contact
between the trailing side of the tool and the wax. If there is such
contact, the measured cutting force will be the sum of forces at
the leading and trailing tool faces, which cannot be separated
using external measurements.
[0078] The measured values of f.sub.s/A versus .theta. are plotted
in FIG. 7b, as well as the shear yield stress of the wax k,
calculated using both the Tresca and von Mises shear yield
criteria, derived from the compressive yield stress, which was
determined through axial compression testing.
[0079] Even though the cutting depth varied from t=20 .mu.m to 100
.mu.m for each trajectory, causing some variance in the data, the
trend is the same for all values of t. For trajectories near
.theta.=.lamda.=60.degree., there is substantial disagreement
between the measurements of f.sub.s/A and the value of k, using
either the Tresca or von Mises yield criteria. The direction of the
cutting force F is nearly antiparallel to the shear plane, causing
f.sub.s to be negative instead of positive. This may be due to
contact forces on the trailing side of the tool because, for
trajectories .theta.>43.degree., it is expected that the
secondary or tertiary bevels will contact the wax on the trailing
side, due to the blade geometry.
[0080] For trajectories .theta.<43.degree., it is expected that
there is no contact on the trailing side of the tool and therefore
the measured value of f.sub.s/A should be equal to k in accordance
with Eq. 5. Indeed, the data for the shallowest trajectory,
.theta.=36.degree., are in agreement with Eq. 5. However, the data
for .theta.=42.degree. are not. This disagreement cannot be
explained completely by the geometry of the blade. In this case, it
is likely that contact is occurring on the trailing side of the
blade. This may be due to elastic recovery of the wax (which was
assumed negligible in the model) or it may be that the tribological
interaction between the tool, lubricant, and mold surface is more
complicated than can be described in this simple model.
[0081] In summary, the evidence appears to invalidate the
assumption that the material on the trailing side of the tool is
rigid, for the majority of the micro-machining trajectories tested.
Theoretical modeling has provided useful qualitative insight into
the micro-machining process, but the models considered here are
unable to explain the actual cutting forces, and they cannot
necessarily be used to predict the deformation of the mold material
in a process that involves multiple cavities being formed in
series. These realizations prompted an empirical investigation of
the micro-machining process.
[0082] Predicting the cutting force is not strictly necessary to
produce a useful adhesive mold insofar as the forces are small
enough not to damage or significantly deflect the micro-machining
tool. However, it is important to ascertain the effect of the
micro-machining trajectory on the shape of the mold cavities. To
accomplish this, a characterization experiment was performed in
which the trajectory angle was varied (again from
.theta.=36.degree. to 60.degree.) while the nominal depth and
tip-to-tip spacing of the cavities were kept constant at 100 .mu.m
and 60 .mu.m respectively. At this depth and spacing, the cavity
shapes were expected to be significantly influenced by neighboring
cavities, so a series of ten cavities was made for each
trajectory.
[0083] PDMS was cast into the mold cavities and the resulting
adhesive samples were cut in cross-section and measured with a
microscope, as shown in FIGS. 8a-8d. Ten cavities appear to be
sufficient to attain a steady-state shape; the boundary conditions
are different for the initial cavity, but this only affects the
first three cavities or fewer. In addition, the final cavity is
sometimes a different shape from the previous ones. In these cases,
the final cavity shows the shape of an incipient cavity before it
has been deformed to its completed shape by the cavity following
it. The 4th-9th cavities are representative of the completed shapes
that would be created in a large adhesive array.
[0084] The height and angular width of the cavities change with the
trajectory angle due to several concurrent effects. For values of
.theta. near 36.degree., the feature height is significantly less
than the nominal height of 100 .mu.m because the cavities intersect
one another below the original mold surface (FIG. 8a). As .theta.
increases past 46.degree., there is an increasingly large
difference in height between the incipient feature and the
completed features (FIG. 8b), indicating that permanent deformation
on the trailing side of the tool is occurring. The feature height
reaches a maximum at .theta.=56.degree., where the trailing-side
deformation causes the edges of the cavities to be raised up above
the original mold surface (FIG. 8c). As .theta. is increased
further to .theta.=.lamda.=60.degree., the features become shorter
again and the tip angle diminishes well below the angular width of
the blade, indicating that the rearward deformation is causing the
cavities to close up at their tips (FIG. 8d). These trends are
plotted in FIG. 9.
[0085] Samples of micromachined adhesives were fabricated to test
their adhesive properties. The blade was held at .theta.=60.degree.
and the trajectory was chosen to be .theta.=48.degree., an angle
approximately parallel to the rear face of the tool, and found
empirically to push most of the displaced material forward. The
nominal depth and tip-to-tip spacing were 100 .mu.m and 60 .mu.m.
