ES2963835T3 - Mechanical computing systems - Google Patents

Abstract

Systems and methods for creating mechanical computing mechanisms and Turing complete systems that include combinatorial logic and sequential logic and are energy efficient. Embodiments of the invention include mechanical computing mechanisms and computing systems that have lower power dissipation, fewer basic parts, and other advantages over prior systems. Multiple embodiments are disclosed including mechanical link logic, mechanical bending logic, and mechanical cable logic, along with design paradigms (including mechanical designs, principles, and a novel classification system that classifies systems as Types 1 to 4) that They teach how to apply general principles to other implementations. (Automatic translation with Google Translate, without legal value)

Description

DESCRIPTION

Mechanical computing systems

The present invention relates to the field of computing technology or computing systems related 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 constructed from mechanical components rather than electronic components.

Methods for mechanical computation are known in the prior art. (Svoboda, “Computing Mechanisms and Linkage”, New York, Den 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 first example of a Turing complete design is probably the motor Babbage's analytical system, which was described in 1837 (although never built), the vast majority of previous proposals for mechanical computing are not Turing complete systems. Rather, they are special-purpose devices not intended to address general-purpose computing at all, or they are partial systems or mechanisms, lacking crucial capabilities, that 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 such as Lego. Note that mechanical logic gates alone, even universal ones, do not by themselves enable Turing-complete computation; Some memory media is also required. Turing complete computation requires a means for combinatorial logic as well as a means for sequential logic.

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; ” , ChemPhysChem, 12, 2009; Reversible Logic Gates with Optically Controlled Bacteriorhodopsin Protein-Coated Microresonators” , Advances in Optical Technologies, 2012).

Document US-2011/278365 A1 describes a method of manufacturing a computer without assembly. To avoid the typical assembly step, a plurality of physical components are produced by additive manufacturing in a three-dimensional pattern such that, at the time said manufacturing is completed, said components are already assembled in said pattern as all or part of said machine. The machine is adapted to perform at least one non-trivial calculation that is carried out, at least in part, by the movement of at least one of said components.

US-7,414,437 B1 describes a nanomechanical computer and, more precisely, an electromechanical nanoscale switching element that can be easily constructed using standard IC techniques. The electrical switching element comprises at least a first nanoscale pillar extending upward from a substrate between the opposing first electrodes to flex between the first electrodes, and at least a second nanoscale pillar extending upward from the substrate between the second opposite electrodes. The second nanoscale pillar is coupled to the first nanoscale pillar to flex with the first nanoscale pillar alternately toward and away from the second alternative electrodes influenced by the bending of the first nanoscale pillar, whereby the bending of the first nanoscale pillar promotes a charge transfer between the opposing second electrodes through the second nanoscale pillar.

The paper Mahboob et al, “Interconnect-free parallel logic circuits in a single mechanical resonator”, NATURE COMMUNICATIONS, (20110215), vol. 2, doi:10.1038/ncomms1201, page 198 describes an electromechanical resonator that employs wavelength division multiplexing with piezoelectric activation and detection.

Sharma et al., “Mechanical logic Devices and Circuits”, (20090000), URL: http://www.nacomm09.ammindia.org/NaCoMM-2009/nacomm09_final_pap/R/RCA18.pdf, (20160218) describes devices and mechanical logic circuits.

While previous designs for mechanical computing vary greatly, previous proposals capable of performing Turing-complete computation (as opposed to limited-purpose devices) tend to respond to a substantial number of basic (or “primitives”) parts. including various types of linear motion gears, shafts and bearings, springs (or other means of energy storage, e.g., some designs use rubber bands), detents, pawls and pawls, or other mechanisms that have the potential to dissipate energy, while increasing the complexity of the device. Note that such designs require these various primitives to function correctly; They are not optional.

That the use of many types of basic parts in a mechanical system can complicate design, manufacturing and assembly, as well as potentially reduce reliability, is obvious. Reducing the complexity of mechanisms is a common goal of invention.

Note also that many of the mechanisms used in previous proposals for mechanical computing generate substantial friction. Eliminating such mechanisms would provide benefits beyond reducing device complexity, including reducing power consumption. However, based on the prevalence of friction-generating mechanisms in mechanical computing systems, it is difficult to solve this problem.

