Note: Descriptions are shown in the official language in which they were submitted.
Title: Mechanical Computing Systems
TECHNICAL FIELD
100011 The present invention relates to the field of computer technology
or
computer systems relating to general purpose devices that can be programmed to
carry out a set of arithmetic or logical operations. More specifically, the
present
invention is directed to mechanical computing, wherein a mechanical computer
is
built from mechanical components rather than electronic components.
BACKGROUND ART
[0002] Methods for mechanical computation are well-known in the prior
art
(Svoboda, "Computing Mechanisms and Linkages," New York, Dover Publications,
1965; Bradley, "Mechanical Computing in Microelectromechanical Systems
(MEMS)," AIR FORCE INSTITUTE OF TECHNOLOGY, AFIT/GE/ENG/03-04,
Ohio, 2003; Sharma, Ram et al., "Mechanical Logic Devices and Circuits," 14th
National Conference on Machines and Mechanisms (NaCoMM-09), 2009) However,
while the earliest example of a Turing-complete design is probably Babbage's
Analytical Engine, which was described in 1837 (although never built), the
vast
Date Recue/Date Received 2021-03-26
majority of previous proposals for mechanical computing are not Turing-
complete
systems. Rather, they are either special-purpose devices not intended to
address
general-purpose computing at all, or they are partial systems or mechanisms,
lacking
crucial capabilities which would allow them to provide Turing-complete
systems. For
example, with respect to partial systems or mechanisms, known examples include
logic gates built from custom parts, kits, or even toys like Lego. Note that
mechanical
logic gates alone, even universal ones, do not by themselves permit Turing-
complete
computing; some memory means is also required. Turing-complete computing
requires a means for combinatorial logic, as well as a means for sequential
logic.
[0003] The mechanical computing literature also includes molecular-scale
implementations of various computational components (again, often not Turing-
complete systems), including (Drexler, "Nanosystems: Molecular Machinery,
Manufacturing, and Computation," New York, John Wiley & Sons, 1992; Hall,
"Nanocomputers and Reversible Logic," Nanotechnology, 1994; Heinrich, Lutz et
al.,
"Molecule Cascades," Science, 2002; Remon, Ferreira et al., "Reversible
molecular
logic: a photophysical example of a Feynman gate," Chemphyschem, 12, 2009;
Orbach, Remade et al., "Logic reversibility and thermodynamic irreversibility
demonstrated by DNAzyme-based Toffoli and Fredkin logic gates," PNAS, 52,
2012;
Roy, Sethi et al., "All-Optical Reversible Logic Gates with Optically
Controlled
Bacteriorhodopsin Protein-Coated Microresonators," Advances in Optical
Technologies, 2012).
[0004] While previous designs for mechanical computing vary greatly,
previous proposals capable of Turing-complete computing (as opposed to limited-
purpose devices) tend to reply upon a substantial number of basic parts (or
"primitives") including various types of gears, linear motion shafts and
bearings,
springs (or other energy-storing means, e.g., some designs use rubber bands),
detents,
ratchets and pawls, or other mechanisms which have the potential to be energy-
dissipative, as well as increasing the complexity of the device. Note that
such designs
require these various primitives to function properly; they are not optional.
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[0005] That the use of many types of basic parts in a mechanical system
can
complicate design, manufacture, and assembly, as well as potentially reducing
reliability, is obvious. Reducing the complexity of mechanisms is a common
inventive goal.
[0006] Note also that many of the mechanisms used in previous proposals
for
mechanical computing generate substantial friction. Removing such mechanisms
would have benefits beyond reducing device complexity, including reduced
energy
expenditure. However, judged by the prevalence of friction-generating
mechanisms in
mechanical computing systems, it is difficult to design around this issue.
[0007] Perhaps less evident than friction are other modes of energy
dissipation, including vibrations, which may, e.g., create heat, or generate
acoustic
radiation. For example, ratchets and pawls, detents, or other mechanisms which
involve the relatively uncontrolled impact of one piece of a mechanism upon
another
can lead to energy-dissipating vibrations, and so the removal of these types
of
mechanisms would also have benefit.
[0008] Waste heat is a well-known issue for computational systems,
electronic
or mechanical, which dissipate far more energy per bit operation than is
required in
theory. In theory, computations can be performed where the energy dissipated
is only
ln(2) kBT per irreversible bit operation. This is called the Landauer Limit
(Landauer,
"Irreversibility and Heat Generation in the Computing Process," IBM Journal of
Research and Development, 1961) and has been confirmed experimentally (Berut,
Arakelyan et al., "Experimental verification of Landauer's principle linking
information and thermodynamics," Nature, 7388, Nature Publishing Group, 2012).
[0009] Note that the Landauer Limit only applies to irreversible
operations.
Reversible operations can, in theory, dissipate zero energy. While
conventional
computers are generally not built upon reversible hardware, reversible
computing has
been studied for decades (Landauer, "Irreversibility and Heat Generation in
the
Computing Process," IBM Journal of Research and Development, 1961; Bennett,
"The Thermodynamics Of Computation," International Journal of Theoretical
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Date Recue/Date Received 2021-03-26
Physics, 12, 1973; "Logical reversibility of computation," IBM Journal of
Research
and Development, 6, 1973; Toffoli, "Technical Report MIT/LCS/TM-151 -
Reversible Computing," Automata, Languages and Programming, Seventh
Colloquium, Noordwijkerhout, Netherlands, Springer Verlag, 1980; Toffoli and
Fredkin, "Conservative Computing," International Jounral of Theoretical
Physics, 3/4,
1982; Bennett and Landauer, "The Fundamental Physical Limits of Computation,"
Scientific American, 1985; Feynman, "Quantum Mechanical Computers,"
Foundations of Physics, 6, 1986). For a general overview of reversible
computing
from a software perspective, see (Perumalla, "Introduction to Reversible
Computing,"
CRC Press, 2014).
[0010] Whether reversible or irreversible, novel designs for mechanical
computational systems that have the potential to reduce device complexity
(along
with the associated design, manufacturing and assembly costs) and use less
energy
per bit operation than existing designs, would be quite useful. Not being
subject to the
Landauer Limit, reversible designs have the potential to ultimately use the
least
energy. However, existing computing systems use energy so far in excess of the
Landauer Limit that even irreversible designs could greatly improve upon the
state of
the art.
BRIEF SUMMARY OF THE INVENTION
[0011] Embodiments of the invention include mechanical computing
mechanisms and computational systems which have lower energy dissipation, a
smaller number of basic parts, and other advantages over previous systems.
Multiple
embodiments are disclosed including mechanical link logic, mechanical flexure
logic,
and mechanical cable logic, along with design paradigms (including both
mechanical
designs, principles, and a novel classification system which categorizes
systems as
Types 1 through 4) that teach how to apply the general principles to other
embodiments.
BRIEF DESCRIPTION OF THE DRAWINGS
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[0012] For a more complete understanding of the present invention,
reference
is now made to the following descriptions taken in conjunction with the
accompanying drawings, in which:
[0013] FIG. 1 depicts a side view of a molecular rotary joint.
[0014] FIG. 2 depicts a side view of a four-bar linkage.
[0015] FIG. 3 depicts a top view of a mechanism which can serve as the
basis
for a NAND or AND gate.
[0016] FIG. 4 depicts a top view of a mechanism which can serve as the
basis
for a NOR, NAND, AND, or OR gate.
[0017] FIG. 5 depicts a top view of a XOR gate.
[0018] FIG. 6 depicts a top view of a Fredkin gate.
[0019] FIG. 7 depicts a top view of a co-planar lock in the (0,0) state.
[0020] FIG. 8 depicts a top view of a co-planar lock in the (1,0) state.
[0021] FIG. 9 depicts a top view of an alternate embodiment of a co-
planar
lock in the (0,0) state.
[0022] FIG. 10 depicts atop view of an alternate embodiment of a co-
planar
lock in the (1,0) state
[0023] FIG. 11 depicts a 3/4 view of a non-co-planar lock in the (0,0)
state.
[0024] FIG. 12 depicts a top view of a non-co-planar lock in the (0,0)
state.
[0025] FIG. 13 depicts a 3/4 view of a non-co-planar lock in the (1,0)
state.
[0026] FIG. 14 depicts a top view of a non-co-planar lock in the (1,0)
state.
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CA 03007614 2018-06-06
WO 2017/116482
PCT/US2015/068359
[0027] FIG. 15 depicts a 3/4 view of a non-co-planar lock in the (0,1)
state.
[0028] FIG. 16 depicts a top view of a non-co-planar lock in the (0,1)
state.
[0029] FIG. 17 depicts a top view of a balance with an input of 0.
[0030] FIG. 18 depicts a top view of a balance with an input of 1 with
an
anchor at the top.
[0031] FIG. 19 depicts a top view of a balance with an input of 1 with
an
anchor at the bottom.
[0032] FIG. 20 depicts a top view of a binary double balance with inputs
(1,0).
[0033] FIG. 21 depicts a top view of a binary double balance with inputs
(1,1).
[0034] FIG. 22 depicts a top view of a switch gate.
[0035] FIG. 23 depicts a top view of a lock and balance-based NAND gate.
[0036] FIG. 24 depicts a top view of a lock and balance-based Fredkin
gate.
[0037] FIG. 25 depicts a top view of a shift register cell in its blank
state.
[0038] FIG. 26 depicts a top view of a shift register cell after input
has been
provided but before a clock signal is set to high.
[0039] FIG. 27 depicts atop view of a shift register cell after input
has been
provided and a clock signal has been set to high.
[0040] FIG. 28a depicts a top view of the left half of a two-cell shift-
register.
[0041] FIG. 28b depicts a top view of the right half of a two-cell shift-
register.
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[0042] FIG. 29 depicts a top view of a canceling group.
[0043] FIG. 30 depicts a top view of a flexure-based lock.
[0044] FIG. 31 depicts a top view of an MCL pulley and associated
mechanisms.
[0045] FIG. 32 depicts a side view of an MCL pulley and associated
mechanisms.
[0046] FIG. 33a ¨ FIG. 33c depict top views of various states of one
embodiment of an MCL lock.
[0047] FIG. 34 depicts a 3/4 view of a knob which can be used to create
a
lock.
[0048] FIG. 35 depicts a 3/4 view of two knobs forming a lock in the
(0,0)
state.
[0049] FIG. 36 depicts a 3/4 view of a lock in the (0,1) state.
[0050] FIG. 37 depicts a 3/4 view of a lock in the (1,0) state.
[0051] FIG. 38 depicts atop view of an MCL oval.
[0052] FIG. 39 depicts a top view of an MCL balance in the (0,0) state.
[0053] FIG. 40 depicts atop view of an MCL balance in the (0,1) state.
[0054] FIG. 41depicts a top view of an MCL balance in the (1,0) state.
[0055] FIG. 42depicts a top view of an MCL balance in the (1,0) state
after
actuation.
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DETAILED DESCRIPTION OF THE INVENTION
Definitions
[0056] The following definitions are used herein:
[0057] "Anchor block" means one or more rigid structures to which basic
parts or higher-level assemblies can be attached, and which may also serve as
heat
sinks. Note that even when written in the singular, there may be more than one
anchor
block, as design needs dictate. The shape of an anchor block can be arbitrary
("block"
should not be taken to mean that the structure is necessarily rectangular, or
any simple
shape). An anchor block can be made from any appropriate material, not limited
to,
but including any of the materials suggested herein from which basic parts
could be
made. An anchor block is assumed to be present as needed whether explicitly
stated
or not.
[0058] "Anchored" means attached to an anchor block, or otherwise
rendered
immobile with respect to other relevant basic parts or mechanisms. Anchoring
may be
permanent or conditional (e.g., depending on data inputs or clock signals),
and a
conditionally anchored part may be referred to by its relevant conditional
state (i.e., if
the part is unanchored in a given situation, it may be referred to as
unanchored, and
vice versa).
[0059] "Atomically-precise" means where the identity and position of
each
atom in a structure are specified by design. Structures such as naturally-
occurring or
bulk-manufactured crystals or quasicrystals, having surface irregularities,
impurities,
holes, dislocations or other imperfections, are not atomically-precise.
Atomically-
precise can, but does not have to, include knowledge of isotopic composition.
[0060] A "balance" is a structure which transmits movement through one
side
or route of a mechanism versus another. Balances can be used, e.g., to perform
computations and to route data. A balance may have any number of inputs and
outputs, some of which may be anchored, or conditionally anchored (as when
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connected to a lock). The word "balance" and forms thereof may also be used in
its
traditional sense (e.g., equal masses or forces 'balance' each other) as
context
dictates.
[0061] A "basic part" is a fundamental building block, or primitive, of
a
mechanism or computational system. For example, the basic parts of MLL are
links
and rotary joints, the basic parts of MFL are links and flexures, and the
basic parts of
MCL are cables, pulleys, and knobs. "Basic part" is synonymous with
"primitive,"
and the distinction between a basic part and a mechanism is that basic parts
are, at
least in their simplest implementations (e.g., a pulley is a basic part
because it can be
monolithic, but some implementations of a pulley could require an axle as a
separate
part), not obviously logically divisible into smaller parts
[0062] A "cable" is a flexible structure used to transmit tensile
forces, e.g.,
directly, or via pulleys.
[0063] "Coaxial" refers to rotary joints which share the same axis of
rotation.
The term may also be applied to the analogous concept in co-planar mechanisms
which have multiple joints that share common arcs of movement.
[0064] "Computing system" and forms thereof including "computational
system" means a system for carrying out general-purpose computations. Such
systems
are Turing-complete. Devices only capable of solving a single, or a limited
class of,
problems, such as planimeters, harmonic synthesizers or analyzers, equation
solvers,
function generators, and differential analyzers, are not capable of general-
purpose
computing, and are therefore not "computing systems." Power sources, motors,
clock
signal generators, or other components ancillary to Turing-complete
computational
means are not part of a computing system. Different types of computational
systems
may be interfaced. For example, an MLL system could take its input, provide
its
output, or otherwise interact with other mechanical or electronic computing
components, systems, sensors, or data sources, although such a system would
only
constitute an MLL computational system if the MLL components themselves
provide
Turing-complete computational means.
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[0065] "Co-planar" refers to a mechanism that moves in one or more
parallel
planes. The term is used to differentiate essentially flat (but potentially
multi-layer)
implementations of mechanisms from those which utilize movement in non-
parallel
planes. The distinction is largely one of convenience for naming and
visualization, as
the mechanisms described herein can be constructed in either a co-planar or
non-co-
planar manner.
[0066] "Data link" means a link that aids in transferring data, from
one
location to another. A data link may be simply called a "link" when context
makes the
meaning clear.
[0067] "Dry switching" as applied to the mechanical computational
components described herein means that no force is applied to mechanisms that
are
not free to move in some way.
[0068] A "flexure" is a type of bearing which allows movement through
bending of a material, rather than sliding or rolling.
[0069] "Fork" means a branch in a line allowing one data link to be
coupled
to more than one other data link. A fork can, e.g., allow the copying of one
input/output to multiple links or lines.
[0070] "Input" means the data, for example encoded by physical
position,
supplied to a mechanism, e.g., for purposes of storing the data in memory,
transmitting the data elsewhere, performing combinatorial logic on the data,
or
actuating the mechanism (e.g., via a clock signal). For a variety of reasons,
including
that the input to one mechanism can be the output from another, that some
mechanisms use the same data as both inputs and outputs (e.g., a circular
shift register
or other mechanisms with a feedback loop), and because some embodiments permit
reversibility, there may be little distinction between "inputs" and "outputs,"
the use of
one term or the other being more for didactic purposes. Therefore, regardless
of
which term is used, both are assumed to apply if appropriate in a given
context.
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[0071] "Line" means a sequence of connected data links. Also called a
"data
line."
