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by George D. Skidmore, Eric Parker, Matthew
Ellis, Neil Sarkar, and Ralph Merkle
Zyvex Corporation, 1321 North Plano Road, Richardson, Texas
A replicative assembly methodology
may be based on assembly stations each with two degrees of
rotational freedom. These stations share translational degrees
of freedom in the three cartesian Cartesian axes by using
a common translating mechanism. The methodology provides replication
of the assembly stations, but due to the common translating
mechanism and control systems, it cannot be termed self-replicating.
The term "exponential assembly" is proposed to differentiate
this from self-replication. The exponential assembly architecture
can use parts made from many manufacturing methods, provided
that parts of considerable complexity can be produced. Because
integrated circuit manufacturing methods used for micro-electro-mechanical
systems (MEMS) allow large numbers of complex components to
be produced, it is one possible method for pursuing such an
approach to manufacturing. The methodology is scalable and
therefore useful for producing assembly stations which might
in turn produce other devices at ever-decreasing length scales
as part of a top-down approach to nanotechnology.
Self-replication and nanotechnology
are commonly discussed together as it has been suggested that
no large-scale nanotechnology industry can develop without
self-replication. Progress towards molecular nanotechnology
is being made on several fronts, producing breakthroughs in
molecular manipulation for chemical bond formation1,
molecular electronics2
and the harnessing of bio-molecular motors3.
The self-replicating entities of the biological arena are
often used as an existence proof for the possibility and inevitability
of self-replicating machinery. Simpler, man-made self-replicating
machinery, however, has not seen much progress since the demonstrations
of the first rudimentary self-reproducing machine demonstrations4,5.
The first artificial, self-replicating
mechanical structures were built by Penrose6,
and the first electro-mechanical systems were created by Jacobson5
decades ago. The structures used by Penrose showed that it
is possible to construct a very simple mechanical analogue
for self-reproduction. The demonstration using model railroading
parts by Jacobson showed that a self-assembly system using
complex parts and one simple assembly step would also result
in a self-reproducing analogue. Neither of these systems was
able to perform a useful function afterwards, but these experiments
did show that mechanical structures could perform self-replication
in a somewhat limited way. These authors simplified self-replication
by showing that it is not inherently a complex problem and
that a rich environment of complex parts and simple reproduction
steps reduces the self-replicating problem to a tractable
one. Unfortunately, these demonstrations did not address the
issues surrounding self-replicating manufacturing systems,
as shown in one report still regarding such systems as complex.7
Completely self-replicating systems
may not prove necessary for nanotechnology, as simpler systems
containing some replicating aspects will undoubtedly be easier
to implement. Self-replicating systems can usefully be divided
into the replicating component on the one hand, and the environment
on the other. It is generally not possible to consider a replicating
system without considering an environment also. By providing
a more structured and more complex environment, the complexity
of the replicating component can be reduced. The self-replicating
methodology described in this paper is achieved by providing
a very structured and complex environment so that certain
aspects of the replication process can be greatly simplified
— in particular, the number and complexity of the assembly
operations.
During the approach to mature molecular
manufacturing, interim systems, showing just enough replicating
aspects to assist the progression to more complex, mature
assembly systems is desired. In examining the evolution toward
nanotechnology, it has been unclear where self-replication
would become necessary or even possible. Previously, it had
been thought that self-replication could only be introduced
near the end of the development process. We may now have the
ability to develop and introduce assembly systems containing
self-replicating aspects within the foreseeable future.
This report outlines a possible
approach to a replication methodology for assembly stations
with individual rotational degrees of freedom but having shared
translational degrees of freedom and shared control. Relying
on an outside source for parts manufacture, this system performs
only the simplest assembly operations to complete construction
of its individual stations. It thus satisfies a definition
of self-replication, but is not a complete self-replicating
system. We thus propose a new term, "exponential assembly"
to describe this methodology, because the operations performed
are assembly operations and after N such assemblies have been
performed there can, in principle, be 2N assembled
stations.
To simplify the required assembly
operations, the system shares certain degrees of freedom and
instructions, as well as off-loading parts manufacture to
some other method. The total assembly system consists of a
translating mechanism capable of accurate positioning in the
three Cartesian axes, a control system and two surfaces with
pre-arranged parts ready for assembly. A schematic of this
system is shown below (in Figure 1). The parts can be manufactured
and arranged by any known method, making the system accessible
to many length scales.