According to one aspect of the invention, the resulting cast
synthetic adhesive can have wedge-shaped ridges with a tip-to-tip
spacing as low as 6 .mu.m.
[0086] Adhesion force data were collected on an instrumented stage
capable of moving the adhesive samples in and out of contact with a
flat glass substrate along a specified trajectory and loading the
adhesive in both the normal and shear directions. The stage (Velmex
MAXY4009W2-S4 and MA2506B-S2.5) is capable of 10 .mu.m positioning
resolution in the shear direction and 1 .mu.m in the normal
direction. The adhesive samples were mounted on a stationary
six-axis force/torque transducer (ATI Gamma SI-32-2.5) with a force
measurement resolution of approximately .+-.10 mN. The transducer
is mounted on a two-axis goniometer to allow the adhesive and
substrate to be precisely aligned.
[0087] A sample of adhesive is tested by bringing it into contact
with the substrate along a 45.degree. approach trajectory until the
adhesive reaches a certain preload depth. The preload depth is
defined as the distance by which the adhesive is pressed into the
substrate, measured normal to the substrate, from the position
where the tips of the adhesive features make first contact. Once
the sample is at the appropriate preload depth, it is pulled out of
contact along a trajectory at a specified pull-off angle. Such
tests are referred to as load-pull tests. To obtain the adhesion
limit curve, a battery of load-pull tests were performed for
preload depths ranging from 30-80 .mu.m and pull-off angles ranging
from 0-90.degree..
[0088] Limit curves were generated for a 1.21 cm.sup.2 patch of
micro-machined adhesive both before and after the post-treatment
process step. For comparison, a limit curve was generated for a
0.37 cm.sup.2 patch of photolithographic micro-wedge adhesive,
having a rectangular pattern of right triangular prisms (not
lamellar ridges), approximately 20 .mu.m wide, 80 .mu.m tall, 200
.mu.m long, and with a tip-to-tip spacing of 40 .mu.m between
features. These features are pictured in FIGS. 1a-1b.
[0089] The limit curves show the adhesives' performance in force
space. Each point corresponds to a combination of normal force and
shear force at which failure occurred. The region above the curve
is the "safe region": Forces above the curve can be sustained by
the adhesive; forces below the curve cause it to fail. The adhesive
test results are consistent with the directional adhesion model for
geckos, in which adhesion increases with increasing shear
force.
[0090] As shown in FIG. 10, the photolithographic adhesive produces
a maximum adhesive stress of approximately 18 kPa when loaded with
a shear stress of approximately 51 kPa, and the micro-machined
adhesive with no post-treatment achieves a maximum adhesion of 13
kPa at a shear stress of 37 kPa. After post-treatment, the
micro-machined adhesive has a maximum adhesion of 38 kPa at a shear
stress of 49 kPa.
[0091] At high levels of shear stress, all of the adhesive samples
show a "roll-off" in adhesion as increasing numbers of features
start to slide along the surface.
[0092] The micro-machining process has several advantages over the
photolithographic process, including increased yield, greater
control over the feature shape, a wider choice of mold materials,
and vastly improved mold turnaround time (a matter of hours instead
of weeks). One drawback is that the wax mold may become damaged
when the PDMS is extracted from it, and cannot then be used a
second time. To make more adhesives, the top layer of the mold is
removed and the underlying material is micromachined anew. However,
the manufacturing flexibility of micromachined adhesives makes up
for this drawback, and they are a particularly attractive option
for applications when rapid design iteration is required.
[0093] The theoretical model above provides qualitative insight
into the mechanics of the micro-machining process and of the
effects of varying the tool and approach angles when trying to make
closely spaced cavities. However, its force predictions were not
substantiated by experimental results. This suggests that a more
sophisticated model, for example using large strain finite element
modeling, is necessary for accurate predictions.
[0094] Empirical evidence shows that a variety of shapes may be
created by changing the trajectory angle .theta., including shapes
which do not match the profile of the micro-machining tool.
Variations with the blade centerline angle .lamda. and with curved
trajectories are possible. Different-shaped features affected by
post-treatment are possible. The post-treatment process has a
dramatic effect on the micro-machined adhesive's performance: the
maximum adhesion increases by nearly a factor of 3. The increase in
adhesion is due to the better surface finish obtained on the
contacting surfaces of the adhesive features (FIG. 5c). According
to an aspect of the invention, the tips of the wedge-shaped
features include a film of cured elastomeric material having a
desired smoothness or texture on one or both sides, in order to
take advantage of this increase in adhesion.