[0072] "Link" means a rigid structure or body connected to one or more
rotary joints.
[0073] A "lock" is a structure with a plurality of inputs where one or
more of
the inputs being set to some pre-defined range of values results in the other
inputs
being locked. For example, in a two-input lock, upon setting one of the inputs
to a
non-zero value, the other input is locked until the non-zero input is returned
to zero.
In a two-input binary lock, the non-zero value being set would typically be 1,
but the
lock mechanism may engage well before the input actually reaches 1 (e.g., an
input of
0.1 on one input may be sufficient to lock the other input).
[0074] "Logic gate" includes traditionally-irreversible gates such as
AND,
CNOT, NAND, NOT, OR, NOR, XNOR, XOR, reversible gates such as Fredkin and
Toffoli gates, or other mechanisms which provide combinatorial logic (e.g.,
reversible
implementations of traditionally-irreversible gates, or special-purpose logic
gates).
[0075] "MCL" stands for Mechanical Cable Logic, a paradigm for creating
computational systems and mechanisms thereof, using cables, knobs, and
pulleys.
[0076] A "mechanism" is a combination of basic parts forming an
assembly
of a level of complexity between that of a basic part and a computational
system. For
example, in MILL, lines, locks, balances, logic gates, and shift registers are
all
components, as are any sub-assemblies which include more than one basic part.
By
virtue of being basic parts, links and rotary joints, or any other basic
parts, are not
mechanisms.
[0077] "MFL" stands for Mechanical Flexure Logic, a paradigm for
creating
computational systems and mechanisms thereof, using links and flexures.
[0078] "MILL" stands for Mechanical Linkage Logic, a paradigm for
creating
computational systems and mechanisms thereof, using links and rotary joints.
Note
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that as the first and most extensively described embodiment, details are
provided for
MLL that are not necessarily repeated for MFL, MCL, or other embodiments. For
example, clocking is described extensively in the context of MLL, but not
other
embodiments. Due to the analogous logical and mechanical nature of the various
embodiments presented, given the teachings herein, it will be apparent how to
apply
information presented for one embodiment to other embodiments.
[0079] "Not-coaxial" refers to two or more rotary joints which do not
share
the same axis of rotation, or the analogous concept in co-planar mechanisms.
[0080] "Output" means the data, for example encoded by physical
position,
provided by a mechanism. See "Input' for additional detail and comments on the
interchangeability of the two terms.
[0081] A "pulley" is a mechanism which facilitates the routing of,
and/or
transmission of forces by, one or more cables. Traditionally, pulleys rotate
as the
cable moves, but this is not necessary, e.g., a cable could slide over a
pulley's surface
if the energy dissipation incurred was suitably low. Pulleys may be anchored
or
unanchored. Unanchored pulleys may be free to move as dictated by their
attached
cables, or may have their movements constrained by a track, groove, or other
guiding
means.
[0082] "Rotary joint" means one or more connections between rigid
bodies
that allow rotational motion about an axis. Rotary joints may be anchored or
unanchored.
[0083] "Support link" means a link that provides physical support or
kinematic restraint for other links.
[0084] "Turing-complete" has its standard meaning as used in the field
of
computer science, with the caveat that, since real-world systems have bounded
memory, time, and other parameters, such practical limitations are
acknowledged to
exist, and so the term "Turing-complete," when applied to an actual system,
may be
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taken to include such limitations (resulting in what may be more precisely
called a
"linear bounded automata").
Introduction
[0085] Herein it is first shown that a mechanical computational system
can be
designed solely from two basic parts: links, and rotary joints (plus an anchor
block to
which these basic parts can be affixed; this will be subsequently assumed and
not
necessarily mentioned each time), using a design paradigm referred to as
Mechanical
Linkage Logic ("MLL"). Subsequently, the paradigms of MLL are generalized to
show other ways in which simple and efficient mechanical computing systems can
be
designed, such as Mechanical Flexure Logic ("MFL") and Mechanical Cable Logic
("MCL") (any of which could also be used in combination). Part of this
generalization
also includes the description of a novel classification system based on ways
in which
mechanical computing systems can dissipate energy.
[0086] These new paradigms can simplify the design and construction of
mechanical computing mechanisms and systems, and reduce or eliminate major
sources of energy dissipation, such as friction and vibration, while still
operating at
useful computational speeds. Such computational systems can also be designed
to
operate reversibly. These, and other factors, offer various benefits over
previously-
proposed computing systems.
[0087] Embodiments of the invention provide all the mechanisms necessary
to
create Turing-complete computational systems. For example, using MLL, this
includes lines, logic gates, locks, and balances, and more complex mechanisms
such
as shift registers, each requiring no basic parts other than links and rotary
joints Other
embodiments (e.g., MFL and MCL) provide analogous basic parts and mechanisms
to
also permit the creation of Turing-complete computational systems.
Energy-Efficient Mechanical Computing
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[0088] As discussed herein, mechanical computing systems can dissipate
energy in several ways, including friction (including drag caused by thermal
movement at the atomic level), and vibrations, which can be caused not only by
running a mechanical system fast enough to excite its resonant frequencies
(something which can be avoided by controlling clock speed), but by part-to-
part
impacts or relatively unconstrained releases of energy. Examples of such part-
to-part
impacts and relatively uncontrolled releases of energy include the snapping
motions
of ratchet and pawl mechanisms, and detents.
[0089] Given these issues, four categories are defined for mechanical
computing devices:
[0090] Type 1: Devices which store potential energy (e.g., in a spring)
and
which then release this energy in a manner unconstrained by the computational
degrees of freedom. Devices which use ratchets and pawls, or detents, are
examples
of a Type 1 device, as the release of stored energy by the ratchet and pawl or
detent
are assumedly not tied to the computational degrees of freedom. In such a
device, if,
e.g., a ratchet and pawl were present, while the snapping motion of the pawl
might
occur with a periodicity controlled by a clock system, the energy release of
that
snapping motion would not be tied to the clock frequency. Rather, the speed of
the
energy release would be a function of, e.g., the force applied to, and the
mass of, the
pawl, regardless of the overall computational speed of the system. The
resulting
collision of the pawl with the ratchet could generate vibrations which waste
energy.
[0091] Type 2: Devices which store potential energy, and then release
this
energy in a manner controlled by the computational degrees of freedom. For
example, in the MLL systems described herein, if a spring was to be placed
between
links in a line, as the system drove the line back and forth, the spring would
compress
and decompress. This compression and decompression would take place gradually,
at
the frequency imposed by a system clock. The spring would not be allowed to
snap an
unconstrained part into place at a speed which, from the perspective of the
system
clock, is arbitrary. Rather, the movement of the spring and attached parts is
governed
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by the computational degrees of freedom. Note that also in the above scenario,
the
spring is part of a continuous linkage, and so no collision of parts occurs
like when a
ratchet is impacted by its pawl. This can also help reduce dissipated energy.
And,
even if part collisions do occur (e.g., see the descriptions of knobs in MCL
systems),
since the speed with which such contacts occur can be coupled to the
computational
degrees of freedom, it is possible to choose speeds which do not dissipate
unacceptable amounts of energy (and in fact, by driving such impacts with the
system
clock, which preferably uses a sine wave-like signal, even a relatively fast
switching
speed can result in very low part velocities at the moment of impact).
[0092] Type 3: Devices which do not store more than trivial amounts of
potential energy, but have parts with non-trivial unconstrained degrees of
freedom.
For example, depending on the implementation, systems could be created using
MLL
where, due to one or more locks being in the blank (0,0) position, connected
links are
free to move in an essentially random manner due to thermal noise, system
vibrations,
or other causes. Among other issues, such unconstrained movement can result in
having to expend energy to periodically set mechanisms to a known state to
ensure
reliable operation. (Note that such situations can be avoided with properly
designed
systems, and this is presented as exemplary only).
[0093] Type 4: Devices which do not store more than trivial amounts of
potential energy, and have no more than trivial unconstrained degrees of
freedom.
For example, a properly designed MLL system where all movement is, directly or
indirectly, coupled to data inputs and/or the system clock. No components are
allowed
to freely "float" as might a link connected only to a lock in the blank state.
With
respect to defining "trivial" unconstrained degrees of freedom, this means
those
which occur in a small enough portion of the overall system (e.g., one
particular type
of mechanism has this issue, but the mechanism is rare in the overall system),
or those
that occur infrequently enough, that they do not materially affect overall
energy
dissipation. An example of infrequently-occurring unconstrained degrees of
freedom
would be when some system mechanisms have temporarily unconstrained degrees of
freedom during an initialization or reset process. Such processes might only
be
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needed very infrequently compared to standard computation operations, and so
would
contribute very little to a system's energy dissipation. With respect to
defining
"trivial" when used in reference to potential energy, note that all mechanical
systems
will store some potential energy. For example, in theory, even very rigid
links deform
slightly when force is applied to them. Assuming no permanent deformation,
they
thus technically store potential energy. Such unavoidable potential energy
storage is
considered trivial. The point of Type 3 and Type 4 systems is the avoidance of
systems which purposefully store potential energy for later release, such as
in a
system with springs, where those springs and their potential energy are
required for
the system to function properly.
[0094] Note that lack of substantial deformation is not the only way to
achieve
a Type 3 or Type 4 system. Flexures may have substantial deformation, but can
be
designed to store trivial amounts of either total or net potential energy, as
is explained
herein. These categories are generally ordered by their potential for energy
efficiency, with Type 1 devices being the least efficient, and Type 4 devices
being the
most efficient. That being said, the energy efficiency of specific systems
depends on
implementation details. A Type 2 system could be less efficient than a Type 3
system.
A poor implementation could make any system energy inefficient. Due to the use
of
ratchets and pawls, detents, springs, or other mechanisms which store and then
release
potential energy in a manner not tied to computational degrees of freedom, all
pre-
existing Turing-complete systems for mechanical computing can be categorized
as
Type 1.
Mechanical Linkage Logic
[0095] An MLL system is built from various basic parts or primitives. In
the
embodiments described, these are rotary joints and links, which together form
mechanical linkages. Mounted on an anchor block, rotary joints and links can
be used
to create higher-order mechanisms such as data transmission lines, locks, and
balances. Still higher order mechanisms, including logic gates (both
reversible and
irreversible) and shift registers can be created by combining locks and
balances, or
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implemented more directly using links and rotary joints. This suffices to
build a
complete computational system.
100961 To demonstrate this, using only links and rotary joints, the
design of
data lines, logic gates, locks, and balances is explained. Subsequently, using
some of
these mechanisms, the building of a shift register is described. Shift
registers are
simple, yet when combined with one or more logic gates which provide for
universal
combinatorial logic, contain all the fundamental elements required for
computation. If
the basic parts can build a shift register and appropriate logic gates, it
follows that an
entire computational system can be built.
[0097] Note that most of the mechanisms described are tailored towards
binary computational systems. As a result, most links will move between two
allowed
positions. Some exceptions exist however, such as designs where, for example,
when
one input is 1, the mechanism drives one or more other inputs "backwards"
(uses of
words such as "forward," backward" and other directions being didactic
conventions
only, since no particular directions need be used in actual mechanisms, nor do
such
directions need to be consistent from one mechanism to the next). In other
words,
given a two bit input that starts at (0,0), an input of I could cause the
mechanism to
end up in a state such as (1,-1) or (1,-0.5) rather than (1,0). As long as the
system is
designed to correctly handle such kinematics, this need not be a problem.
Also, links
internal to the implementation of various mechanisms may move between more
than
two allowed positions, even if the inputs and outputs are still binary. Binary
is used
for exemplary purposes because it is the most common type of computational
system
used in conventional computers. Ternary, quaternary, or other non-binary
computational systems could obviously be built using the teachings herein.
[0098] The mechanisms herein were frequently simulated or diagrammed
with
Linkage v3 (free from www.linkagesimulator.com), Autodesk Inventor 2015/2016,
or
for molecular models, HyperChem, GROMACS, or Gaussian. Many of the figures
herein represent sub-assemblies taken out of the context of a complete
computational
system. As a result, they are not necessarily functional as shown. For
example, a
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given mechanism may not being fully constrained as depicted because, in a
complete
system, the mechanism would attach to other components to satisfy missing
constraints, or would attach to some manner of actuation (e.g., a clock
signal).
Realistic routing of data has sometimes been omitted in favor of, e.g.,
straight lines,
for clarity. Ancillary support structures, such as anchor blocks, or links
which serve
only to provide rigidity ("support links"), are generally omitted.
[0099] Some diagrams depict parts within mechanisms which are not basic
parts of MLL. The most prevalent example of this is the use of linear slides
in
Linkage models. This is a programmatic convenience because some method of
driving inputs is required to run a simulation in Linkage. In an actual
system, linear
slides would be replaced with, e.g., connections to appropriate
inputs/outputs, such as
data lines or clock signals. Note that the kinematic solver used by Linkage v3
has no
concept of clock cycles, so it cannot drive various inputs sequentially. And,
Linkage,
and other programs, may fail on valid mechanisms simply because the solver
cannot
compute the kinematics correctly. Due to these, and other, caveats, the
figures herein
should not be taken as complete, working mechanisms, but rather as didactic
examples which, given the teachings herein, can be readily adapted to create
working
mechanisms, and combined to create complete computational systems.
Rotary Joints
[0100] Friction in a rotary joint can be made smaller and smaller as the
size of
the rotary joint gets smaller and smaller. At the molecular scale, a rotary
joint
comprising two atoms rotating around a single bond arguably has zero contact
area,
and various rotary joints which rotate around the axis of single chemical
bonds have
been analyzed and found to have very little friction. For example, carbon-
carbon
single bonds, using carbon atoms mounted on diamond supports, are one way to
create a rotary joint that provides rotation with very little energy
dissipation.
[0101] FIG. ldepicts a molecular model of one possible implementation of
a
rotary joint being used to hold a rotating member. An upper support structure
101 and
lower support structure 102, which would be connected to, e.g., an anchor
block, in a
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complete device, are used to connect a set of upper and lower bonds, along the
same
axis of rotation, to a rotating member 103. The upper bonds include upper
carbon-
carbon single bond 104, upper carbon-carbon single bond 105, and upper carbon-
carbon triple bond 106. The lower bonds include lower top carbon-carbon single
bond
107, lower bottom carbon-carbon single bond 108, and lower carbon-carbon
triple
bond 109
[0102] The rotary joint is bonded to the support structures by several
oxygen
atoms, including upper oxygen atom 110 and lower oxygen atom 111. The rotating
member 103 as depicted is a roughly circular slab of diamond, but this is
representative only, as are the other structures. The rotating member could be
a link, a
flywheel (e.g., to generate a clock signal), or anything else that needs to
rotate, in any
shape.
[0103] Molecular dynamics simulations indicate that, with or without the
acetylenic units exemplified by upper carbon atoms and triple bond 106 and
lower
carbon atoms and triple bond 109, this structure allows rotation with
remarkably little
drag. However, interposing an acetylenic unit between the surrounding single
bonds
further reduces the energy dissipation of such a rotary joint.
[0104] Given this example it will be obvious that varied
implementations,
including other molecular structures, could provide the same type of
mechanism. For
example, with small modifications to the model depicted in FIG. 1, the oxygen
atoms
exemplified by oxygen atom 110 and oxygen atom 111, might be replaced with
nitrogen, or another element with an appropriate valence, bond strength, and
steric
properties. Similarly, carbon could be replaced with silicon or other
appropriate
elements. Or, entirely different structures could be used, including carbon
nanotubes
or other structures, preferably those which can stiffly hold molecular-scale
rotary
joints.