Figure 1. The above schematic shows
the necessary components for an exponential assembly system.
A translating mechanism capable of translating in the three
Cartesian axes, a control system for controlling the stations
and the shared translating mechanism, and two facing surfaces
with pre-arranged arrays of unassembled components.
The surfaces are divided into grids,
with a set of components for a station located at each grid
site. The control system knows the location of each part as
well as the assembly procedure. Each site on the first surface,
defined as surface A, is uniquely addressed by a right-handed
Cartesian coordinate system with the convention A(x,y). The
lower-leftfirst grid site has address A(1,1), the upper-right
hasfinal site has A(n,n) as depicted in Figure
2a. The first step is to manually assemble a single station
at die site A(1,1). This is accomplished by whatever means
are available, as it only needs to be done once.
Figure 2a. Two mirror image sufaces
for exponential assembly are shown.
Figure 2b. Surface B is then rotated 180
degrees about its z-axis and translated such that site B(1,1)
is across from A(1,1).
Figure 2c. The next translation locates
A(1,1) and B(1,1) across from B(2,1) and A(2,1) respectively
as shown here.
Figure 2d. Translating again positions
A(1,1) and B(1,1) across from B(4,1) and A(4,1) respectively
as shown here.
At this point, the first surface has an assembled
and functioning station. The functioning station is then placed
into the system facing an opposing surface. This second surface,
fabricated as a mirror image of the first, contains another
set of grid sites with components ready for assembly. This
second surface, defined as surface B, is addressed with a
left-handed Cartesian coordinate system — thus positionwith
the convention B(x,y). This sites are thus labeled B(1,1)
is in the lower right, and positionthrough B(n,n) as shown
in Figure 2a. is in the upper left. This surface needs to
be arranged to face surface A such that translations are equivalent
from each of the reference frames. This is done by rotating
surface B 180 degrees about its z-axis as depicted in Figure
2b.
Initially, site A(1,1) is located
across from B(1,1). The assembly process is started and station
A(1,1) assembles station B (1,1). The assembly process for
a suggested station will be outlined in detail in the next
section. The station at site A(1,1) is then returned to its
as-assembled configuration and the station at B(1,1) is enabled
for operation. The surfaces are then translated such that
site A(1,1) is across from B(2,1), which implies that the
newly constructed B(1,1) is across from A(2,1) as shown in
Figure 2c. Because surface B is a mirror image copy of surface
A, the same assembly sequence will work for B(1,1) in constructing
A(2,1) as works for A(1,1) in constructing B(2,1). The two
can perform the assembly sequence simultaneously. When the
sequence is completed there is newly assembled stations at
A(2,1) and at B(2,1). This iteration ends by returning the
operating stations (those at A(1,1) and B(1,1)) to their as-assembled
configurations and enabling the newly assembled stations at
A(2,1) and B(2,1) for operation. The next large translation
locates A(1,1) across from B(4,1) as shown in figure 2d and
the four operating stations can assemble another four. After
some number of assembly iterations, each surface contains
an entire row of assembled and functioning stations. The next
translations will therefore position row A(n,1) across from
row B(n,2), which also positions row B(n,1) across from row
A(n,2). Entire rows are now assembled simultaneously. After
iterating through the rows in a similar manner, both surfaces
will be completely assembled. after iterating through the
rows.
The assembly station can be configured
in many ways with varying degrees of complexity. The exponential
assembly station we will describe has the ability to rotate
about two orthogonal axes, each with 90 degree range of motion,
and the ability to grip and release parts. A schematic of
this simple station is shown with the components arranged
flat in Figure 3a. The components
are quite complex, as is necessary for easy assembly. The
base piece contains a rotational stage with an attachment
mechanism for connecting the second component. The arm piece
contains another rotation stage with an attached arm, terminating
with a gripper mechanism. Also shown on the arm piece is a
place for gripping the component, termed the handle, as well
as the attachment mechanism for connecting to the base component.
To assemble the device, the arm piece must be lifted from
the surface, rotated about the y-axis and attached to the
base piece using the attachment points. If the attachment
mechanism is secure, the entire assembly operation is complete
and the device is shown in Figure 3b.