Perhaps less obvious than friction are other modes of energy dissipation, including vibrations, which can e.g. e.g., create heat or generate acoustic radiation. For example, ratchets and pawls, detents, or other mechanisms that involve the relatively uncontrolled impact of one part of a mechanism on another can lead to energy-dissipating vibrations, so elimination of these types of mechanisms would also be beneficial.

Waste heat is a well-known problem for computational systems, electronic or mechanical, which dissipate much more energy per bit operation than is required in theory. Theoretically, calculations 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 (Bert, Arkelyan et al., “Experimental verification of Landauer's principle linking information and thermodynamics”, Nature, 7388, Nature Publishing Group, 2012).

Note that the Landauer limit only applies to irreversible operations. Reversible operations can, in theory, dissipate zero energy. Although conventional computers are generally not built on 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 Theortical Physics, 12, 1973; “Logical reversibility of computation”, IBM Journal of Research and Development, 6, 1973; Languages and Programming, Seventh Colloquium, Noordwijkerhut, Netherlands, Springer Verlag, 1980, “Conservative Computing”, International Journal of Theoretical Physics, 3/4, 1982; , Scientific American, 1985; Feynman, “Quantum Mechanical Computers”, Foundations of Physics, 6, 1986). For an overview of reversible computing from a software perspective, see (Perumalla, “Introduction to Reversible Computing”, CRC Press, 2014).

Whether reversible or irreversible, new mechanical computing system designs that have the potential to reduce device complexity (along with associated design, manufacturing and assembly costs) and use less energy per bit operation than conventional designs would be quite useful. existing. Not being subject to the Landauer limit, reversible designs ultimately have the potential to use the least amount of energy. However, existing computing systems use energy so far above the Landauer limit that even irreversible designs could greatly improve the state of the art.

Based on the above, it is an objective to provide a binary mechanical computing mechanism that reduces the disadvantages of the prior art, described above.

The objective is solved by a binary mechanical computing mechanism according to claim 1. The dependent claims discuss preferred embodiments of the invention.

According to the invention, a binary mechanical computing mechanism is provided with an anchor block and an assembly, configured to perform a combinatorial logic operation and/or a sequential logic operation, which assembly only requires mechanical link logic primitives, logic primitives mechanical bending and/or mechanical wiring logic primitives. One or more such primitives define one or more inputs for data, encoded by the physical position of the inputs,

one or more of said primitives define one or more outputs for data, encoded by the physical position of the outputs, where

The primitives are connected together to selectively allow or prevent the movement of other primitives with respect to the anchor block based on the physical position of the one or more inputs, so that one or more outputs are the result of the logical operation on the one or more entries.

The mechanical computing mechanisms according to the invention have lower power dissipation, a smaller number of basic parts and other advantages over previous systems. Multiple embodiments are described including mechanical link logic, mechanical bending logic, and mechanical wiring logic, along with design paradigms (including mechanical designs, principles, and a novel classification system that categorizes systems as types 1 to 4) that They teach how to apply general principles to other implementations.

For a more complete understanding of the present invention, reference is now made to the following descriptions taken together with the accompanying drawings, in which:

Figure 1 represents a side view of a molecular rotary joint.

Figure 2 represents a side view of a four-bar linkage.

Figure 3 represents a top view of a mechanism that can serve as a base for a NAND or AND gate.

Figure 4 represents a top view of a mechanism that can serve as the basis for a NOR, NAND, AND, or OR gate.

Figure 5 represents a top view of an XOR gate.

Figure 6 represents a top view of a Fredkin door.

Figure 7 represents a top view of a coplanar lock in the (0,0) state.

Figure 8 represents a top view of a coplanar lock in state (1,0).

Figure 9 represents a top view of an alternative embodiment of a coplanar lock in the (0,0) state.

Figure 10 represents a top view of an alternative embodiment of a coplanar lock in the (1,0) state. Figure 11 represents a 3/4 view of a non-coplanar lock in the (0,0) state.

Figure 12 represents a top view of a non-coplanar lock in the (0,0) state.

Figure 13 represents a 3/4 view of a non-coplanar lock in state (1,0).

Figure 14 represents a top view of a non-coplanar lock in state (1,0).

Figure 15 represents a 3/4 view of a non-coplanar lock in the (0,1) state.

Figure 16 represents a top view of a non-coplanar lock in the (0,1) state.

Figure 17 represents a top view of a scale with an input of 0.

Figure 18 represents a top view of a scale with an input of 1 with an anchor at the top.

Figure 19 represents a top view of a scale with an input of 1 with an anchor at the bottom.