[0105] Additionally, such a rotary joint does not need to consist of
only a
single bond or pair (e.g., upper and lower) of bonds. For example, in larger
implementations, the rotary joint could be replaced with a vee jewel bearing,
a rolling
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element bearing, nested fullerenes (e.g., carbon nanotubes), or any one of
many ways
known to allow rotation, preferably with low friction. Also, multiple co-axial
rotary
joints can be used to create a stronger joint (e.g., using a structure similar
to the
interdigitated design of a door hinge). And, at the molecule scale, adding
additional
rotary joints on the same rotational axis could further reduce the rotational
barrier if
appropriate attention is paid to symmetry. Note that while a rotary joint can
be
formed using one bond, device strength and stiffness can benefit from a
rotating part
being held on two sides, as depicted in FIG. 1, and/or using multiple bonds,
such as in
the "door hinge" example. With respect to molecular-scale embodiments, for
ease of
description, rotary joints may be referred to as rotating about a single bond,
although
in some cases it would be more precise to say that multiple bonds may be used
to
form a single axis of rotation for the overall rotary joint.
[0106] The magnitude of the rotational barriers, the torque required to
overcome them, the length of the lever arms (e.g., links), and the time to
rotate the
link through the necessary range of the rotary joint (and how far that range
is) all
depend on the design of a particular system. As an example, molecular dynamics
simulations show that the energy required to rotate a link connected to a
molecular
rotary joint through one radian at a speed of 1x10E9 radians/sec and a
temperature of
180K can be below 1x10E-25 J. The Landauer Limit is 1.72x10E-21 J at 180K.
This
number is so far above the 1x10E-25 J figure for a one radian rotation of a
link
around a rotary joint that even mechanisms that use many rotary joints to
perform a
single bit operation could do so under the Landauer Limit. Further, it is
expected that
viscous drag from rotary joints, and energy loss from other vibrational modes,
will
rapidly decrease as operating temperature decreases due to phonons becoming
frozen
out.
Links
[0107] At their most basic, links are stiff, rod-like structures,
although some
implementations may have different or substantially more complex shapes. Most
of
the analysis herein which requires estimations of values such as link mass,
resonant
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frequencies, and heat conduction, assume a link is composed of a diamond rod
approximately 20nm in length and 0.5-0.7nm in diameter. However, links could
be
larger, or smaller, or completely different in shape (as seen in the non-co-
planar lock
examples).
[0108] One of the smallest ways to implement a link would be to use a
single covalent bond as a link. For example, there are many molecules which
have
more than one possible configuration, and the transition between
configurations
("conformers") could constitute the movement of a link. One specific example
is
cyclohexane, which has several possible conformations, including two chair
conformations, the basic boat conformation, and the twist boat conformation.
Switching between different conformations can occur through bond rotation
(although
other changes, such as changes in bond angle or torsion, may also be present
and
used), similar to that in the previously-described rotary joint, and results
in the
movement of one or more of the atoms in the structure.
[0109] The ability of such molecular conformational changes to
propagate
over relatively long distances and through complex networks is known to exist
in
biology, where it is termed "conformational spread". (Bray and Duke,
"Conformational spread: the propagation of allosteric states in large
multiprotein
complexes," Annu Rev Biophys Biomol Struct, 2004), and it will be apparent
that
synthetic systems could be designed that work on the same principles as larger
linkages, but using only a single bond as a link Such designs could allow link
lengths
in the angstrom range.
[0110] Regardless of the exact implementation of links and rotary
joints, one
of the basic tasks in a computational system is to move data from place to
place. The
exemplary systems described use links connected by rotary joints to move data.
While
many types of linkages would work, including linkages that provide true
straight-line
movement, 4-bar linkages are frequently used as an exemplary manner of
precisely
constraining link movement. FIG. 2 depicts a side view of such a 4-bar linkage
(note
that these are sometimes called 3-bar linkages, since the support structure
may or may
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Date Recue/Date Received 2021-03-26
not be considered an additional bar), comprising an anchor block 205, left
support
link 202, right support link 207, and data link 204, wherein the lower end of
the left
support link 202 is connected to the left side of the anchor block 205 by left
anchored
rotary joint 203 and the lower end of the right support link 207 is connected
to the
right side of the anchor block 205 by right anchored rotary joint 206, and the
upper
end of the left support link 202 is connected to the left side of the data
link 204 by
upper left rotary joint 201 and the upper end of the right support link 207 is
connected
to the right side of the data link 204 by upper right rotary joint 208. Left
anchored
rotary joint 203 and right anchored rotary joint 206 are prevented from moving
with
respect to each other by the anchor block 205. Data link 204 transmits the
movement
of one support link to another support link. The left support link 202 and
right support
link 207 are shown shifted to the left. The left-leaning support links put the
data link
204 in a position to the left of the left anchored rotary joint 203 and right
anchored
rotary joint 206. Arbitrarily, this left position can be called "0" or "low",
while if the
left support link 202 and right support link 207 were leaning to the right,
that position
could be called "1" or "high." This provides a basis for a binary system of
data
storage and transfer.
[0111] It will be apparent, even in the absence of the anchored rotary
joint
symbol, that left anchored rotary joint 203 and right anchored rotary joint
206 are
anchored rotary joints because they terminate on anchor block 205. In
subsequent
figures the anchor block may not be explicitly shown. Rather, the diagrammatic
convention is often adopted where unfixed rotary joints are depicted as a
circle at the
intersection of multiple links (which are generally represented as straight
lines or
bars, although some may have more complex shapes), while fixed or anchored
rotary
joints are depicted as a circle and a triangle with short diagonal lines at
its base. In
other figures, generally to reduce complexity, some of these conventions may
be
changed or eliminated. The figure descriptions and context will make it
obvious how
such diagrams are to be interpreted.
[0112] As has already been described, information can be transmitted
along
the length of a single data link. However, more complex transmission and
routing of
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Date Recue/Date Received 2021-03-26
data can be useful. One data link can be connected to any number of other data
links
to continue the transmission of data. Data transmission can continue in a
straight line
across additional support links (while effectively just a longer data link, it
may be
useful to include additional support links to increase stiffness), or can
change
direction at rotary joints, at whatever angle and in whatever plane desired.
And, one
link can connect to multiple other links not only sequentially, but also
through forking
structures, effectively copying the data for use in multiple locations. This
provides
considerable flexibility in routing data.
[0113] Data transmission may occur in both directions. Movement of a
first
data link causes a second data link to move, and movement of the second data
link
causes the first data link to move. By this means every data link in the chain
is tied to
its neighbors. All the data links in a chain, which can be of some significant
length,
can be made to share a common movement, a property that can be used to share a
single binary value along the entire length of the chain. A set of connected
links is
called a line.
Scale
[0114] MLL could be implemented using basic parts of virtually any size
desired. For example, at macroscopic scales, conventional machining or 3D
printing
could be used, with, e.g., vee jewel bearings or rolling-element bearings for
rotary
joints and conventional beams or rods for links. At a smaller scale, e.g., 3D
printing,
lithography-based techniques, or any of the other well-known ways in which
NEMS/MEMS devices can be manufactured, could be used to create devices with
mechanisms in the nanometer to micron range. At an even smaller scale, MLL
mechanisms could be molecular-scale. Due to the higher operational frequencies
and
reduced energy dissipation which tend to be afforded by smaller parts, MLL
systems
would preferably be implemented at the smallest scales feasible (while taking
into
account factors such as performance requirements and budget). For this reason,
while
most of the teachings herein are scale-independent, estimations of energy
dissipation
focus on an exemplary molecular-scale embodiment.
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Date Recue/Date Received 2021-03-26
[0115] Molecular bearings, gears, and rotors have been studied both
theoretically and experimentally, and representative literature includes (Han,
Globus
et al., "Molecular dynamics simulations of carbon nanotube-based gears,"
Nanotechnology, 1997; Kottas, Clarke et al., "Artificial Molecular Rotors,"
Chem
Rev., 2005; Khuong, Dang et al., "Rotational dynamics in a crystalline
molecular
gyroscope by variable-temperature 13C NMR, 2H NMR, X-ray diffraction, and
force
field calculations," J Am Chem Soc, 4, 2007; Frantz, Baldridge et al.,
"Application of
Structural Principles to the Design of Triptycene-Based Molecular Gears with
Parallel
Axes," CHIMIA International Journal for Chemistry, 4, 2009; Wang, Liu et al.,
"Molecular Rotors Observed by Scanning Tunneling Microscopy," Three-
Dimensional Nanoarchitectures, 2011; Isobe, Hitosugi et al., "Molecular
bearings of
finite carbon nanotubes and fullerenes in ensemble rolling motion," Chemical
Science, 3, 2013; Carter, Weinberg et al., "Rotary Nanotube Bearing Structure
and
Methods for Manufacturing and Using the Same," US Patent 9150405, 2015).
[0116] Molecular motors, while not necessarily required to drive MILL
systems, are commonplace enough now that entire books and conferences are
devoted
to the topic. (Joachim and Rapenne, "Single Molecular Machines and Motors:
Proceedings of the 1st International Symposium on Single Molecular Machines
and
Motors," Springer, 2013; Credi, Silvi et al., "Molecular Machines and Motors,"
Topics in Current Chemistry, Springer, 2014)
[0117] Additionally, molecular-scale computing, in various forms
(generally
not Turing-complete), already exists. (Heinrich, Lutz et al., "Molecule
Cascades,"
Science, 2002; Reif, "Mechanical Computing: The Computational Complexity of
Physical Devices," Encyclopedia of Complexity and System Science, Springer-
Verlag, 2009; Remon, Ferreira et al., "Reversible molecular logic: a
photophysical
example of a Feynman gate," Chemphyschem, 12, 2009; Orbach, Remade et al.,
"Logic reversibility and thermodynamic irreversibility demonstrated by DNAzyme-
based Toffoli and Fredkin logic gates," PNAS, 52, 2012; Roy, Sethi et al.,
"All-
Optical Reversible Logic Gates with Optically Controlled Bacteriorhodopsin
Protein-
Coated Microresonators," Advances in Optical Technologies, 2012).
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[0118] In addition to other techniques present in the literature,
molecular-scale
MLL mechanisms and computational systems could be created using, e.g.,
molecular
manufacturing using mechanosynthesis, or assembly of properly functionalized
molecules using atomic force microscopy-type equipment Conventional chemistry
or
self-assembly (including DNA origami-type techniques) may also be a feasible
route
for manufacturing molecular-scale MLL mechanisms. Given the very limited
number
of basic parts required (e.g., links and rotary joints in MLL) for the
presented
embodiments, synthesis and assembly of the necessary basic parts and
mechanisms is
in many ways simpler than the complexities of manufacturing a conventional
electronic computer or than implementing previous proposals for mechanical
computing.
Energy Dissipation
[0119] As noted, an entire MLL system can be constructed with nothing
but
links and rotary joints. Since, particularly at the molecular-scale, there is
very little
energy loss from rotation around a well-designed rotary joint, a complete
computational system can be designed which dissipates very little energy.
Additional
MLL design paradigms (e.g., torque and mass balancing to reduce or prevent
acoustic
radiation) are also discussed herein, and these can help reduce energy
dissipation even
further. Beyond the physical design of the computational system, operating
conditions can also affect energy dissipation. For example, if an MLL system
is
operated in a vacuum, acceleration and deceleration of links takes place
smoothly,
and the applied forces are small enough that deformation of basic parts
contributes
negligible energy dissipation, energy dissipation may be reduced further.
[0120] The design of MLL mechanisms, and their interaction with the
clocking system, may also affect energy dissipation. For example, MLL systems
can
be designed such that, by using clock phases appropriately, force is not
applied to
mechanisms that are not free to move (e.g., such a system does not try to move
a
locked mechanism without first unlocking it). This is the MLL version of "dry
switching," a term normally used in the field of relays to indicate that
switches have
-25-
Date Recue/Date Received 2021-03-26
no voltage across them when changing state, but herein will be used in the
context of
MLL. Note that while it is a major novel finding of MLL that complete
computational systems can be designed with nothing beyond links and rotary
joints,
MLL systems may incorporate, or interface with, additional components For
example, it is described herein how cams and cam followers are one way to
generate
clock signals. However, even though cams and cam followers can be designed (as
is
explained herein) to have minimal energy dissipation, such mechanisms are
ancillary
to, not actually part of, MLL. Motors or other ways of powering the movement
of
MLL systems are another example of a function that may be coupled to an MLL
system, but are not considered part of MLL, and the same could be said for,
for
example, input/output interfaces which bridge, e.g., MLL and electronic
systems or
non-MLL mechanical systems.
[0121] Any mechanical system can dissipate substantial energy if run
fast
enough to excite internal mechanical resonances. To keep power dissipation as
low as
possible, proper design can avoid low frequency vibrational modes being
coupled to
the clock, and the remaining vibrational modes can be computed and avoided by
picking a speed of operation slow enough to avoid exciting them, as well as a
clocking waveform that minimizes their excitation. In a molecular-scale
mechanical
system such resonant frequencies can be in the gigahertz range, and the limits
they
impose on switching speed can therefore be correspondingly high.
[0122] The switching speed of an MLL system will, just as in electronic
computers, be determined by one or more clocks which produce clock signals. If
the
frequency spectrum of a clock signal has a component of its energy at or above
the
resonant frequencies of the mechanisms to which it is attached, then a greater
fraction
of the clock energy could be dissipated than is necessary.
[0123] In an MLL system, changes in a clock signal are preferably
gradual so
as not to generate higher frequency components. For example, the gradual
changes
inherent in a sine wave-like transition between 0 and 1 (potentially with flat
areas at 0
and 1 between transitions to allow for non-perfect synchronization of
mechanisms
-26-
Date Recue/Date Received 2021-03-26
between different clock phases) allow a clock signal to avoid placing greater
strain on
system mechanisms than necessary as parts accelerate and decelerate more
uniformly
than if, e.g., a square wave, was used.
[0124] There are many ways of generating clock signals. One way of
generating a gradually-changing clock signal is to use a spinning mass whose
rotational motion is converted into linear or quasi-linear motion. This is,
conceptually,
the equivalent of a flywheel and crank, and such a device can be made with
only links
and rotary joints. Some embodiments of MILL systems may couple to other
methods
of generating clock signals, such as spring and mass systems, or cams and cam
followers, which are described herein.
[0125] Several possible sources of energy dissipation were analyzed,
including stress induced thermal disequilibrium, and acoustic radiation. These
were
not the primary limiting factors in operating frequency, at least for the
exemplary
systems analyzed (e.g., molecular-scale, diamond-based systems). Mechanical
resonances and inertia are the primary limits to switching speed for these
systems.
[0126] While thermal equilibration turns out not to be a limiting factor
for the
exemplary systems analyzed, in some situations it could be, and one objective
when
seeking to minimize energy dissipation could be to operate mechanisms
isothermally.
For this reason, short thermal equilibration times can be desirable. To
achieve this, the
basic parts of the system are preferably well-coupled to one or more thermal
reservoirs. For example, links are generally bonded to a rotary joint which is
bonded
to an anchor block, or to rotary joints that bond to other links, which are in
turn
bonded to an anchor block. While the exact path length can vary based on the
implementation, this tends to keep the path from any link to an anchor block,
which
can serve as a thermal reservoir, short.
[0127] Note that diamond is used as an exemplary anchor block material
(and
may also be used for basic parts), for among other reasons, due to its high
stiffness
(Young's Modulus of about 1000 Gpa). Diamond also has good heat conduction,
which can be over 2000 W/mK in natural diamond, and higher in defect-free and
-27-
Date Recue/Date Received 2021-03-26
isotopically purified diamond (a principle which applies to other materials as
well).