The simple two-component assembly station is
shown (in Figure 3a) with the parts arranged flat on a surface.
Figure 3a. The rotational stages
are labeled as are the gripper, handle, and attachment points.
Figure 3b. When the two components
are assembled, the assembly station is as shown.
This first device is now assembled. It has not
been discussed with what mechanism this first assembly station
is assembled, but an external gripper and set of assembly
stages under manual or automated control would likely be sufficient.
The translating stages shown in Figure
1, in conjunction with added rotation capability, should
suffice. An animation of this first assembly sequence can
be found at http://www.zyvex.com/research/exponential.html.
Regardless of its construction method, once assembled, the
first device is ready to begin the exponential assembly process.
To perform exponential assembly, two arrays
of pre-arranged components are mounted facing each other.
As discussed above, the second array can be a mirror image
of the first. The first assembled station then performs the
rotational motions and gripping while the shared translational
mechanisms provide the Cartesian displacements necessary to
assemble the station on the opposite surface. The assembly
operation sequence showing the first component assembling
the second is outlined in Figure 4 and in the animation found
at http://www.zyvex.com/exponential/____. Figure
4a shows the four components comprising two mirror image
stations ready for assembly. Figure
4b shows the two components after one has been rotated
and positioned such that the two are facing each other in
the necessary arrangement. Figure 4c
shows the situation after the first component has been assembled
by the external mechanism. The assembled station first rotates
90 degrees about the z-axis, as shown in Figure
4d, then it translates to grip the arm-stage as shown
in Figure 4e. The base rotation
stage of the assembled station then rotates about the y-axis
and translates until the attachment points align as shown
in Figure 4f. After the attachment
is made, the gripper releases and translates. The assembly
is now completed, as shown in Figure
4g. The two components are now separated a safe distance
and the two rotation stages of the first station are returned
to their original, as-assembled configuration. The two assembled
stations are now ready to begin another assembly sequence
and are translated such that each is across from a fresh set
of components. The same sequence of operations is now provided
to both assembled stations and they repeat the exponential
assembly process until each array of components is assembled.
In principle, assuming 100% yield of both components and assembly
operations, the sequence produces 2N assembly stations after
N assembly sequences.
Shown below is the sequence of assembly operations
necessary for the first station to assemble the second.
.
Figure 4a. The stations are first shown
unassembled.
Figure 4b. After rotating one of the stations,
the two are shown facing each other.
Figure 4c. The first is then assembled.
Figure 4d. The assembled station
first rotates about the z-axis.
Figure 4e. It then translates to grip the
component of the other.
Figure 4f. The other second rotation stage
of station one then rotates 90 degrees and translates such
that the attachment points are aligned with translation.
Figure 4g. After the attachment is
made the gripper releases and the assembly is completed.
The assembly rate will suffer if
individual devices can not enabled as assumed above. The above
sequence of operations presumes that a single station, once
assembled, is enabled, or "turned-on" and ready for motion.
If another approach is taken — for example, an approach
where all of the stations on a surface are "hard-wired" to
move simultaneously, even when unassembled — the above
operations will not work. This is because the unassembled
base rotation stages are moving at an undesirable time. This
problem is easily overcome by operating only one surface during
an assembly sequence, leaving the other surface inactive.
After one sequence, the first surface is made inactive and
the second is operated. Thus, the first assembly station assembles
first one on the opposing surface, and then another. There
are now two assembled on the second surface and one on the
first. The second surface is then enabled and used to build
two more on the first while the first remains inactive. The
end result is a ping-pong mode of assembly where progression
follows a Fibonacci sequence instead of the aforementioned
2N sequence. The growth rate of assembled stations
has been diminished, but the control system or wiring of stations
has been greatly simplified.
We have described a conceptually
simple assembly station. In practice, we expect that more
complex operations and structures will prove desirable; these
more evolved and complex systems evolving naturally from the
original concept. For example, the attachment may be insecure
and require additional bracing support, which can easily be
included by adding pieces and assembly operations. More complex
components could also be used, giving the stations additional
degrees of freedom, larger range of motion, or advanced features
of many kinds. Although this additional functionality is unnecessary
for exponential assembly, it adds to the usefulness of the
station by assembling devices other than like-copies of itself.