Figure 20 represents a top view of a double binary scale with inputs (1,0).

Figure 21 represents a top view of a double binary scale with inputs (1,1).

Figure 22 represents a top view of a switching door.

Figure 23 represents a top view of a NAND gate based on locks and scales.

Figure 24 represents a top view of a Fredkin door based on locks and scales.

Figure 25 depicts a top view of a shift register cell in its blank state. Figure 26 depicts a top view of a shift register cell after input has been provided but before a clock signal is set high.

Figure 27 depicts a top view of a shift register cell after input has been provided and a clock signal has been set high.

Figure 28a represents a top view of the left half of a two-cell shift register.

Figure 28b represents a top view of the right half of a two-cell shift register.

Figure 29 represents a top view of a cancellation group.

Figure 30 represents a top view of a flex-based lock.

Figure 31 represents a top view of an MCL pulley and associated mechanisms.

Figure 32 represents a side view of an MCL pulley and associated mechanisms.

Figure 33a-Figure 33c represent top views of various states of one embodiment of an MCL lock.

Figure 34 represents a 3/4 view of a handle that can be used to create a lock.

Figure 35 represents a 3/4 view of two handles that form a lock in the state (0,0).

Figure 36 represents a 3/4 view of a lock in the (0,1) state.

Figure 37 represents a 3/4 view of a lock in state (1,0).

Figure 38 represents a top view of an MCL oval.

Figure 39 represents a top view of an MCL balance in the (0,0) state.

Figure 40 represents a top view of an MCL balance in the (0,1) state.

Figure 41 represents a top view of an MCL balance in state (1.0).

Figure 42 represents a top view of an MCL balance in the state (1.0) after actuation. Definitions

The following definitions are used herein:

“Anchor block” means one or more rigid structures to which basic parts or higher-level assemblies can be attached, and which can also serve as heat sinks. Note that even when written in the singular, there may be more than one anchor block, as determined by design needs. The shape of an anchor block can be arbitrary (“block” should not be understood to mean that the structure is necessarily rectangular, or any simple shape). An anchor block may be manufactured from any suitable material, not limited to, but including any of the materials suggested herein from which basic parts could be manufactured. An anchor block is assumed to be present as needed, whether explicitly stated or not.

“Anchored” means fixed to an anchor block, or rendered immobile with respect to other relevant basic parts or mechanisms. Pinning can be permanent or conditional (e.g., depending on data inputs or clock signals), and a conditionally pinned part can be named according to its relevant conditional state (i.e., whether the part is not pinned on a given situation can be called unanchored, and vice versa).

“Atomically precise” means where the identity and position of each atom in a structure is specified by design. Structures, such as naturally occurring or mass-produced crystals or quasicrystals, that have surface irregularities, impurities, holes, dislocations, or other imperfections, are not atomically precise. Atomically precise may include, but does not necessarily include, knowledge of isotopic composition.

A “scale” is a structure that transmits motion through one side or path of a mechanism versus another. Scales can be used, e.g. e.g., to perform calculations and route data. A scale can have any number of inputs and outputs, some of which can be anchored, or conditionally anchored (such as when connected to a lock). The word “scale” and forms thereof can also be used in its traditional sense (e.g., equal masses or forces “balance” each other) as the context dictates.

A “basic part” is a fundamental building block, or primitive, of a mechanism or computational system.

For example, the basic parts of MI,L are links and rotary joints, the basic parts of MFL are links and bends, and the basic parts of MCL are cables, pulleys and handles. “Basic part” is synonymous with “primitive,” and the distinction between a basic part and a mechanism is that basic parts, 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 might require a shaft as a separate part), they are not obviously logically divisible into smaller parts.

A “cable” is a flexible structure used to transmit tensile forces, e.g. e.g., directly or through pulleys.

“Coaxial” refers to rotating joints that share the same axis of rotation. The term can also be applied to the analogous concept in coplanar mechanisms that have multiple joints that share common arcs of motion.

“Computing system” and forms thereof including “computing system” means a system for carrying out general purpose calculations. Such systems are Turing complete. Devices only capable of solving a single problem 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 calculations and therefore , are not “computing systems” The power supplies, motors, clock signal generators, or other auxiliary components of Turing-complete computing media are not part of a computing system. Different types of computing systems can be interconnected. 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 computing system if the components themselves MLLs provide Turing-complete computational means.