Many other materials could be used, for both anchor blocks and basic parts,
although
high stiffness would be preferred for various reasons, including raising the
frequency
of resonant vibrations, and good heat conduction would be preferred if fast
thermal
equilibration is desired. Other exemplary materials include Carbyne (Young's
Modulus of 32,100 GPa), various Fullerenes (e.g., carbon nanotubes can have
Young's Moduli of over 1000 GPa, thermal conductivity of 3180-3500 W/mK or
higher), Silicon Carbide (Young's Modulus of 450 GPa), and Silicon (Young's
Modulus of 130-185 GPa, thermal conductivity of 148 W/mK). Note that these
values
are approximate, and generally represent values measured at 300K (room
temperature). The values may vary substantially depending on a material's
atomic
structure, purity, isotopic composition, size and shape, and temperature. For
example,
while Silicon's thermal conductivity is 148 W/mK at 300K, it can exceed 3000
W/mK at temperatures around 20K.
[0128] Further, note that MLL systems need not be composed of only one
type of material. Various materials each have different pros and cons,
including not
only bulk properties such as stiffness, thermal conductivity, and thermal
expansion,
but at the molecular scale, the strength of individual bonds may become
important, as
may be the exact size of various basic parts and their inter-atomic spacing
(e.g., so
that they mesh properly with other basic parts, among other concerns). Given
this,
MILL systems may use a variety of different materials.
[0129] The estimated thermal equilibration time of one exemplary
molecular-
scale embodiment using diamond links about 20nm in length is ¨0.54 ps. Given
this,
even a few nanoseconds of thermal equilibration makes the energy dissipated
due to
thermal disequilibrium essentially 0. Therefore, thermal equilibration time is
not the
limiting factor in switching time for such an embodiment.
[0130] In theory, a reversible operation can be carried out with 0
energy,
while irreversible operations result in the dissipation of ln(2) kBT of heat (-
3 x 10-21
J at room temperature) per bit erased, regardless of the hardware's efficiency
(the
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Date Recue/Date Received 2021-03-26
Landauer Limit). To reduce the energy dissipation of a program running on a
conventional (irreversible) computer, the logic elements of the hardware might
be
redesigned to dissipate less energy during the computational process. This
could
result in a significant improvement in energy efficiency because a
conventional
computer dissipates much more than ln(2) lcBT per erased bit. In fact, even
when
executing instructions that erase no bits at all, a conventional computer
dissipates
much more than ln(2) kBT per operation. As a consequence, it is possible to
reduce
the energy dissipation of a conventional computer without paying any attention
to
reversibility.
[0131] However, if the energy efficiency of a computer is improved to
the
point that the Landauer Limit becomes significant, reversibility becomes
important, as
it allows computations to be carried out under the Landauer Limit.
Consequently,
MILL mechanisms are designed to allow reversibility, although both reversible
and
irreversible computational systems can be implemented using MLL. Note that
reversibility can occur at several levels. For example, an individual Fredkin
gate is
reversible. However, reversibility may also be implemented at higher levels,
such as
when using a retractile cascade to uncompute a series of previous
computations. Such
techniques are well-known in the literature, along with appropriate clocking
schemes
such as Bennett Clocking and Landauer Clocking.
Conventional Logic Gates
[0132] Links and rotary joints not only serve as the basic parts for
moving
data from place to place, but also form the basis for logic gates. An
important finding
of MLL is that any logic gate, reversible or irreversible, can be implemented
with
only links and rotary joints, affixed to an anchor block to hold them in place
(and
which may also serve as a thermal sink).
[0133] For example, FIG. 3 shows a mechanism that can serve as both an
AND and a NAND gate. Anchor 301 and linear slide 302 serves as the first input
to
the gate, connecting to rotary joint 306. Anchor 303 and linear slide 304
serves as the
second input to the gate, connecting to rotary joint 307. Anchored rotary
joints 305
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Date Recue/Date Received 2021-03-26
and 309, plus unanchored rotary joints 306, 307, 308, 310 and 311 are
connected via
the appropriate links. AND output 310 and NAND output 311 provide for the use
of
the gate as an AND or NAND gate. The functioning of this gate is as follows.
If
linear slide 302 pushes on rotary joint 306 (an input of "1", whereas no
movement of
the linear slide would be an input of 0) and linear slide 304 pushes on rotary
joint 307,
the effect will be to drive AND output 310 forward, producing an output of
"1." If
either of the inputs (or both) are 0, AND output 310 ends up in the same
position it
started, producing an output of "0." This reproduces the truth table expected
of an
AND gate.
[0134] Since a NAND gate is an AND gate with inverted output, the same
mechanism can be used as a NAND gate by reading NAND output 311 instead of
AND output 310, assuming that, since NAND output 311 moves in the opposite
direction of AND output 310, no movement at NAND output 311 represents an
output
of "1" and movement to the left represents a "0". Of course, for use only as
an AND
gate, NAND output 311 need not be present. And, for use only as a NAND gate,
the
AND output 310 can be ignored. The two are combined for illustrative purposes;
they
would not necessarily be so combined in actual use. Since NAND is known to be
a
universal gate (meaning, all other gates can be created with the appropriate
combination of NAND gates), this mechanism alone would suffice to create any
combinatorial logic. However, it may be more efficient to construct other
types of
gates directly, rather than through the combination of NAND gates, and to
demonstrate other types of gates, including an alternate embodiments of the
NAND
gate, additional logic gates are subsequently described.
[0135] FIG. 4 shows a NOR gate made with only links and rotary joints.
Input
1 comprises linear slide anchor 401 and is connected via a rotary joint to
inverter 405.
Input 2 comprises linear slide anchor 403 and linear slide 404 and is
connected via a
rotary joint to inverter 406. As in all such figures, the linear slides are
present as a
diagrammatic or programmatic convenience and should be taken to represent some
appropriate connection when these individual mechanisms are combined into a
higher-level assembly. Inverters 405 and 406 invert a leftward signal to a
rightward
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signal and vice-versa and connect via rotary joints to upper right portion of
the
mechanism 407, and lower right portion of the mechanism 408, respectively. Due
to
the inverters, when either of the inputs pushes to the right, the movement
gets
inverted into a leftward motion in the upper right portion of the mechanism
407 and
the lower right portion of the mechanism 408. The position of output 409
replicates
the expected truth table, with the illustrated position representing a "1" and
the
position where the output moves to the left representing a "0". While other
implementations are possible, this gate was shows the modular nature of the
mechanisms. A NOR gate is equivalent to an AND gate with both inputs inverted.
The upper right portion of the mechanism 407 and the lower right portion of
the
mechanism 408 therefore show an alternate implementation of an AND gate, with
an
inverter attached to each input to instead create a NOR gate. Removing the
inverters
and connecting the inputs directly to the appropriate locations in the upper
and lower
right portion of the mechanism would result in an AND gate. Also, as was shown
in
FIG. 3, this mechanism could then also serve as a NAND gate by inverting the
output
of the AND gate. Finally, if the inverters are left in place, but the output
inverted, the
NOR gate becomes an OR gate.
[0136] Finally, FIG. 5shows an XOR gate implemented using only links and
rotary joints. Input 1 comprises anchored rotary joint 501 and linear slide
502, while
input 2 comprises anchored rotary joint 504 and linear slide 503. Input 1 and
input 2
are coupled to output 505 via a series of links, anchored rotary joints, and
unanchored
rotary joints. The movement, or lack thereof, at output 505 replicates the
expected
truth table for XOR.
[0137] The foregoing demonstrates that any logic gate can be directly
implemented using only links and rotary joints. Note that by carrying the
input data
forward along with the expected output of a logic gate so that no data is lost
in the
computation, logic gates which are traditionally considered irreversible can
be made
reversible. There are also well-known logic gates which are inherently
reversible,
such as the Toffoli gate and Fredkin gate, which can also be implemented in
many
ways using MLL.
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Reversible Logic Gates
[0138] FIG. 6 shows a Fredkin gate (also called a CSWAP gate), a well-
known universal reversible gate. The three inputs to the gate 601, 602 and 603
are
connected, via a series of links, anchored rotary joints, and unanchored
rotary joints,
to outputs 604, 605 and 606. It may be of interest to note that this
particular
implementation of a Fredkin gate is composed of three XOR gates, and an AND
gate,
plus some forked data lines used to replicate data so that it can be used at
more than
one place within the gate. This demonstrates not only more sophisticated
routing of
data than the previous gates, but that reversible logic can be constructed
from
irreversible logic. A Fredkin gate does not erase any data and so need not be
subject
to the Landauer Limit.
[0139] Given the foregoing logic gate examples, it will be obvious that
any
type of logic gate necessary for implementing a complete general-purpose
computing
system, reversible or irreversible, can be implemented within the design
paradigms of
MILL, using only links and rotary joints. Note that each of the foregoing
logic gate
examples are co-planar mechanisms. This means that they operate in one or more
parallel planes, with movement occurring parallel to the plane of the image.
One of
the advantages to co-planar designs is that they are easy to represent on
paper, to
provide the reader with an intuitive understanding of how such mechanisms
work.
This is not the only way to implement logic gates, or any MILL mechanism, and
mechanisms that move in more than one plane are also discussed herein. Also
note
that in the co-planar mechanisms, hidden or dotted lines are generally not
used to
show which links are behind which other links. This is because it largely does
not
matter. In most cases, a given link could be on top of, or below, some other
link, and
the function of the mechanism would not be affected, subject to considerations
such
as not having links bump into each other during movement. One may also wish to
consider issues such as arranging the links in a manner which minimizes the
distance
to a heat sink, or maximizes mechanism strength or stiffness, but these
exemplary
designs are meant to be didactic, not to provide an optimal implementation.
Optimized implementations could differ with the requirements of a particular
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computational system, including the types of computations to be performed, the
desired computational speed, the desired size or mass of the system, the
materials
from which the mechanisms are made, and the operating environment (e.g.,
operating
temperatures).
Locks
[0140] Various ways in which multiple data links or lines can interact
have
already been described For example, they can share data by tying their
physical
movements to each other around a common rotary joint. And data links or lines
can
provide input/output for a logic gate (not to mention being used inside a
logic gate).
However, additional methods of interaction can be useful in implementing a
complete
computing system.
[0141] Another way multiple links or lines can interact is via a
mechanism
which causes links to interfere with each other's movements. That is, the
position of a
first link can allow or prevent one or more other links from moving, and vice
versa.
For example, consider a two-input mechanism, where each input can be 0 or 1.
The
design can be such that when both inputs are 0, either input could become 1,
but when
either input is 1, the other is locked into place and must therefore remain 0.
In this
example, more than one input cannot become 1 at the same time, although other
designs are possible. This mechanism is referred to as a lock. It is common
for a lock
to have inputs and outputs, just like a logic gate. E.g., a 2 input lock has 2
inputs, and
can have 0, 1 or 2 outputs. Each input line to the lock can either continue as
an output
line, or it can terminate at the lock.
[0142] One of the uses of a lock is to create a conditional anchor
point. As has
already been explained, a rotary joint can be anchored or not anchored, often
depending on whether the rotary joint is affixed to an anchor block. However,
affixing a rotary joint to an anchor block is not the only way to render it
immobile.
Rather, a rotary joint can be connected to one or more links which, due to the
configuration of the one or more links (whether this configuration is
permanent or
transient), does not permit movement of the rotary joint. For example,
consider a
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Date Recue/Date Received 2021-03-26
triangle made of three links. Each link is affixed to the two other links by
rotary joints
at each end. If two of these rotary joints are also connected to an anchor
block, even if
the third rotary joint is not connected to an anchor block, it is effectively
anchored, as
the entire triangle is rigid. None of the triangle's links can move with
respect to each
other, or the anchor block. In this simple example, assuming there is no way
to
change the link configuration, the third rotary joint is effectively anchored.
There are
situations where it is useful to have a rotary joint sometimes anchored and
sometimes
not anchored. Locks allow this: The side of the lock that is locked cannot
move, and
so as long as it is locked, it can effectively act as an anchor point. The
utility of
conditional anchor points will be explained subsequently. Another useful
aspect of
some embodiments of locks is that, for example, a binary lock with two inputs
can
have three possible states: (0,0), also called "blank," (0,1), and (1,0). The
blank state
can be useful in saving state, and allowing reversible computation, as can be
seen
herein in the description of how an exemplary shift register can be
implemented.
[0143] As with all MILL embodiments, there are multiple ways of
implementing locks using only links and rotary joints. FIG. 7 and FIG. 8
depict a two-
input co-planar lock in two different states. FIG. 7 shows the position of the
lock
where both inputs are 0, while FIG. 8 shows the position of the lock when one
of the
inputs is 1. Top input 701 and bottom input 702 connect via rotary joints to
the top
and bottom halves of the lock, respectively. Each half of the lock comprises a
4-bar
linkage, comprising links 703, 705 and 712 on the upper half, and links 704,
706, and
713 on the lower half. In addition, four diagonal links 707, 708, 710 and 711,
hold an
additional link 709, which connects to the two 4-bar linkages via unanchored
rotary
joints. The functioning of the mechanism is as follows: When one of the inputs
701
or 702, moves from 0 to 1, the respective 4-bar linkage is moved. The movement
of
the 4-bar linkage, via either links 707 and 710 for the top half, or links 708
and 711
for the bottom half, causes the rotation of link 709 Link 709, being the same
length
as links 703, 704, 712, and 713, as well as initially being at the same angle,
allows
either of the inputs to assume a value of 1 by pivoting through the same arc
that the 4-
bar linkage must follow when moved by an input.
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Date Recue/Date Received 2021-03-26
[0144] However, once an input has moved either the top or bottom 4-bar
linkage, along with link 709, the other 4-bar linkage (and so its associated
input/output) is no longer free to move. The reason is that link 709 is now
not parallel
with, depending on which input was set to 1, links 703 and 712, or links 704
and 713.
Because of this, the rotation of link 709 will not follow that of the second 4-
bar
linkage, should it try to move. In essence, one of the links (link 705 for the
top, if not
already moved, or link 706 for the bottom, if not already moved) will be
trying to
move through two different arcs at once, resulting in the mechanism locking.
This is
essentially a co-planar version of rotary joints being not-coaxial (described
elsewhere
herein), but instead of the rotary joint axes changing (which does happen, but
these
axes were never co-axial in the literal sense to begin with), the point here
is that the
arc through which the connected links would move changes. Once one of the
inputs is
set to 1, the only allowed movement is to set that input back to 0 so that
either (but
not both simultaneously) sides are again free to move to the "1" position.
[0145] The lock design of FIG. 7 has the property that it locks quickly
and
unlocks slowly. For example, virtually any movement of one of the inputs locks
the
other input. And, once an input has been set to 1, locking the mechanism, that
input
must be brought essentially all way back to 0 before the lock unlocks. It may
be
desirable to design locks which have more gradual locking properties, and this
may
have advantages including smoother changes in entropy (resulting in reduced
energy
dissipation), reduced maximal force on the mechanisms at a given switching
speed,
and a reduced time between lock/unlock cycles, since there is less concern
that one
input must be allowed to settle to almost exactly 0 before the other input can
start to
move. The inclusion of springs in connections to a lock can also aid in the
operation
of a lock, as the mechanism can then be driven as desired even when small
positional
errors are present which would otherwise lock a mechanism which almost
instantly
locks when not exactly in the unlocked position (i.e., at "0"). Another method
of
accomplishing this is to replace link 709 with a spring of the same length (or
add a
spring and shorten the link) which has a suitably chosen spring constant. If
link 709
is, or incorporates, a very stiff spring, the lock will allow only small
positional errors.
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If link 709 is, or incorporates, a softer spring, the lock will allow larger
positional
errors.
[0146] FIG. 9 and FIG. 10 depict a lock where, due to gradually changing
torque as the mechanism moves from unlocked to locked, the locking action is
more
gradual. FIG. 9 shows the lock when inputs 901 and 902, are 0, while FIG. 10
shows
the state of the lock after input 901 has been set to 1 while input 902 is
still 0. Inputs
901 and 902 are connected to the rest of the mechanism via unanchored rotary
joints.