Once an array of these components
is assembled, it can be used to do parallel assembly of additional
like-stations such that complete arrays can be assembled in
one sequence. It might also prove useful to assemble arrays
of more complex robotic manipulators, end products, etc. A
wide range of assemblies could be constructed using these
or similar stations, provided that the parts are of appropriate
size and arrangement, and that collisions can be avoided during
assembly.
There has been no discussion about
the length-scales involved in this exponential assembly methodology.
In principle, the system is not confined to any specific size
regime — it should be possible to construct systems having
many sizes. The replicative demonstration by Jacobson mentioned
above was built using model railroading parts and the exponential
assembly system defined here could likely be demonstrated
at such a scale. It is not yet known the scale at which such
a system would perform an economically useful function. Developments
in micro-electro-mechanical systems (MEMS)8how
that it is possible to fabricate large numbers of micro-machine
components onto a silicon wafer with high precision and great
complexity. MEMS technology may be an appropriate starting
technology for manufacturing the arrays of components necessary
for an exponential assembly demonstration.
Exponential assembly at length-scales
smaller than that at the MEMS scale may help in furthering
nanotechnology. Commercial MEMS multi-project wafers are today
fabricated with minimum feature sizes of 2um9.
Current integrated circuit minimum feature sizes are closer
to 0.18um. The use of more expensive processing currently
available to high performance integrated circuits would enable
MEMS systems to follow Moore's Law downward in scale. Progress
towards making assemblies using MEMS components has been discussed
by this group elsewhere10.
Smaller lithography has been demonstrated using electron beam
lithography11, electron
beam induced deposition12,
and scanning probe microscopy13.
These smaller-scale lithogaphies will require extensive research
before they can be used to produce the complex components
necessary for exponential assembly, as described here. It
may be even more difficult to scale such systems into the
molecular realm. While molecular motors capable of rotation
have been shown3,
these motors are not reported to be well-controlled, nor do
they turn in both directions, making them unsuitable for such
a system. These same motors have been arranged onto a surface
in a controlled manner demonstrating a first needed step —
complex, functional molecular components pre-arranged in known
locations on a flat surface. Despite these shortcomings, there
appear to be no fundamental obstacles to scaling exponential
assembly downward.
Exponential assembly has been proposed
as a possible replicative methodology for assembly-based manufacturing
systems. Separate assembly stations having two rotational
degrees of freedom are, in principle, able to assemble like-copies
when coupled to shared translating mechanisms and a control
system. The methodology should be possible to implement at
different length scales, but the integrated circuit manufacturing
technology used in MEMS appears to be well suited as a starting
point for component production. If this methodology is scalable,
it may be useful for nanotechnology, as it does allow for
an exponential increase in assembly capability, making possible
the production of large numbers of assembled systems.
1.
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Reinerth W A, Jones L, Burgin T P, Zhou C-W, Muller C J, Deshpande
M R, Reed M A and Tour J M 1998 Nanotechnology 9(3) 246-250
3. Montemagno
C, Bachand G, Stelick S and Bachand M 1999 Nanotechnology
10(3) 225-231
4. Penrose
L S 1959 Scientific American 200 105-114
5. H.
Jacobson H 1958 American Scientist 46 255-284
6. Penrose
L S, Penrose R 1957 Nature 179 1183
7. Freitas
R and Gilgreath W P (editors) 1982 Advanced Automation for
Space Missions NASA CP-2255 http://www.islandone.org/MMSG/aasm/
8. Madou
M 1997 Fundamentals of Microfabrication CRC Press Boca Raton,
Florida
9. MUMPs
process available from Cronos Integrated Microsystems, 3021
Cornwallis Road, Research Triangle Park, NC 27709
10. Skidmore
G D, Ellis M, Parker E, Sarkar N, Merkle R 2000 Proceedings
of the International Symposium on Micromechatronics and Human
Science IEEE Catalog Number:OOTH8530 pp.3-9
11. Carr
D W and Craighead H G 1997 J. Vac. Sci. Technol. B 15 2760-2765
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H W P Kretz J, Rudolph M, Weber M, Dahm G, and Lee K L 1994
Jpn. J. Appl. Phys. 33 7099-7107
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M C, Guisinger N P, and Lyding J W 2000 Nanotechnology 11(2)
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