“Coplanar” refers to a mechanism that moves in one or more parallel planes. The term is used to differentiate essentially planar (but potentially multilayer) implementations of mechanisms from those that use motion in non-parallel planes. The distinction is largely a matter of convenience for naming and display, since the mechanisms described herein can be constructed in a coplanar or non-coplanar manner.

“Data link” means a link that helps transfer data from one place to another. A data link may simply be called a “link” when the context makes the meaning clear.

“Dry switching,” as applied to the mechanical computing components described herein, means that no force is applied to mechanisms that are not free to move in some manner.

A “flex” is a type of bearing that allows movement through the bending of a material, rather than sliding or rolling.

“Fork” means a branch in a line that allows one data link to be coupled to more than one other data link. A fork can e.g. e.g., allow copying of an input/output on multiple links or lines.

“Input” means the data, for example encoded by physical position, supplied to a mechanism, e.g. e.g., in order to store the data in memory, transmit the data to another location, perform combinatorial logic on the data, or drive the mechanism (e.g., via a clock signal). For a variety of reasons, including the fact that the input to one mechanism can be the output of another, why some mechanisms use the same data as inputs and outputs (e.g., a circular shift register or other mechanisms with a feedback loop), and because some embodiments allow reversibility, there may be little distinction between “inputs” and “outputs,” with the use of one term or the other being more for didactic purposes. Therefore, regardless of which term is used, both are assumed to be used, if applicable, in a given context.

“Line” means a sequence of connected data links. Also called “data line”

“Link” means a rigid structure or body connected to one or more rotating joints.

A “lock” is a structure with a plurality of inputs where one or more of the inputs being set to some predefined range of values results in the other inputs being locked. For example, in a two-input lock, when one of the inputs is set to a non-zero value, the other input is locked until the non-zero input returns to zero. In a two-input binary lock, the non-zero value set would typically be 1, but the locking mechanism may engage well before the input actually reaches 1 (e.g., an input of 0.1 in a input may be enough to block the other input).

“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 that provide combinatorial logic (e.g. ., reversible implementations of traditionally irreversible gates or special-purpose logic gates).

“MCL” stands for Mechanical Cable Logic, a paradigm for creating computer systems and mechanisms using cables, handles, and pulleys.

A “mechanism” is a combination of basic parts that form a set of a level of complexity between that of a basic part and a computational system. For example, in MI,L, lines, locks, scales, logic gates, and shift registers are all components, as are any subsets that include more than one basic part. Because they are basic parts, links and rotating joints, or any other basic parts, are not mechanisms.

“MFL” stands for Mechanical Flexure Logic, a paradigm for creating computer systems and mechanisms using links and flexures.

“MI,L” stands for Mechanical Linkage Logic, a paradigm for creating computer systems and mechanisms using rotating links and joints. Please note that, as the first and most widely described embodiment, details are provided for MLL that are not necessarily repeated for MFL, MCL or other embodiments. For example, synchronization is broadly described in the context of MLL, but not in other embodiments. Due to the analogous logical and mechanical nature of the various embodiments presented, and taking into account the teachings herein, it will be apparent how to apply the information presented for one embodiment to other embodiments.

“Non-coaxial” refers to two or more rotating joints that do not share the same axis of rotation, or the analogous concept in coplanar mechanisms.

“Output” means the data, for example encoded by physical position, provided by a mechanism. See “Input” for additional details and comments on the interchangeability of the two terms.

A “pulley” is a mechanism that facilitates the routing and/or transmission of forces through one or more cables. Traditionally, the pulleys rotate as the cable moves, but this is not necessary; p. For example, a cable could slide across the surface of a pulley if the energy dissipation incurred was low enough. Pulleys can be anchored or not anchored. Unanchored pulleys can move freely as dictated by their attached cables, or their movements may be restricted by a track, groove, or other guiding means.

“Rotating joint” means one or more connections between rigid bodies that allow rotational movement about an axis. Rotating joints can be anchored or unanchored.

“Support link” means a link that provides physical support or kinematic restraint to other links.

“Turing complete” has its standard meaning as used in the field of computer science, with the proviso that, since real-world systems have limited memory, time, and other parameters, it is recognized that such practical limitations exist and, Therefore, the term “Turing complete”, when applied to a real system, can be considered to include such limitations (resulting in what can be more accurately called a “bounded linear automaton”).