Note that the setting of one input to 1 results in driving the other input
backwards
slightly in this design. The overall system can be designed to allow this, or
the
backwards motion could be kept internal to the mechanism, such as by using
springs
that absorb such motion rather than transmitting it directly to other links.
[0147] Being made of the same basic parts, all MILL mechanisms tend to
share similar concerns. The concepts of sudden versus gradual changes in
entropy,
limiting maximum forces, and designing mechanisms to allow reduced latency
between clock phases, can apply to any MILL mechanism, not just locks.
Non-Co-Planar Mechanisms
[0148] Many of the mechanisms herein are of co-planar design. While co-
planar designs are emphasized for clarity of presentation, MLL mechanisms need
not
be co-planar. Any MILL mechanisms can be implemented in a manner which is non-
co-planar. For example, FIG. 11 depicts a lock, constructed of links and
rotary joints,
which is not co-planar. Rather, as will be subsequently explained, the rotary
joints
allow the links to move perpendicular, rather than parallel, to the face of
the Anchor
Block.
[0149] In FIG. lland subsequent views of the same mechanism, link 1101
will be referred to as Linkl, link 1102 as Link2, link 1103 as Link3, space
1104 as
OpenJoint4, space 1105 as OpenJoint5, space 1106 as OpenJoint6, space 1107 as
OpenJoint7, rotary joint 1108 as Jointl, rotary joint 1109 as Joint2, rotary
joint 1110
as Joint3, rotary joint 1111 as Joint4, and anchor block 1112 as the Anchor
Block.
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The Anchor Block provides anchor points for the rotary joints Joint' and
Joint4,
which are connected to Linkl and Link2, respectively. Linkl is connected to
Link2
by Joint2, and Link3 is connected to Link2 via Joint3. All Joints and Link 1,
Link2,
and Link3 are shown in the unlocked position.
[0150] In the unlocked position, which may be referred to as "(0,0)",
the axis
of Joint3 is aligned with the axis of Jointl, and the axis of Joint2 is
aligned with the
axis of Joint4. Jointl and Joint 3 may thus be referred to as coaxial, as can
Joint2 and
Joint4. If either Linkl or Link3 were to pivot, one of their rotary joints
would move
out of their current plane, and thus, depending on which link was pivoted,
some of the
joints would no longer be coaxial with each other (a condition referred to as
"not-
coaxial"). The concepts of coaxial and not-coaxial are important as, in this
embodiment, these conditions are what define locked versus unlocked. The
reason for
this is that in the unlocked position, Linkl and Link3 each have an axis about
which
they might pivot. For Linkl, this is the axis defined by Joint1 and Joint 3
when they
are coaxial. For Link3, this is the axis defined by Joint2 and Joint4 when
they are
coaxial. When these sets of joints are not in the coaxial position, the lack
of alignment
between the two axes prevents pivoting, as a rigid object with one degree of
freedom
cannot simultaneously pivot around two different axes. As a result, when
either Joint1
and Joint3 are not-coaxial, or Joint2 and Joint4 are not-coaxial, the lock is
locked and
the only allowed motion is to return to the unlocked position.
[0151] Note that technically, virtually any amount of pivoting of Linkl
or
Link3 would create a locked condition. However, for the purposes of
explanation,
subsequent figures show about 30 degrees of rotation. This is arbitrary, and
any
amount of pivoting which will allow the system to act reliably could be used
(as could
any other angle, as opposed to perfectly perpendicular to the face of the
Anchor
Block). Analogously with the co-planar lock, if Link 2 were replaced with a
spring of
similar length, the tolerance of the lock for positional errors in its inputs
could be
increased, to the extent thought desirable. It will be obvious given this
explanation
that if either Linkl or Link3 were to pivot a suitable amount, whichever link
had not
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Date Recue/Date Received 2021-03-26
pivoted would then be prevented from doing so until the pivoted link was
returned to
the unlocked position.
[0152] To accomplish this pivoting, OpenJoint4 and OpenJoint6 are
connection points where other links could connect to Link3, and OpenJoint5 and
OpenJoint7 are connection points where other links could connect to Link 1.
These
other links can serve as inputs to the lock. Linkl and Link3 each have a pair
of
connections (OpenJoint5 and OpenJoint7, and OpenJoint4 and OpenJoint6,
respectively) not to allow four inputs (although that is possible, that is not
the intent
of this particular design), but rather to allow an input line to continue on
past the lock
if desired. For example, OpenJoint5 may be thought of as a continuation of
OpenJoint7 (or vice versa) and OpenJoint4 may be thought of as a continuation
of
OpenJoint6 (or vice versa).
[0153] FIG. 12 shows a top-view of the same mechanism as FIG. 11, with
only link 1101 and anchor block 1112 being visible in this view.
[0154] FIG. 13 shows the same mechanism as FIG. 11, but in a locked
position that could be called "(1,0)". In this state, 1101 has rotated, via
rotary joints
1108 and 1110, making rotary j oints 1109 and 1111 not-coaxial. Because 1109
and
1111 are not-coaxial, 1103 is no longer free to rotate, hence the locked
state. The
rotation of 1101 would be accomplished by other links (not depicted) connected
to
1105 and/or 1107.
[0155] FIG. 14 shows atop view of the state of the mechanism in FIG. 13.
In
this top view, it can be seen that 1101 has pivoted about 30 degrees
counterclockwise.
1102 cannot be seen in this view, but would pivot with 1101 in this instance,
revealing 1103 below it. Note that the direction of rotation is arbitrary.
Both
clockwise and counterclockwise rotations would have the same effect of locking
the
lock. This is true of 1103 as well.
[0156] FIG. 15 shows the same mechanism as FIG. 13, but in a locked
position due to the rotation of 1103 instead of 1102. This position could be
called
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Date Recue/Date Received 2021-03-26
"(0,1)." In this state, 1103 has rotated, via rotary joints1109 and 1111,
making rotary
joints 1108 and 1110 not-coaxial, thereby locking 1101. The rotation of 1103
would
be caused by other links (not shown) connected to one or more of the Open
Joints,
1104 and 1106, of 1103
[0157] FIG. 16 shows a top view of the state of the mechanism in FIG.
15. In
this top view it can be seen that 1103 has rotated about 30 degrees clockwise,
while
1101 is still in its original position. As with 1101, the direction of
rotation is arbitrary.
Either clockwise or counterclockwise would allow proper function of the lock,
and
either or both could be used.
[0158] Given these examples and the principles of MLL, many other
designs
(for locks and all other MILL mechanisms) will be obvious. The specific
implementations which work most efficiently may be case-dependent, and the
exemplary embodiments herein are not provided as examples of optimized
mechanisms, but rather to demonstrate how all elements necessary for a
generalizable
computational system can be created using only links and rotary joints, and
that even
within the constraints of only using links and rotary joints, many different
logical and
mechanical options are available, including virtually any type of logic gates,
reversible and irreversible, and mechanisms that largely function in two
dimensions
("co-planar"), or three dimensions (non-co-planar), complete with robust
routing of
data, at whatever angles are desired.
Balances
[0159] Force and motion can be transmitted from one end of a link to the
other end using a rotary joint about which the link pivots. Such a mechanism
will be
called a "balance," since frequently the input is in the center of a link, and
one side
moves "up" or "down," conceptually similar to a classic pan balance. Of
course, the
exact movement will depend on the forces applied, the exact mechanism design,
and
the state of the system.
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Date Recue/Date Received 2021-03-26
[0160] A simple balance is depicted in two different states in FIG. 17
(showing an input of 0, the linear slide of input 1701 being retracted) and
FIG. 18
(showing the same mechanism with an input of 1, the linear slide of input 1701
being
extended). In these figures, input 1701 is connected to the link 1702 by
rotary joint
1703. Upper rotary joint 1704 and lower rotary joint 1705 connect via links to
upper
output 1706 and lower output 1707, respectively. Upper rotary joint 1704 is
anchored
in these depictions, preventing upper output 1706 from moving, while lower
rotary
joint 1705 is unanchored, allowing lower output 1707 to move if input 1701
moves.
[0161] FIG. 19 depicts what would happen if upper rotary joint 1704 and
lower rotary joint 1705 were reversed (meaning, if upper rotary joint 1704
were
unanchored and lower rotary joint 1705 were anchored), given an input of 1.
The
output movement would occur at upper output 1706 instead of lower output 1707.
One of the interesting properties of balances is that they can be designed to
conserve
the sum of their inputs. In the foregoing example, if the input is 0, the
output is 0. If
the input is 1, the output is 1. This would be true of a simple line as well,
but complex
balances with multiple inputs can be constructed that still sum their outputs.
[0162] Another advantage to balances is that they can route data
differently
depending on other input. Other input, for example, may control the state of
locks
connected to a balance. The locks act as conditional anchors, routing data
down one
line or another depending on the state of the locks and allowing a balance to
function
as a switch, or "switch gate." For example, a single balance with conditional
anchors
could be put into any of the configurations shown in FIG. 17, FIG. 18, and
FIG. 19,
since the anchor points can be changed (this concept is demonstrated in
subsequent
figures).
[0163] FIG. 20 and FIG. 21 illustrate one way in which balances with
multiple
inputs can be used to conserve the sum of the inputs, and to route data. Two
states of
the same mechanism are depicted, which is formed by connecting two 2-input
balances together (a "binary double balance"). Inputs 2001 and 2002 are
connected to
link 2005 by rotary joints Link 2005 is connected to link 2007 via a rotary
joint. Link
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Date Recue/Date Received 2021-03-26
2007 connects to link 2006 via a rotary joint. Link 2006 connects to outputs
2003 and
2004 via their respective rotary joints. The fixed length of link 2007 causes
the sum
of the inputs to be conserved Since link 2007 cannot change in length, if
either input
2001 or 2002 moves, a corresponding move must take place at output 2003 or
2004.
FIG. 20 shows the state of the mechanism when input 2001 is 1, and input 2002
is 0.
FIG. 21shows the state of the mechanism when input 2001 and 2002 are both 1.
Note
that the mechanism in these figures (as is frequently the case due to the
complexity of
more complete systems and the need for clear illustrations of the basic
underlying
mechanisms of MILL) is not attached to other mechanisms as it would be in an
actual
MILL system. In this particular case, without additional constraints this
mechanism
will not be reliable. For example, when moving from an input of (0,0) to
(1,0), the
sum of the outputs must be 1, since the sum of the inputs is 1. However, there
is no
way to tell if the outputs will be (0,1) or (1,0), or even something like
(0.5,0.5). In an
actual system, one way of solving this problem is with locks. By conditionally
locking one of the outputs, the other output is forced to move in a
predictable manner.
Switch Gates
[0164] As
previously described, balances, in conjunction with locks, are one
way in which a switch gate can be implemented. FIG. 22 shows a switch gate
with a
top input 2201, a bottom input 2202, and a center input 2203. The middle input
is
connected, via a balance, to top output 2204 and bottom output 2205. The top
and
bottom inputs control whether the middle input is routed to the top output or
the
bottom output. For example, if top input 2201 is set to 1, then the upper lock
to which
top input 2201 is connected, is locked. Since that means that the line going
to top
output 2204 cannot move, when an input of 1 is provided at middle input 2203,
the
balance to which middle input 2203 is connected must move the line which leads
to
bottom output 2205. The top and bottom input would generally never both be 1
at the
same time, so these could actually be condensed into one input which controls
both
locks, e.g., and input of 0 locking the upper lock, and an input of 1 locking
the lower
lock, or vice-versa.
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[0165] Binary double balances coupled with locks can also be used as
switch
gates. Given a binary double-balance, one input is locked permanently, while
one
input is unlocked permanently and connected to an input (typically a clock). A
single
line can then be used to switch two complementary locks that are connected to
the
two remaining inputs of the double-balance. In essence, the clock input is
routed
through the double balance to one or the other "input" by the single line
which
controls the two complementary locks. Note that switch gates (and other MLL
mechanisms that have locked states) can be used even when dry switching is
desired.
In the case of a switch gate like that in FIG. 22, the clock force is applied
via a
balance connecting two locks. Since the system can be designed so that both
locks are
never locked simultaneously when the clock force is applied, one side is
always free
to move. Therefore, the clock force is not directed to an immobile mechanism,
but
rather to a mechanism that is always conditionally mobile in one direction or
the
other.
Logic Gates using Locks and Balances
[0166] An interesting property of locks and balances is that they can be
used
to create all the traditional logic gates (in addition to other mechanisms),
reversible
and irreversible. Before describing one way in which this can be done, it will
facilitate understanding the exemplary lock-based logic gate to discuss an
alternate
method of providing input to a mechanism (in this case, a lock). It is typical
to think
of one binary input as being a single connection to a line. For example, in
the
previously-described logic gates such as AND, NAND, NOR, and XOR, these logic
gates each took two inputs, often represented as two linear actuators, but
what in an
actual MILL system would be, e.g., two connections to data lines. The Fredkin
gate
takes three inputs, and so had three locations where data lines could be
connected.
Each of the inputs to these exemplary logic gates was binary, meaning, the
mechanism was designed such that one position represented 0, while a second
position represented 1. Although other implementations are possible,
frequently an
input of 0 has been represented as no movement occurring at that input, while
an
input of 1 was represented by some forward or rightward movement.
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Date Recue/Date Received 2021-03-26
[0167] However, there are other ways to represent input. For example,
instead
of a binary input using one connection which provides one of two possible
values (0
or 1), a binary input could consist of two connections, one representing 0,
and the
other representing 1. In this scenario, one of the connections to an input
would always
move: The 0 line would move if the input was 0, and the 1 line would move if
the
input was 1. This is in contrast to 0 being previously represented by no
movement of
an input. This strategy of using two lines per binary input is useful with
locks
because it allows either value, 0 or I, to create a locked state. An input of
0 locks one
side of the lock, while an input of 1 locks the other. One use to having both
0 and 1
resulting in a locked state on different sides is that this permits a lock to
act as two
different conditional anchor points. This can, for example, be used to control
which
side of a balance moves when input is fed into the balance. The following
example
shows a mechanism which illustrates how this property of locks can be combined
with balances to create logic gates.
[0168] FIG. 23 depicts one way in which a NAND gate can be constructed
using locks and balances. Clock input 2301 is connected to balance 2302, which
is in
turn connected to balance 2303, which is in turn connected to balance 2304.
Via a
series of locks and lines, the clock input is then routed to balances 2305 and
2306, and
finally results in the movement of upper output 2312 or lower output 2311.
Inputs
2307 to 2310 provide inputs to the gate, with four input lines being used to
represent
two binary inputs, as previously described. Specifically, input 2307 will be
referred to
as "AO" (meaning that it is associated with input "A," and will move if the
"A" input
is 0), input 2308 as "BO," input 2309 as "Al," and input 2310 as "B 1." Note
that for
inputs 2307 to 2310, there are two inputs each with the same label. This is
because the
same input data is used in two different places within the gate. In reality,
this would
not require two separate inputs for each, but rather one input for each could
be forked
using simple rod-like links, or connected to a single link which provides
multiple
connection points The depiction in FIG 23was chosen for clarity, not because
this
need be exactly how the mechanism is actually implemented (which is generally
true
for all the mechanisms described herein). The mechanism works as follows: If
actuated, inputs 2307 to 2310 move the side of the gate to which they are
connected,
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and lock the gate. In other words, if the input (A,B) is (0,1), the AO lines
will move,
and the B1 lines will move. Since A is not 1, the Al lines will not move, and
since B
is not 0, the BO lines will not move. Obviously, and input, (0,0), (0,1),
(1,0) or (1,1) is
allowed. The inputs establish a pattern of which gates are locked and which
are not.
This pattern in turn determines which side of each balance is free to move.