[0095] The post-treated micro-machined adhesive also achieves more
than twice the maximum adhesion obtained previously with
photolithographic wedges. For practical reasons, it is difficult to
make the photolithographic wedges at the same angle of inclination
as the micro-machined wedges; instead, they have one vertical and
one angled surface. Consequently, they are stiffer in the normal
direction and produce a larger elastic force that subtracts from
the net adhesive force. The micro-machining process affords more
freedom to vary the angle of inclination and taper, which affect
the available adhesion at various levels of applied shear
force.
[0096] As a further illustration of the effects of varying wedge
shape and orientation, the data in FIG. 10 also show much greater
adhesion for post-treated micro-machined wedges at low levels of
applied shear. As a consequence, the post-treated micro-machined
adhesive can support a maximum loading angle of 80.degree. away
from the surface for light loads. Whether post-treated or not, the
micro-machined adhesives are controllable because they have the
property of frictional adhesion: the adhesion increases as the
shear load increases, and the adhesion goes to zero as the shear
load is removed because the limit curve goes through the origin.
This property makes it possible for a climbing robot to detach its
feet with very little effort, simply by removing the applied shear
force. The result is smooth, efficient climbing.
[0097] In addition to climbing, potential applications for
gecko-inspired directional adhesives range from fumble-free
football gloves to manufacturing processes involving the handling
of materials.
[0098] By following the process according to the embodiments of the
invention, it is possible to create relatively large patches of
gecko-inspired directional adhesives using inexpensive equipment.
The wedge micro-machining process also permits greater freedom to
control the shapes of the features than is possible with molds
produced by photolithography. In the present case, by creating
features with two angled surfaces instead of one vertical and one
angled surface, and utilizing a simple post-treatment "inking"
process, it is possible to obtain a much higher maximum loading
angle at low levels of shear loading. This could be useful for
applications involving lightweight robots such as micro air
vehicles or for handling delicate materials.
[0099] Two requirements of the process described here are (1) a
suitable mold material with near-rigid/plastic behavior and (2) the
ability to control the trajectory of the tool, thereby controlling
the movement of displaced material, so that mold cavities can be
spaced close together while simultaneously controlling the cavity
shape. The micro-machining process does not yet match the smooth
surface finish obtained with photolithographic methods, but the
addition of a post-treatment step can provide a very smooth
contacting face and allows more than double the maximum adhesion
obtained with corresponding adhesives from photolithographic molds
on a flat glass substrate.
[0100] The current invention uses inexpensive and readily available
materials, including a computer-controlled stage with at least two
degrees of freedom (e.g., a CNC milling machine), a microtome blade
for the cutting tool, blocks of wax for the molds, and dish soap
for the lubricant. Many embodiments are clearly possible. The
indenting trajectory may be modified to create different shaped
features, with higher aspect ratios, narrower tips, or different
angles. Preliminary experiments suggest that even with the present
tool and a suitable lubricant, it may be possible to cut directly
into a soft metal. The resulting mold would be much more durable
and could survive many molding cycles. Other possibilities include
machining a temperature-hardening material such as polymer clay, or
using an investment casting process to create a second-generation
mold from a more durable material than wax.
[0101] The adhesives perform very well on glass, but do not perform
as well on rougher surfaces. To improve the adhesion on everyday
surfaces with micro-scale roughness, a siping step could be
employed after de-molding the adhesive. Specifically, the features
could be cut perpendicular to their longest dimension at a desired
frequency (see FIG. 5b), thereby allowing small, independent
sections of the feature to conform to surface roughness.
[0102] Additionally, with suitably precise and stiff positioning
equipment, much smaller terminal features should also be possible.
Even more complicated cavity geometries could be generated using a
machining apparatus with a rotational degree of freedom (allowing
the tool to change its angle during cutting), or by using a
custom-shaped micro-machining tool or multiple tools in sequence.
Such a process could create a hierarchical structure, with
nano-features on the surfaces of larger micro-wedges. Such
developments could lead to a gecko-inspired directional adhesive
that performs well on rough surfaces, a goal that has thus far
remained elusive.
[0103] The present invention has now been described in accordance
with several exemplary embodiments, which are intended to be
illustrative in all aspects, rather than restrictive. Thus, the
present invention is capable of many variations in detailed
implementation, which may be derived from the description contained
herein by a person of ordinary skill in the art. All such
variations are considered to be within the scope and spirit of the
present invention as defined by the following claims and their
legal equivalents.
* * * * *