Introduction

This report shows, first of all, that a mechanical computing system can be designed only from two basic parts: links and rotating joints (plus an anchor block to which these basic parts can be fixed; this will be assumed later and is not necessarily mentioned every time), using a design paradigm called Mechanical Linkage Logic (“MLL”). Subsequently, the MI,L paradigms are generalized to show other ways in which simple and efficient mechanical computing systems can be designed, such as Mechanical Bending Logic (“MFL”) and Mechanical Wiring Logic (“MCL”) (either of which could also be used in combination). Part of this generalization also includes the description of a new classification system based on ways in which mechanical computing systems can dissipate energy.

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 operating at useful computational speeds. Such computational systems can also be designed to operate reversibly. These and other factors offer several benefits over and above those of previously proposed computing systems.

Embodiments of the invention provide all the mechanisms necessary to create Turing complete computing systems. For example, using MLL, this includes lines, logic gates, locks and scales, and more complex mechanisms such as shift registers, each of which does not require basic parts other than rotating links and joints. Other embodiments (e.g., MFL and MCL) provide analogous basic parts and mechanisms to also enable the creation of Turing-complete computing systems.

Energy Efficient Mechanical Computing

As discussed herein, mechanical computing systems can dissipate energy in several ways, including friction (which includes drag caused by thermal motion at the atomic level) and vibrations, which may be due not only to the fact that running a mechanical system fast enough to excite its resonance frequencies (something that can be avoided by controlling the clock speed), but also to impacts between parts or relatively unconstrained releases of energy. Examples of such part impacts and relatively uncontrolled energy releases include the snap-in movements of ratchet and trigger mechanisms and detents.

With these issues in mind, four categories are defined for mechanical computing devices: Type 1: Devices that store potential energy (e.g., in a spring) and then release this energy in an unconstrained manner through computational degrees of freedom. . Devices that use ratchets and triggers, or detents, are examples of a type 1 device, since the release of stored energy by the ratchet and trigger or detent is assumed not to be tied to computational degrees of freedom. On said device, if e.g. For example, if a ratchet and trigger were present, while the snapping movement of the ratchet could occur with a periodicity controlled by a clock system, the energy release of that snapping movement would not be linked to the frequency. of clock. Rather, the rate of energy release would be a function of e.g. e.g., the force applied to, and the mass of, the ratchet, regardless of the overall computational speed of the system. The resulting collision of the trigger with the pawl could generate vibrations that waste energy.

Type 2: Devices that store potential energy and then release this energy in a manner controlled by 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 drives the line back and forth, the spring would compress and decompress. This compression and decompression would occur gradually, at the frequency imposed by a system clock. The spring would not be allowed to snap an unconstrained part into place at a rate that, from the perspective of the system clock, is arbitrary. Rather, the motion of the spring and the attached parts are governed by computational degrees of freedom. Note that also in the above scenario, the spring is part of a continuous linkage and therefore no collision of parts occurs as when a ratchet is impacted by its trigger. This can also help reduce power dissipation. And, even if collisions of parts occur (e.g., see descriptions of handles in MCL systems), since the speed at which such contacts occur can be coupled to the computational degrees of freedom, it is possible choosing speeds that do not dissipate unacceptable amounts of power (and, in fact, by causing such impacts with the system clock, which preferably uses a sinusoidal type signal, even a relatively fast switching speed can result in very low part speeds at the moment of impact).

Type 3: Devices that store no more than trivial amounts of potential energy, but have parts with unconstrained non-trivial 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 position (0,0), the connected links are free to move essentially randomly due to thermal noise, system vibrations or other causes. Among other problems, such unrestricted movement can result in having to expend energy to periodically adjust mechanisms to a known state, to ensure reliable operation. (Please note that such situations can be avoided with properly designed systems, and this is presented as an example only.)

Type 4: Devices that store no 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 coupled, directly or indirectly, to data inputs and/or the system clock. Components are not allowed to “float” freely, as a link connected only to a lock would in the blank state. Regarding the definition of “trivial” unconstrained degrees of freedom, this refers to those that occur in a sufficiently small portion of the overall system (e.g., a particular type of mechanism has this problem, but the mechanism is rare in the overall system), or to those that occur infrequently, which do not materially affect overall power 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 reboot process. Such processes may only be needed very infrequently compared to standard calculation operations and would therefore contribute very little to a system energy dissipation. Regarding the definition of “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 technically store potential energy. Such unavoidable potential energy storage is considered trivial. The goal of type 3 and type 4 systems is to avoid systems that intentionally store potential energy for later release, such as in a spring-loaded system, where those springs and their potential energy are required for the system to function properly.