The clock
input then actuates the balances, with the end result being that either bottom
output
2311, representing (A NAND B)0, will move, or top output 2312, representing (A
NAND B)1, will move. The resulting output generates the NAND truth table:
Inputs Outputs
Al AO B1 BO (A NAND B)1 (A NAND B)0
0 1 0 1 1 0
0 1 1 0 1 0
1 0 0 1 1 0
1 0 1 0 0 1
[0169] As has already been mentioned, NAND is a universal gate.
Therefore,
it follows from this example that a system of locks and balances could be used
to
design any other desired logic gates, reversible or irreversible, using
combinations of
NAND gates. However, this may not be the most efficient way to implement any
desired logic, and similar lock and balance-based mechanisms can be used to
implement any other logic gate directly, including AND, OR, NOR, XOR, XNOR,
NOT, CNOT, Toffoli and others.
[0170] One implementation of a Fredkin Gate was already described. Locks
and balances can also be used to build a Fredkin gate. A Fredkin gate has
three inputs
and three outputs. The three inputs will be called A, B, and C, and the three
outputs
X, Y, and Z. Input A always connects to Output X. If Input A is 0, then Input
B
connects to Output Y and Input C connects to Output Z. If Input A is 1, then
Input B
connects to Output Z and Input C connects to Output Y. As previously noted,
Fredkin
gates are universal gates, meaning that any logical or arithmetic operation
can be
computed with only Fredkin gates. This is not to say that a practical MLL
computing
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system need be composed solely of Fredkin gates, as this would not necessarily
be the
most efficient configuration for many computing tasks. As will be obvious from
the
teachings herein, many other types of gates can be implemented using MLL
Fredkin
gates are used as one exemplary embodiment because they are both universal and
reversible.
[0171] FIG. 24 depicts a Fredkin gate made using locks and balances. Due
to
the complexity of the mechanism, a simplified notation is used where anchored
rotary
joints are not explicitly shown, but assumed to be on the unconnected ends of
appropriate links. The clock input or signal (actuator not shown, as with all
inputs to
this mechanism) would be attached to rotary joint 2401. Input for Al, AO, Bl,
BO, Cl
and CO input would be attached to rotary joints 2402, 2403, 2404, 2405, 2406
and
2407, respectively. BI, BO, Cl and CO inputs would also be connected to rotary
joints
2408, 2409, 2410 and 2411, respectively. The clock signal and inputs are
connected
via a series of links and locks, and for some outputs, balances, to X1 output
2412, XO
output 2413, Y1 output 2414, YO output 2415, Z1 output 2416 and ZO output
2417.
Note that the X1 and XO outputs are not shown on the right side next to the
other
outputs to reduce figure complexity. In reality, obviously they could be
routed to any
location desired. Note that links 2418 and 2419 are part of 4-bar linkages,
not
balances, constraining these links to stay vertical when moving. Black
triangles 2420
and 2421 exemplify rigid linkages (a straight line is not used to avoid a
representation
with excessive lines which cross each other, and this representation is only
diagrammatic; the actual mechanisms could be implemented in many ways).
[0172] The blank state is depicted in FIG. 24. Conceptually, from this
state,
the A, B, and C inputs are set during one clock phase. During a subsequent
clock
phase, the clock signal connected to rotary joint 2401 is set to "1," which
causes the
movement of the various balances within the mechanism, resulting in the X, Y
and Z
outputs being set as appropriate. While one straightforward approach to
building a
system would be to use Fredkin gates throughout, and to use three-phase
Landauer
Clocking, other approaches are feasible. As will be obvious from the various
well-
known clocking schemes, there may be additional clock phases, and using Bennet
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Clocking, the number of clock signals will depend on the number of steps one
desires
to allow in a retractile cascade.
Shift Registers
[0173] Shift registers can be used as a foundation for implementing
sequential
logic in a computational system. For example, two numbers to be added,
subtracted,
ANDed or ORed are stored in two shift registers and clocked out into an
arithmetic
and logic unit consisting of a handful of gates, with the result being sent to
the input
of a third shift register called the accumulator. In reversible digital
circuits, a shift
register can be defined as a series of "cells," each cell having three stable
states. 0, 1
and blank (b), which can be used to store state information. The cells are
clocked by
successive clocks. The output of each cell is connected to the input of the
next cell in
the chain. The data stored in the chain is shifted by one position after each
clock
cycle; data (0,1, or b) at the input is shifted in while data at the end of
the array is
shifted out. Binary clocked shift registers can be implemented using only the
clocks
and the rotary joints connected by links (creating locks and balances)
previously
described. Shift registers are simple, yet when combined with the appropriate
combinatorial logic, contain all the fundamental elements required for a
computational system.
[0174] A shift register can be built by combining locks and balances,
and
assuming the presence of a clock system, so that each cell (which might be
viewed as
a flip-flop, and which may also be thought of as a buffer and can be used to
synchronize clock phases of different processes by introducing clock phase
delays) of
the shift register is related to its neighbor by virtue of relying upon a
preceding or
succeeding clock phase, as appropriate. This enables the copying and shifting
of data
through the shift register, rather than deterministically setting the contents
of the
entire shift register simultaneously.
[0175] FIG. 25, FIG. 26 and FIG. 27 depicts a single cell of a shift
register, in
three different states. In these figures, the 0 input 2501 is connected via a
rotary joint
to one side of lock 2505. The 1 input 2502 is connect via a rotary joint to
one side of
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lock 2506. Clock signal 2503 (although diagrammed differently to provide a
mechanism that is more complete when standing alone, this would, in an actual
system, be a connection to the clock system), is attached to balance 2504.
Locks 2505
and 2506 determine which of the outputs 2507 or 2508 move when the clock
signal
becomes 1. The lock which contains outputs 2507 and 2588 can be thought of as
the
output lock for the overall cell, while locks 2505 and 2506 are holding area
locks. The
importance of this concept will become clear when connecting multiple cells in
series.
[0176] FIG. 25 depicts the cell in its blank state, before any input has
been
provided, and while the clock signal is low or 0. FIG. 26depicts the cell
after input
2501 has been set to 1, but before the clock signal has moved to high or 1.
This results
in the locking of lock 2505.
[0177] FIG. 27depicts the mechanism from the previous state once the
clock
signal has moved to high. As clock signal 2503 pushes on balance 2504, because
lock
2505 is locked, only one side of balance 2504 is free to move. Thus, the clock
signal
moving to high is transmitted through lock 2506 and to output 2508. Note that
the
movements between states such as those illustrated in FIG. 25, FIG. 26 and
FIG. 27
do not take place simultaneously but rather are governed by clock signals and
data
inputs (which themselves may be tied to clock signals). This sequential
behavior is
what allows the proper functioning of this cell or buffer (also analogous to a
latch in
electronic computing) Such behavior is easy to realize and well-known in
electrical
implementations, but more involved in a mechanical implementation.
[0178] FIG. 28a, comprising the left half, and FIG. 28b, comprising the
right
half, collectively depicts a two cell shift register to illustrate how two
cells would be
connected and to explain how data would move from one cell to the next. In
FIG. 28a,
cell 1 2801, and in FIG. 28b, cell 2 2802, are each equivalent to the
mechanism
depicted in FIG. 25. In FIG. 28a, cell 1 2801 has a connection to a clock
signal via
link 2803 (depicted as a partial link to indicate connection to a clock system
that is
not shown), and in FIG. 28b, cell 2 2802 has a connection to a clock signal
via link
2806. Links 2804 and 2805 connect the cell 1 2801 and cell 22802.
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[0179] Like in FIG. 25, FIG. 26 and FIG. 27, a multi-phase clock signal
is
assumed to be present, and links 2803 and 2806, and the data inputs associated
with
each cell would preferably all operate on different clock phases, requiring at
least a
three-phase clock for this particular design. The operation of a single cell
has already
been described, but demonstrating how cell 1 2801 passes data to cell 2 2802
may be
instructive. The sequence of events is as follows: (1) on clock phase 1, the
clock for
cell 1 2801 was already at 0, and the data inputs are set for cell 1 2801.
Either the
upper or lower lock of cell 1 2801 locks, depending on which input was set to
1; (2)
on clock phase 2, the clock signal for cell 1 2801 is set to 1. This results
in the
unlocked side of the balance present in cell 1 2801 moving, which in turn
moves
either link 2804 or link 2805. This locks one of cell 2's 2802 holding area
locks,
copying the data from cell 1 2801 into cell 2's 2802 holding area. Note that
the output
lock of cell 2 2802 still has not moved; (3) on clock phase 3, the clock
signal for cell
2 2802 is set to 1. This copies the data from the holding area locks into cell
2's 2802
output lock. In detail, one of cell 2's 2802 holding area locks was already
locked, so
when the clock signal for cell 2 2802 changes from 0 to 1, only the unlocked
line
could move. When this unlocked line moved, it locked cell 2's 2802 output
lock. It
also locked the second of cell 2's 2802 two holding area locks; and (4) the
clock
signal for cell 1 is set to 0. This unwrites cell l's 2801 data from cell 2
2802 by
unlocking only the cell 2 2802 holding area lock that was originally locked
when cell
l's 2801 clock was set to 1, as the other lock was just locked by the clock
signal to
cell 22802. This cycle then repeats itself as new data is input into cell 1.
In step 2
above, it is noted that the output lock of cell 2 2802 still has not moved.
This allows
these exemplary shift register cells to store previous data, whereas
mechanisms such
as some of the logic gates described herein have their state completely
determined by
the current data inputs. This is because a cell can contain not only a
previous input
(which ends up being shifted to its output lock during clock phase 3), but
also the
current input, which is stored in the holding area locks.
[0180] It will be apparent from this description that if reversibility
at the shift
register cell (or other mechanism) level is desired, all that need be done is
to run the
clock phases in the opposite order. If a retractile cascade is desired, then a
scheme
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like Bennett clocking can be used, coupled with the appropriate hardware
design (e.g.,
the ability to store "junk" bits so that no infoimation is lost, allowing the
computation
to be reversible to as many levels deep as desired). In the current example,
the shift
register being only 2 cells long, only 2 numbers can be stored. In an actual
system,
such a shift register can be arbitrarily long. Further, while this particular
implementation is a serial-in/serial-out design, it will be obvious given this
example
that MLL can be used to make any other type of shift register desired, such as
parallel-in/parallel-out, serial-in/parallel-out, and others.
Momentum Cancellation
[0181] It can be useful to perform computation without altering either
the
center of mass or the moment of inertia of a group of computing structures, so
that the
forces that these changes would cause are not coupled to the overall system,
potentially contributing to energy dissipation. This can be accomplished by
using sets
of structures whose movements cancel out changes in the center of mass or the
torque
around any axis (a "canceling group"). Such techniques can apply to any
structure,
such as links, lines, locks, logic gates, balances, clocks, and larger
aggregate
structures. For example, consider a link or line which is used to transmit
data from
one place to another. Such a structure may be replaced with four parallel
structures,
conceptually grouped as two pairs. Each member of a pair moves in the opposite
direction, canceling changes in the center of mass and linear momentum.
However,
each pair could still create torque. So, the direction of movement of each
link is
reversed from the first pair to the second pair, resulting in torque
cancellation. Given
this type of arrangement, no net force is coupled to the overall device and so
such
canceling groups can be used to transmit data while reducing energy coupled
into the
rest of the structure.
[0182] FIG. 29 illustrates this concept using groups 2901 and 2902, each
containing two members, 2903 and 2904, and 2905 and 2906, respectively. Within
a
group, each member moves in the opposite direction from the other member
(while
each member is not connected to the others in the diagram, in an actual system
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movements would be synchronized, e.g., by clock signals). For example, as
depicted,
member 2903 has moved to the right, while member 2904 has moved to the left.
The
accelerations that take place during these movements will generate forces on
the
underlying support structure (the anchor block, not shown) Since members 2903
and
2904 accelerate in opposite directions, the linear components of their
momentum will
cancel. However, in this arrangement they will still generate a net torque on
the
anchor block. Adding the second pair of members 2902 containing members 2905
and 2906, which also move in opposite directions within the pair, but generate
a
torque that is opposite the torque of group 2901, allows complete
cancellation.
[0183] Obviously, many other designs could be used to either cancel
momentum, or reduce the need to do so in the first place (e.g., by reducing
mass, or
reducing the radii to centers of rotations) Given this, momentum cancellation
is not
limited to any particular arrangement. Nor are cancelling groups limited to
some
specific number of members. Even odd numbers could be used, such as where the
members of a canceling group do not have the same masses or momentum. For
example, two members could be used to cancel one other member that generates
twice the momentum. And, momentum cancellation need not be complete.
Additionally, forces along any axis may be addressed similarly. For example,
in
actual designs, forces which cause torque along the Z axis, which is defined
for this
example as perpendicular to the figure plane, may also need to be cancelled.
The
complexity and increased mass of complete cancellation may outweigh the
benefits,
and the appropriate amount of cancellation (if any), and which force
components to
cancel, if any, will vary on a case by case basis.
Clocks
[0184] In an MLL system, a clock system synchronizes the mechanisms, and
also provides force to drive the mechanisms. It is well-known in the field of
computer
science that computational systems with different numbers of clock signals (or
phases) can be used. At least 2 phases are required, but 3 phases can be
advantageous,
and higher numbers can also be used. An MLL clock system could consist of one
or
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more clocks which create a plurality of clock signals. These signals could
take the
form of reciprocating motion transmitted through the mechanisms, such as via
lines,
or the use of rigid frames (which are actually just links of specialized
shape, for
example, a rigid frame could connect to a clock at a single location, and then
branch
out, potentially in multiple directions or dimensions) to connect to many
gates or
other mechanisms), supported by support links as necessary. The optimal number
of
mechanisms connected to a single clock or clock signal will be implementation-
specific, depending on factors like the mass which is being driven, the
rigidity of the
system, and the switching speed. Alternatively, clock signals could be
generated by
multiple local clocks, such as oscillators or rotating masses, with
communication
between the clocks as required to keep them synchronized.
[0185] Clock signals could be generated in a variety of ways. For
example,
rotating masses, harmonic oscillators, or cams and cam followers could all be
used,
creating periodic motion in links where, for example, one position may
represent "0"
and another position may represent "1". A rotating mass, which is essentially
a
flywheel, can serve as a simple oscillator. Flywheels, coupled to links by
rotary joints,
could be used to drive each clock signal back and forth and require no parts
beyond
links and rotary joints. A flywheel could be kept in constant motion by some
sort of
energy source or motor, which replenishes the energy lost to dissipative
mechanisms
in the system. A discussion of exactly how such an energy source or motor
might be
implemented is beyond the bounds of the invention. It is obvious from the
literature,
which contains substantial work on both macro-scale motors, and molecular-
scale
motors, including bio-motors (e.g., ATPases, flagella) and synthetic motors,
that there
are many ways to implement such motors, and many ways to power such motors,
including chemical, light, direct current, and external electrical fields.
[0186] Other designs for clocks introduce parts beyond links and rotary
joints,
and so do not technically fall under the definition of MLL. However, as the
use of
alternate clocking systems connected to an MLL system may have utility, it is
described how such alternate clock implementations can be designed for minimal
energy dissipation. Further, since a single clock can drive many logic
elements, even
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if the clock itself were to be somewhat dissipative, overall, computation
could still be
quite efficient.
101871 One alternate clocking system would be to use simple harmonic
oscillators, preferably with a high Q factor. The use of simple harmonic
oscillators
has the advantage that a single clocking frequency would be used, and that the
clocking frequency would be provided by a very simple mechanism. Using such an
oscillator, components would preferably be designed to use sine-like clock
signals
(including signals with sine-like transitions between 0 and 1 with flat areas
in
between for timing purposes), and designed in such a way that they did not
generate
significantly higher frequency overtones during operation (as, for example, if
one
moving part collided with another moving part). Alternatively, a sum of simple
oscillators could be used, the sum approximating the desired clock signal. The
use of
a sufficient number of oscillators could, in principle, approximate the
desired clock
signal as accurately as desired, at the expense of additional parts. One way
to
implement a harmonic oscillator is with a spring (in which is included a
flexure or
other structures of similar purpose), which could be made of any material with
the
appropriate properties and spring constant, including the same materials as
the links.