Note that lack of substantial deformation is not the only way to achieve a type 3 or type 4 system. Flexures can have substantial deformation, but can be designed to store trivial amounts of total or net potential energy, as explained In the present memory. These categories are generally ordered by their energy efficiency potential, with type 1 devices being the least efficient devices and type 4 devices being the most efficient. That said, the energy efficiency of specific systems depends on implementation details. A type 2 system could be less efficient than a type 3 system. Poor implementation could make any system energy inefficient. Due to the use of pawls and triggers, detents, springs, or other mechanisms that 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 classified as type 1.

Mechanical linkage logic

An MLL system is built from several basic parts or primitives. In the described embodiments, these are rotary joints and links, which together form mechanical linkages. Rotating joints and links are mounted on an anchor block, and can be used to create higher-order mechanisms such as data transmission lines, locks, and scales. Higher order mechanisms, including logic gates (both reversible and irreversible) and shift registers, can be created by combining locks and scales, or implemented more directly using rotating links and joints. This is enough to build a complete computer system.

To demonstrate this, using only rotating links and joints, the design of data lines, logic gates, locks and scales is explained. Subsequently, using some of these mechanisms, the construction of a shift register is described. Shift registers are simple, but when combined with one or more logic gates that provide universal combinatorial logic, they contain all the fundamental elements required for computation. If the basic parts can construct a shift register and the appropriate logic gates, it follows that a complete computer system can be constructed.

Note that most of the described mechanisms are adapted to binary computing systems. As a result, most links will move between two allowed positions. However, there are some exceptions, such as designs where, for example, when one input is 1, the mechanism drives one or more inputs “backward” (uses of words such as “forward,” “backward,” and other directions are teaching conventions only, since it is not necessary to use particular addresses in the actual mechanisms, nor is it necessary for those addresses to be consistent from one mechanism to the next). In other words, given a two-bit input starting at (0,0), an input of 1 could cause the mechanism to end up in a state such as (1, -1) or (1, -0,5) in instead of (1,0). As long as the system is designed to handle such kinematics correctly, this does not have to be a problem. Furthermore, the internal links in the implementation of various mechanisms can move between more than two allowed positions, even if the inputs and outputs remain binary. The term binary is used for illustrative purposes because it is the most common type of computing system used in conventional computers. Obviously, ternary, quaternary or other non-binary computing systems could be constructed using the teachings contained herein.

The mechanisms described herein were simulated or diagrammed, often with Linkage v3 (free from www.linguagesimulator.com), Autodesk Inventor 2015/2016 or, for molecular models, HyperChem, GROMACS or Gaussian. Many of the figures herein represent subsets taken from the context of a complete computer system. As a result, they are not necessarily functional as shown. For example, a given mechanism may not be fully constrained as illustrated because, in a complete system, the mechanism would be attached to other components to satisfy the missing constraints, or it would be attached to some form of actuation (e.g., a clock signal). Realistic data routing has sometimes been omitted in favor of e.g. e.g., straight lines, for greater clarity. Auxiliary support structures, such as anchor blocks, or links that serve only to provide rigidity (“support links”), are generally omitted.

Some diagrams represent parts within the mechanisms that are not basic parts of MLL. The most common example of this is the use of linear sliders in Linkage models. This is a programmatic convenience since some method of driving input is required to run a simulation in Linkage. In a real system, linear sliders would be replaced, e.g. e.g., by connections to appropriate inputs/outputs, such as data lines or clock signals. Note that the kinematic solver used by Linkage v3 does not have the concept of clock cycles, so it cannot drive multiple inputs sequentially. And Linkage and other programs can fail on valid mechanisms simply because the solver cannot correctly calculate the kinematics. Due to these and other reservations, the figures herein should not be taken as complete working mechanisms, but rather as teaching examples which, given the teachings contained herein, can be easily adapted to create working mechanisms and combined to create complete computing systems.

Rotating joints

The friction in a rotating joint can get smaller and smaller as the size of the rotating joint gets smaller and smaller. At the molecular scale, a rotating joint comprising two atoms rotating around a single bond potentially has zero contact area, and several rotating joints rotating around the axis of single chemical bonds have been analyzed and found to have very little contact area. friction. For example, carbon-carbon single bonds, using carbon atoms mounted on diamond supports, are one way to create a rotating joint that provides rotation with very little energy dissipation.

Figure 1 represents a molecular model of a possible implementation of a rotary joint used to hold a rotating member. An upper support structure 101 and a lower support structure 102, which would be connected, e.g. e.g., to an anchor block, in a complete device, they are used to connect a set of upper and lower links, along the same axis of rotation, to a rotating member 103. The upper links include a single link 104 carbon -top carbon, a single 105 carbon-top carbon bond and a 106 top carbon-carbon triple bond. The bottom bonds include a top carbon-carbon single bond 107, a bottom carbon-carbon single bond 108, and a bottom carbon-carbon triple bond 109. The rotary joint is attached to the supporting structures by several oxygen atoms, including atom 110 of upper oxygen and the lower oxygen atom 111. The rotating member 103 as shown is an approximately circular diamond slab, but this is only representative, 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 must rotate, in any way.

Molecular dynamics simulations indicate that, with or without the acetylenic units illustrated by the upper carbon atoms and triple bond 106 and the lower carbon atoms and triple bond 109, this structure allows rotation with remarkably little drag. However, interposing an acetylene unit between the surrounding single bonds further reduces the energy dissipation of such a rotating joint.

Given this example, it will be obvious that various implementations, including other molecular structures, could provide the same type of mechanism. For example, with minor modifications to the model depicted in Figure 1, the oxygen atoms illustrated by oxygen atom 110 and oxygen atom 111 can be replaced by nitrogen or another element with suitable valence, bond strength, and steric properties. Similarly, carbon could be replaced with silicon or other appropriate elements. Or, completely different structures could be used, including carbon nanotubes or other structures, preferably those that can rigidly hold rotating joints on a molecular scale.

Furthermore, said rotating joint need not consist of only a single joint or pair (e.g., upper and lower) of joints. For example, in larger implementations, the rotating joint could be replaced with a V-shaped jewel bearing, a bearing with rolling elements, nested fullerenes (e.g., carbon nanotubes), or any of the many known ways to allow rotation, preferably with low friction. Additionally, multiple coaxial rotating joints can be used to create a stronger joint (e.g., using a structure similar to that of the interdigitated design of a door hinge). And, on a molecular scale, the addition of additional rotary joints on the same axis of rotation could further reduce the rotational barrier if due attention is paid to symmetry. Note that while a rotating joint can be formed using one joint, the strength and rigidity of the device can benefit from a rotating part held on two sides, as depicted in Figure 1, and/or using multiple joints. , such as in the “door hinge” example. With respect to the molecular scale embodiments, for ease of description, reference may be made to the rotary joints rotating around a single joint, although in some cases it would be more accurate to say that multiple joints may be used to form a single axis of rotation. rotation for the general rotating joint.

The magnitude of the rotation barriers, the torque required to overcome them, the length of the lever arms (e.g., links), and the time for the link to rotate through the required rotary joint range (and at how much the interval is) 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 with a radian rotation speed of 1 x 10 E9 radians/s and a temperature of 180 K can be below 1 x 10 E-25 J. The Landauer limit is 1.72 x 10 E-21 J at 180 K. This number is well above the figure of 1 x 10 E-25 J for a rotation expressed in radians of a link around a rotating joint, which even mechanisms that use many rotating joints to perform a single-bit operation could do so under the Landauer limit. Furthermore, the viscous drag of rotating joints and the energy loss of other vibration modes are expected to decrease rapidly as the operating temperature decreases due to phonon freezing.

Links

In their most basic form, links are rigid, rod-like structures, although in some implementations they may have different or substantially more complex shapes. In most of the analysis performed herein, which requires estimates of values such as link mass, resonance frequencies, and heat conduction, it is assumed that a link is composed of a diamond rod approximately 20 nm in length and 0.5-0.7 nm in diameter. However, the links could be larger or smaller, or have a completely different shape (as seen in the non-coplanar lock examples).

One of the smallest ways to implement a link would be to use a simple covalent bond as a link. For example, there are many molecules that have more than one possible configuration, and the transition between configurations ("conformers") could constitute the movement of a link. A specific example is cyclohexane, which has several possible conformations, including two chair conformations, the basic boat conformation and the twisted boat conformation. The change between different conformations can occur through rotation of the bond (although other changes, such as changes in bond angle or torsion, may also be present and used), similar to that of the rotary joint previously described, and gives as results in the movement of one or more of the atoms in the structure.