[0188] Cams and cam followers are another way to generate a clock
signal. A
cam and cam follower can be used to generate a very smooth clock signal, as is
subsequently described. A cam can also be used to generate a clock signal with
an
essentially arbitrary waveform A cam could be made, for example, from a
rotating
link supported by rotary joints at either end. The link thus forms an axle
which can be
used as a camshaft. The cam would be affixed to the camshaft (or the camshaft
could
actually be the cam, assuming it has the appropriate cross-sectional shape). A
cam
follower could be constructed, for example, using a wheel connected to two
rotary
joints, connected to a lever arm. Rotating the camshaft would rotate the cam.
The cam
follower wheel would ride up and down on the cam, causing the lever arm to go
up
and down along with it. The lever arm would be a link in a suitable linkage.
Many
other geometries and relative positions for the cam and cam follower could be
used,
including designs where the cam follower surrounds the cam, or vice versa,
such as
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with an eccentric rotor and stator, as well as variations in the types of
motion the cam
makes, such as designs where the cam simply rocks back and forth, or moves in
a
manner that is itself under programmatic control, as well as combinations of
the
foregoing and obvious variations.
[0189] While it may not be obvious how smooth curves can be made at the
molecular level, since angles and distances are quantized by the nature of
chemical
bonds, this issue can be overcome. For example, in diamond, buried Lomer
dislocations could be used to create smooth curves on the surface of a
Lonsdaleite
(hexagonal diamond) cam. Similarly-gradual changes could be accomplished with
diamond and other materials, by using changes in bonding patterns, the
incorporation
of elements of varying atomic radii, using strain to slightly displace an atom
or atoms,
or using naturally curved structures such a nanotubes. Using these strategies,
a
molecular implementation of cam and cam followers (and indeed, any pieces of
such
a system) could be made to almost arbitrarily precise tolerances, even to
distances
below a single atomic diameter.
[0190] Using a rotating mass to generate clock signals requires only
rotary
joints and links, the basic parts of MLL systems. If a cam and cam follower
were
used, the rotary joints connecting the cam follower's lever arm to the wheel,
and those
which allow the cam to rotate, have again, already been discussed. However, in
a
cam-based system, there is rotating contact between the cam and cam follower
wheel
surfaces, a situation not present when considering the basic parts of MLL
While this
may seem like a mechanism that creates undesirable sliding friction, it need
not be.
The two surfaces do not have to slide over each other, but rather rotate
synchronously.
Analysis indicates that, especially given a molecular-scale, atomically-
precise (or
nearly so) implementation, the energy dissipation from such a mechanism would
be
very low.
[0191] In such a molecular-scale mechanism, the very slight distortion
in the
shape of the wheel and the very slight variation in attractive force (van der
Waal s)
between the surface and the wheel could cause very slight phonon generation.
Viewed
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Date Recue/Date Received 2021-03-26
in the frame of reference of the cam follower, the wheel and surface would be
static
other than the very high frequency shifting of the crystal structures within
them. As a
consequence, there should be no generation of low frequency phonons. And,
inertia
and positional uncertainties caused by thermal noise will prevent the
mechanism from
being able to reproduce the highest frequency components in the signal on the
cam,
even in the absence of a low pass filter on the output (which could be used if
desired,
and could be implemented, e.g., as a simple spring and mass device).
[0192] Also, various cancelation methods could be used to minimize the
high
frequency signal component that is encoded on the cam's surface. This might be
done, for example, by using a plurality of cam follower wheels that read a
plurality of
tracks on the cam surface, each track being staggered by some distance.
Attaching
each cam follower wheel to the cam follower would then effectively sum or
average
their outputs, canceling at least some of the high frequency noise signal. Any
number
of tracks and cam follower wheels could be used, with any desired shape for
each
track (e.g., different canceling signals could be encoded in each track),
resulting in
arbitrary accuracy of the aggregate signal. Another method to reduce high
frequency
noise would be to rotate the crystal axis of the material from which the cam
is made,
and perform a corresponding rotation of the crystal structure of the wheel
which is
meshing with them. By choosing the crystal rotation and width of the cam and
cam
follower appropriately, other high frequency signals may be eliminated due to
the
change in timing and atomic spacing as the cam contacts the cam follower
wheel. Yet
another method of reducing the transmission of high frequency signals is to
reduce
the stiffness of the coupling of the cam and cam follower to the rest of the
system. For
example, reducing the spring constant of the cam follower arm, or reducing the
stiffness of the bonds on which the cam follower is mounted, would help filter
high
frequency signals.
[0193] Given these examples, it will be obvious that these are not the
only
ways to reduce high frequency components. There are many ways to ensure that
parts
in rotating contact do not create or transmit high frequency signals, and the
use of
atomically-precise parts in particular allows the minimization of such
signals. As the
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cam follower rises and falls on the curved cam surface, following the clock
signal
encoded in that surface, it will subject the cam surface to inertial forces.
Each
acceleration or deceleration of the cam follower will create a corresponding
force on
the surface of the cam. These periodic forces will create phonons at the clock
frequency. This source of energy dissipation can be canceled if two cam
followers
follow two cams, the two cams encoding equal but opposite signals. And, since
the
clock frequency is arbitrary, this frequency can be reduced until energy
dissipation
caused by coupling of the high frequency components of the clock signal to
mechanical vibrational modes is under desired levels. Note that the cam
follower
mechanism described can exert a relatively strong force when the cam is
pushing on
the cam follower. However, during movement in the opposite direction, the
force is
limited by the van der Waals force between the cam and the wheel. This can be
rectified, if need be, for example, by using two cam followers and two cams
(with the
encoded signals appropriately rotated with respect to each other), where the
cam
followers are on opposite sides of their respective cams. The first cam
follower can
exert a strong force in one direction, while the second cam follower can exert
a strong
force in the opposite direction.
Exemplary Switching Time Analysis
[0194] The basic constitutive equations of simple Newtonian motion and
assumptions about the size and physical strength of links can be applied to an
analysis
of the switching time, mass, force, and resonant frequency for a molecular
scale
implementation of MLL mechanisms. To provide a concrete example, several
assumptions must be made, all of which could vary greatly depending on the
exact
implementation, but the exact performance of a given system is not the point,
rather,
the goal is to calculate an estimate of one possible operating speed of an
exemplary
molecular-sized system. Links are assumed to be ¨20nm in length and about
0.5nm to
0.7nm in diameter. Links are assumed to be made of diamond or similar
material, and
to be braced to increase their stiffness (e.g., a beam with triangular
bracing, rather
than just a straight beam). The positional difference between "0" and "1" is
assumed
to be ¨2nm. Rotary joints are assumed to be like those shown in FIG. 1, and
the
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system is assumed to be operating a room temperature. These assumptions allow
the
calculation of link and rotary joint stiffness. To determine the resonant
frequency,
mass must be determined.
[0195] The mass of a typical mechanism can vary widely. Even using a
given
type of link, the mass will be quite different depending on whether the
mechanism is a
single 4 bar link, a lock, a balance, a logic gate, etc., and on the exact
implementations of such structures. To use round figures, the moving mass of a
link
might be about 8 x 10-23 kg, while the moving mass of a mechanism made of
several
links might be on the order of 10-21 kg. Using these assumptions, the resonant
frequency for an exemplary molecular-scale mechanism may be around 13 GHz. A
square wave clock signal would lead to substantially higher than necessary
energy
dissipation Therefore, it is assumed that the clock waveform is generated as a
sinusoidal wave, convolved with a Gaussian to reduce undesirable high
frequency
components, or optimized using standard linear systems theory to minimize the
generation of undesired resonances. In addition, to be conservative, the clock
can be
operated at a frequency well below the 13 GHz resonant frequency calculated.
Depending on various assumptions, such as just how much energy dissipation is
acceptable, and with how much margin for error, this results in switching
times in the
ins to lOns range. Obviously, this is only exemplary. Larger structures would
likely
operate at slower speeds, while smaller structures, stiffer structures,
designs which
move shorter distances between "0" and "1", lower operating temperatures, or
relaxation of some of the conservative design parameters assumed, would result
in
faster switching times.
MLL Summary
[0196] MLL has been shown to be able to create mechanisms including
lines,
logic gates, locks, balances, switch gates and shift registers, using only
rotary joints
and links. MLL provides for any combinatorial logic by using various
combinations
of logic gates which, either alone (e.g., NAND or Fredkin gates) or in
aggregate, are
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universal. Sequential logic, and therefore memory, can be provided by flip-
flops or
cells, which can be combined into shift registers.
101971 Given the availability of both combinatorial logic and sequential
logic,
it will be obvious that a complete computational system can be built using
MILL. For
example, the Von Neumann architecture, a well-known Turing-complete
architecture,
requires three main components: A control unit, an arithmetic logic unit, and
memory.
Using combinatorial logic and flip-flops, a finite state machine can be
created which
can be used as a control unit. Combinatorial logic can be used to create an
arithmetic
logic unit. And, flip-flops can be used to create memory. This is all that is
needed for
a complete computational system. Of course, such a system does not need to be
based
on the Von Neumann architecture; this is simply an example to illustrate the
fact that
all the necessary components of a Turing-complete system can be provided using
MILL. Depending on the exact mechanisms used, and the clocking scheme
employed,
an MILL-based computational system can be irreversible, reversible, or some
combination thereof. The ability to create mechanical computing mechanisms,
and
complete computational systems, using only links and rotary joints can provide
advantages which include reduced friction (and therefore power consumption and
waste heat generation), device design and manufacture simplification, and
device
robustness (e.g., operation at more extreme temperatures than permitted by
many
other known computational systems, given that mechanical logic could function
up to
near the melting point of its constituent parts, whereas, electronic computing
suffers
from bandgap issues at extreme temperatures).
Mechanical Flexure Logic
[0198] Flexures can take the place of the rotary joints used in MILL,
resulting
in Mechanical Flexure Logic ("MFL"). With the substitution of flexures for
rotary
joints, all MILL mechanisms have analogous MFL mechanisms. For example, FIG.
30
shows the MFL version of the MLL lock depicted in FIG. 7. Link ends 3001 and
3002
of links 3003 and 3004, respectively, are one place where input mechanisms
could be
connected. Anchored link ends 3007 and 3008 of links 3003 and 3004, act in a
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manner analogous to anchored rotary joints. Note that there are no actual
rotary joints
present in the MFL version of a lock. Rather, flexures, exemplified by the
semi-
circular cutouts 3005 and 3006, provide bendable points between various parts
of the
structure. These flexures allow force, which may be input at link ends 3001 or
3002,
to be transmitted through triangular links 3010 or 3011, respectively, and on
to link
ends 3012 or 3013 (which may be thought of as outputs), respectively. Link
3009
serves the same purpose as link 709 in the co-planar MLL lock of FIG. 7. The
entire
mechanism of FIG. 30 can be made (although it need not be) from a single piece
of
material, where the different links are monolithic, but logically separable
because
they are bounded by flexures.
[0199] Overall, the movement and function of the MFL and MLL locks is
completely analogous, but changes in the relative angle between links in MFL
are
facilitated by flexures instead of rotary joints. While locks are used to
demonstrate
the analogy between MFL and MLL, it will be apparent that the same analogies
can
be made between any mechanisms, and therefore by replacing rotary joints with
flexures, a Turing-complete system can be made using MFL. Of course, flexures
require suitable materials, which may differ from that of links, and the
geometry of
flexures need not be only that depicted in FIG. 30. Flexures are well-known in
the
mechanical arts, and suitable designs and materials could be adapted for
almost any
degree of motion, size, operating temperature, or other parameters.
Mechanical Cable Logic
[0200] Another method of implementing computing mechanisms and systems
which are analogous to MLL (and hence also to MFL) is to replace links and
rotary
joints with cables, pulleys, and knobs. This design paradigm will be referred
to as
Mechanical Cable Logic ("MCL"). With respect to the basic parts, or
primitives,
MCL cables are analogous to MLL links, and MCL pulleys are analogous to MLL
rotary joints. Knobs are an additional primitive that do not have a direct
counterpart in
MLL or MFL. Knobs are used to aid in the interaction of cables, for example,
to
create locks, and in that respect, aid in the building of mechanisms with
analogous
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logical functions, even if the part itself does not have a direct analog. It
will be
obvious given the teachings herein, that by applying force to a cable,
movement can
be transmitted down the cable and to other mechanisms as desired (hence their
analogy to links) Similarly, it will be apparent that pulleys can be used to,
among
other purposes, allow bends in cables so that movement can be routed in any
direction
desired (hence their analogy to rotary joints).
[0201] The MCL primitives can be used to create, among other structures,
balances and locks. While MCL implementations of balances and locks may look
different than their MLL counterparts, viewed from a "black box" perspective,
MCL
balances and locks can be implemented so as to be logically equivalent to the
respective mechanisms in MLL. Given this, MCL also provides for Turing-
complete
systems.
Tracks and Channels
[0202] Like MLL rotary joints, MCL pulleys can be anchored or
unanchored.
However, in MLL links are rigid and this aids in constraining the movement of
unanchored rotary joints. In MCL, cables are not rigid, so the proper
geometric
constraints need to be provided in a different manner. One way to do this
would be to
keep tension on the appropriate cables (e.g., clock cables) so that pulleys
connected to
such lines cannot move unless, in this example, the clock lines move, in which
case
pulley movement is constrained to the path the clock cables define. Another
way of
addressing this issue would be to mount pulleys on links where such constraint
was
necessary (although another primitive is then required, and since this blurs
the
distinction between MLL and MCL, such an embodiment is not addressed further).
Yet another way is the use of channels, tracks, or other guiding means on the
anchor
block. By virtue of being affixed in a sliding manner to the guiding means,
the motion
of unanchored pulleys are appropriately constrained.
[0203] FIG. 31 and FIG. 32 show a top view and side view, respectively,
of a
pulley which can slide in a channel. Anchor block 3101 contains channel 3104.
Pulley
3102 is monolithic with, or connected to (in a fixed or rotary manner) axle
3103. Axle
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3103 connects itself and pulley 3102 to channel 3104 in a slidable manner.
Actuating
cable 3105 is affixed to axle 3103 and enables the movement of the pulley in
the
channel (e.g., actuate using a clock line). Note that this is but one way of
actuating
and guiding pulley movement, and of affixing a pulley to a track, channel, or
other
guiding means. Many other designs would be obvious, such a pulley with an axle
extending through the anchor block with an expanded lower part protruding so
that it
cannot come out of the channel, a beveled channel and axle (e.g., similar to a
dovetail
joint in profile) which could accomplish the same goal, or the addition of
another axle
structure on top of the pulley, along with an another anchor block, pinning
the pulley
between the two.
[0204] Another way of providing guiding means would be rails mounted on
the anchor block, the pulley being affixed to the rails in any one of many
known
means, The point is not the exact mechanical implementation, but rather to
provide
some guiding means, preferably with low friction, in light of the flexibility
of cables;
any of many well-known guiding means could be used.
[0205] Understanding now how pulley motion can be constrained without
the
need for links, the analogies between MILL, MFL, and MCL become easier to
describe. Since it has already been shown that, in MILL, locks and balances
suffice
(although they are not the only way) to create Turing-complete systems, it
follows
that if analogous mechanisms exist in MCL, MCL is also capable of being used
to
create Turing-complete systems. It has already been stated that, with respect
to the
basic primitives, MILL links can be likened to MCL cables, and MILL rotary
joints can
be likened to MCL pulleys. To prove this, and show exactly how cables and
pulleys
can be used to create the underlying mechanisms of Turing-complete computing,
the
design of a lock and a balance is described.
MCL Locks
[0206] Locks can be created in MCL using knobs that are integral with,
or
affixed to, cables or other structures. With the appropriate design, these
knobs allow
the reproduction of the features of an MILL lock. Specifically, with respect
to a binary
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embodiment with two inputs, from the (0,0) unlocked state, there are two
allowable
movements, those being from the (0,0) unlocked state to one of the locked
states,
(0,1) or (1,0). From either of the locked states, the only allowable movement
is back
to the unlocked state. Note that there is no reason that knobs cannot be
attached to
virtually any structure, as convenient, and the construction of locks are not
the only
use of knobs.
[0207] One way to implement the desired logic is depicted in FIG. 33a-c.
In
FIG. 33a, a first cable 3301 is crossed by a second cable 3302. Two knobs 3303
and
3304, and 3305 and 3306, respectively, are affixed to each cable. FIG. 33a
shows the
lock in the (0,0) position, where either cable is free to move. FIG. 33b shows
the lock
in the (0,1) position, the second cable having moved, thus locking the first
cable by
virtue of the fact that one of the second cable's knobs 3305 is between the
first cable's
knobs 3303 and 3304, preventing their movement in either direction. FIG.
33cshows
the lock in the (1,0) position, the first cable having moved, thus locking
second cable.
[0208] Many other designs are possible which allow knobs to act as
locks.
FIG. 34, FIG. 35, FIG. 36, and FIG. 37 depict an exemplary knob design which
can
also enforce the constraint that the only allowed movement in a lock from the
(0,1) or
(1,0) state is to (0,0). This knob design is more complex, but requires only
two knobs
(one on each cable) instead of four, to create the desired lock logic.
[0209] FIG. 34 shows a single knob 3401. Generally a cable would be
attached to either end (not shown), but such knobs could be used in other
scenarios as
well, such as connected to MILL links.
[0210] FIG. 35 shows how two such knobs 3501 and 3502, mesh with each
other to form a lock. In this figure, the lock is shown in the blank state
(meaning,
neither knob is positioned to block the movement of the other).
[0211] FIG. 36 and FIG. 37 depict the same knobs 3501 and 3502 in the
(0,1)
and (1,0) state (or vice versa; since the mechanism is symmetric, the knob
that is
defined as the 0 knob and that which is defined as the 1 knob is arbitrary).
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[0212] It can be seen by inspecting the shape of these knobs and their
relative
positions in the blank, (0,1), and (1,0) states that if two cables or other
structures
interact via the appropriate movement of such knobs, that constraint that the
only
movement allowed from the (0,1) or (1,0) state is to the (0,0) state, is
enforced.
MCL Ovals
[0213] Conceptually, it can be useful to define a structure in MCL
called an
"oval" since this arrangement of basic parts is one way to create more complex
mechanisms such as balances and shift registers.
[0214] As depicted in FIG. 39, one way to implement an oval uses a
closed
loop of cable 3801 (referred to as the "logic cable" to distinguish it from
cables
serving as inputs/outputs, including those providing clock signals, although
this
distinction is for clarity of description only, since logic cables can also
provide
input/output, as in the case of crossed ovals which can be used to form cells
and shift
registers), which may include one or more structures such as knob 3802, and
which
goes around one or more pulleys such as pulley 3803 (two pulleys are depicted
but
other numbers could be used to change the shape, length, vibrational and
entropic
characteristics, or other characteristics of the oval, which despite the name,
need not
be oval in shape). If one or more of the pulleys can be unanchored, guiding
means
such as track 3804 may be included. Unanchored pulleys may be actuated (moved
along their guiding means) by cable 3805, which may be, e.g., tied to a clock
signal.
[0215] One or more cable housings such as that exemplified by housing
3806
may be included to reduce energy loss, as described elsewhere herein. Knobs
facilitate interaction with other structures and may be connected to one or
more
input/output cables 3807 and 3808. By itself and in its simplest form, an oval
merely
takes an input and may (but does not have to), pass it on as an output. For
example, if
cable 3807 moves and the pulleys are anchored, the opposite side of the logic
cable
must also move, causing the movement of cable 3808. Thus, the oval may relay
data,
but no substantial computation is taking place. However, ovals can be designed
to
carry out computations by interacting with other structures (including, e.g.,
other
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ovals, or cables). When coupled with locks, this is one way to construct a
balance via
MCL.
MCL Balances
[0216] FIG. 39 depicts a balance as part of an oval. Balances and ovals
can
also serve as part of a shift register. The balance includes pulley 3902 and
the left part
of logic cable 3901. FIG. 39 depicts an oval with unanchored pulleys and two
crossed
cables which provide data input, the two crossed cables coming from, e.g.,
data
cables, or another oval. Optional structures such as cable housings are
omitted for
clarity, and as usual, an anchor block is assumed to be present, but not
depicted.
Logic cable 3901 goes around pulley 3902 (and its mate, unlabeled). Both
pulleys are
mounted on tracks, exemplified by 3903. Clock line 3904 actuates the mechanism
by
pulling on the pulleys, which will cause them to slide in their tracks. The
logic cable
has two pairs of knobs 3905 and 3906, and 3907 and 3908. Cables 0 3909 and
cable
1 3910 provide input to the oval. Each crossed cable has a pair of knobs 3911
and
3912, and 3913 and 3914, respectively. By crossing the oval (at right angles
in this
diagram, but other angles and designs can be used), cables 0 and 1 can
position their
knobs to interact with the knobs of the oval. Triangular knobs 3915 and 3916
(shown
as triangular only to visually distinguish them from the other knobs; this
shape is not
significant) are connected to the 1 output line 3917, and the 0 output line
3918,
respectively. This configuration is just exemplary. The output lines could
just as
easily be, e.g., positioned differently, or connected to the appropriate lock
knobs
rather than using separate knobs.
[0217] FIG. 39, FIG. 40, and FIG. 41 differ only in the position of the
input
cable knobs. In FIG. 39, both locks are in the blank position; meaning that
the input
cable knobs and the logic cable knobs would not interact if the mechanism were
actuated. In FIG. 40, cable 3909 has moved knobs 3911 and 3912 so that knob
3911
is now between two of the knobs on the logic cable, 3905 and 3906. This can be
considered an input of 0, since the zero input line has moved. If the
mechanism were
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actuated in this state, the upper side of the oval would be prohibited from
moving, as
knobs 3905, 3906, 3911 and 3912 form a lock which is then locked.
102181 In FIG. 41, cable 3909 has not moved, but instead cable 3910 has
moved. This can be considered an input of 1, since the 1 cable has moved. The
effect
is to lock the opposite side of the oval by placing knob 3913 between knobs
3907 and
3908. This locking of one side or the other of an oval is analogous to locking
one
side or the other of the appropriate link in an MLL balance. The functioning
of the
oval-based balance is as follows: Assume that the starting position of the
pulleys is at
the left side of their respective tracks. When the inputs are set, the input
cables lock
either the upper or lower side of the oval. The clock line then moves the
pulleys from
the left to the right. The lateral movement of the pulleys is the same
regardless of the
inputs. However, the side of the logic cable that moves is determined by the
inputs.
Whichever side of the logic cable is locked is forced to remain stationary.
Therefore,
when the pulleys move, only the unlocked side of the logic cable moves. This
results
in the movement of the 0 output line if an input of 0 was provided, and
movement of
the 1 output line if an input of 1 was provided.
[0219] FIG. 42 shows the position of the mechanism assuming that an
input of
1 was provided and then the clock line moved the pulleys to the right. Since
knob
3913 had moved between knobs 3907 and 3908, the lower side of the oval was
locked. Therefore, when the pulleys move to the right, the logic cable must
follow in
the only manner possible: by rolling the logic cable so that knob 3915, and
thus the 1
output line 3917, moves to the right. Note that data cables such as 3909 and
3910 are
not the only manner of providing input to an oval, and output cables such as
3917 and
3918 are not the only way of obtaining output from an oval. For example,
crossed
ovals can interact directly, the logic cable of one oval serving as an input
to a
neighboring oval. Given that, when coupled with locks, input can be used to
control
which side of an oval moves, this is analogous to the functioning of an MLL or
MFL
balance. And, since Turing-complete systems were shown to be possible using
only
locks and balances in MILL, it follows that MCL can also implement Turing-
complete
systems.
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Moving Mass
[0220] One advantage to some MCL embodiments is reduced moving mass as
compared to some embodiments of MLL or MFL. Because cables are not required to
be rigid, they can have a smaller cross section and correspondingly lower mass
than
MILL links of equivalent length. A conventional example of this principle is
to
compare the mass of a cable with the mass of a beam-like structure. In
general, a
structure which only has to withstand tensile forces can be made less massive
than a
structure which must also withstand, e.g., compressive or bending forces. At
the
molecular scale, examples of strong but flexible structures which might be
used as
cable include carbyne (linear acetylenic carbon), polyacenes, polyethylene,
and
polyiceanes, although many other structures could be used.
[0221] A potential disadvantage to the use of cables is that the
flexibility can
allow vibrational modes that would not exist in a stiffer structure. Further,
these
vibrational modes may change as the length of a given section of cable
changes. For
example, if the distance between two pulleys changes, changing the length of
the
cable segment between them, the allowed vibrational modes may change, just
like
fretting a guitar string at different positions. This also results in entropic
changes to
the system. Either of these effects can lead to energy dissipation.
[0222] However, these vibrational and entropic issues can be addressed
while
still keeping the moving mass of the mechanisms low. This can be accomplished
by
constraining cables in such as manner as to prevent them from being free to
vibrate.
One embodiment of this concept would be to have cables lie in trenches in the
anchor
block. Such trenches, if thought of as having a rectangular cross section
(though this
need not be the case) would constrain the cable on three sides, with the
fourth side
being open to facilitate routing the cable out of the trench to interact with
pulleys. It is
also possible to constrain a cable on all sides, such as the way a Bowden
wraps its
inner cable in a sheath or housing. If this sheath is relatively rigid, and
the internal
space of the sheath appropriately sized as compared to the cable, essentially
no
vibration will be permitted within the sheath. A molecular example of this
would be a
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polyyne cable in a (9,0) SWNT (single-walled nanotube), but obviously many
structures could be used, preferably those which are rigid, closely fit the
cable and the
sheath, and which allow the cable to slide freely in the sheath (but not to
vibrate
substantially).
[0223] While short segments of cable may be exposed between trenches,
sheaths, or other types of housings, and where the cable contacts a pulley,
these
segments will be relatively short compared to overall cable length,
marginalizing the
energy loss from cable vibrations and entropic changes. Since the cable
housings
need not move with the cable, moving mass is kept low, potentially allowing
systems
with higher switching frequencies as compared to systems that require more
massive
rigid links instead of flexible cables
[0224] Also, a cable system could be implemented with fluids inside
housings. A solid plug at one end of the housing would push on the fluid,
which in
turn pushes on another plug at the opposite end of the housing. Like a closed
loop of
cable, by actuating at either end, this can effectively provide a "cable.'
(though made
of a fluid, which includes a gas) which can be pushed or pulled on by
actuating the
appropriate end. Such designs could also be used to implement balances and
locks,
moving the parts hydraulically rather than via a solid link or cable. While a
hydraulic
system would not traditionally be called a cable, it is considered to be a
cable system
herein as the logical and mechanical functioning is almost identical to that
of a solid
cable.
Type 1-4 Systems
[0225] As mentioned previously, due to the use of ratchets and pawls,
detents,
springs, or other mechanisms which store and then release potential energy in
a
manner not directly tied to the systems' computational degrees of freedom, all
pre-
existing Turing-complete systems for mechanical computing can be categorized
as
Type 1. Due to possible energy savings, all other things being equal, Type 2-4
systems would be preferred over Type 1 systems, with Type 4 systems being most
preferred. MILL, MTL, and MCL are all capable of creating Type 2-4 systems. In
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fact, most of the embodiments described herein would result in Type 4 systems,
while
adding, e.g., springs to some mechanisms (such as between the gradual lock
depicted
in FIG 9 and other mechanisms, to permit backlash) could result in a Type 2
system,
and some designs which, e.g., could leave locks in the (0,0) state with some
non-
trivial frequency could result in a Type 3 system (although this can be
avoided with
proper design; locks being in the (0,0) state need not mean that parts are
free to move,
as can be seen in the mechanism described herein).
[0226] It may not be immediately apparent that MFL can be used to create
Type 3-4 systems, as flexures may seem to store potential energy by their very
nature.
Indeed, some flexure-based designs, if using the flexures to store potential
energy and
then release it to some effect on the system, would be categorized as Type 1
or Type
2. However, in MFL, flexures need not be used for potential energy storage.
Rather,
their function can be solely to provide kinematic restraint, just as the
analogous
structure in MILL, the rotary joint, does. As such, the force needed to bend a
flexure
can be arbitrarily small as long as the flexure still provides the necessary
rigidity with
respect to the relevant degrees of freedom. This leads to the conclusion that
the
potential energy storage of flexures can be trivial, just like the potential
energy stored
in the stretching of MCL cables, or the stretching, bending, or compression of
MLL
links.
[0227] Further, even if the force required to bend a flexure were
substantial,
since flexures are not being using to actuate movement in a Type 3-4 system,
systems
can be designed where the net potential energy of the flexures is essentially
0. For
example, a pair of flexures connected to a link could be pre-stressed in
opposite
directions. The movement of the link in one direction would increase the
potential
energy of one of the flexures, while decreasing the potential energy of the
other
flexure, resulting in no net change (and therefore no net increase in the
force required
to move the link) over some allowed range of motion.
Summary
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[0228] Three exemplary paradigms for mechanical computing, MLL, MFL,
and MCL, have been described. Each of these paradigms are capable of providing
both the combinatorial logic and the sequential logic required to create a
Turing-
complete computational system. Each design paradigm also allows for reversible
computing, and simulations of a molecular-scale mechanism indicate that
properly
designed embodiments of MLL can compute with levels of energy dissipation
under
the Landauer Limit. There is no reason to think that MFL and MCL cannot
provide
similar efficiency.
[0229] Four classes of computing systems have been described, designated
Types 1-4. Type 1 systems have the lowest ultimate potential for energy
efficiency,
and are the only type of computational system previously enabled. MLL, MFL,
and
MCL share physical and logical parallels, in some sense being three
embodiments of
the same concepts. Each is capable not only of Turing-complete computing, but
also
of providing Type 2, Type 3, and Type 4 systems (alone, or in combination with
each
other), allowing for decreased energy dissipation. Each also has a very low
number
of types of required primitives, with MILL and MFL only requiring two basic
parts,
and MCL requiring three, reducing the complexity of system design,
manufacture,
and assembly. Further, not only are a very small number of basic parts
required, but
none of the basic parts include gears, ratchets and pawls, detents, or many
other
common mechanisms that are widely used in other systems, but which are likely
to
dissipate excessive energy through friction or vibration. Finally, each are
capable are
creating computational systems which use dry switching; no power need be
wasted by
applying force to a basic part or mechanism, only to find that it will not
move due to
its logical state.
[0230] Given the teachings herein, including multiple embodiments that
demonstrate the overarching design principles of being able to provide Turing-
complete computing, reversible if desired, via Type 2-4 systems, with very few
types
of primitives, which lend themselves to the creation of energy-efficient
mechanisms,
both due to the nature of the mechanisms themselves, and because such
mechanisms
and systems can be designed to use dry switching, it will be apparent that
variations
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using different mechanisms or primitives could be created, and it is the high-
level
design paradigms, not the specific embodiments, which should be seen as the
boundaries of the invention.
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