Such ability of molecular conformation change to spread over relatively long distances and through complex networks is known to exist in biology, where it is called “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 evident that synthetic systems could be designed that work under the same principles as for larger bonds, but using just a single link as a link. Such designs could allow link lengths in the range expressed in angstroms.

Regardless of the exact implementation of rotating links and joints, one of the basic tasks in a computer system is to move data from one location to another. Illustrative systems described use links connected by rotating joints to move data. While many types of linkages would work, including linkages that provide true straight-line motion, 4-bar linkages are frequently used as an illustrative way to precisely restrict link motion. Figure 2 represents a side view of said 4-bar linkage (note that these are sometimes called 3-bar linkages, as the supporting structure may or may not be considered an additional bar), comprising an anchor block 205, the left support link 202, the right support link 207 and the 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 the left anchor 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 the right anchor 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 the rotary joint 201 upper left and the upper end of the right support link 207 is connected to the right side of the data link 204 by the rotary joint 208 upper right. The left anchored rotary joint 203 and the right anchored rotary joint 206 are prevented from moving relative to each other by the anchor block 205. The data link 204 transmits movement from one support link to another support link. The left support link 202 and the right support link 207 are shown offset to the left. The left-inclined support links place the data link 204 in a position to the left of the left anchored rotary joint 203 and the right anchored rotary joint 206. Arbitrarily, this left position can be called "0" or "low", while if the left support link 202 and the right support link 207 were tilted to the right, that position could be called "1" or "high". This provides a basis for a binary data storage and transfer system.

It will be evident, even in the absence of the anchored rotary joint symbol, that the left anchored rotary joint 203 and the right anchored rotary joint 206 are anchored rotary joints because they end in the anchor block 205. In the following figures, it is possible that the block anchoring is not shown explicitly. Instead, the schematic convenience of representing non-fixed rotating joints as a circle at the intersection of multiple links (which are usually represented as straight lines or bars, although some may have more complex shapes) is often adopted, while joints Fixed or anchored rotating bodies are represented as a circle and a triangle with short diagonal lines at their base. In other figures, usually to reduce complexity, some of these conveniences may be changed or removed. The descriptions of the figures and the context will make it evident how these diagrams should be interpreted.

As already described, information can be transmitted along the length of a single data link. However, more complex transmission and routing of data may be useful. A data link can connect to any number of other data links to continue data transmission. Data transmission can continue in a straight line via additional support links (although in reality it is just a longer data link, it may be useful to include additional support links to increase rigidity), or it can change direction in rotating joints, at any angle and in any desired plane. And, a link can connect to multiple other links not only sequentially, but also through hairpin structures, effectively copying data for use in multiple locations. This provides considerable flexibility in data routing.

Data transmission can 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. This means that each data link in the chain is linked to its neighbors. It is possible to make all data links in a chain, which may be of some significant length, share a common motion, a property that can be used to share a single binary value across the entire length of the chain. A set of connected links is called a line.

Scale

MLL could be implemented using basic parts of virtually any desired size. For example, on a macroscopic scale, conventional machining or 3D printing could be used, with, e.g., V-shaped jewel bearings or rolling element bearings for the rotating joints, and conventional beams or rods for the links. . On a smaller scale, e.g. For example, 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. On an even smaller scale, MLL mechanisms could be molecular scale. Due to the higher operating frequencies and reduced power dissipation that tends to be achieved with smaller parts, MLL systems would preferably be implemented at scales as small as feasible (taking into account factors such as performance requirements and the budget). For this reason, while most of the teachings herein are scale independent, the energy dissipation estimates focus on an illustrative embodiment at the molecular scale.

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; Kotttan, Clarke et al. , “Artificial Molecular Rotors”, Chem. Rev., 2005; J Am Chem Soc, 4, 2007; 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; , Weinberg et al., “Rotary Nanotube Bearing Structure and Methods for Manufacturing and Using the Same,” U.S. Patent No. 9150405, 2015).

Molecular motors, although not necessarily required to drive MLL systems, are quite common now that all the books and conferences are devoted to the topic. (Joachim and Rapenne, “Single Molecular Machines and Motors: Proceedings of the 1 st International Symposium on Single Molecular Machines and Motors” Springer, 2013; Calle, Silvi et al., “Molecular Machines and Motors”, Topics in Current Chemistry, Springer , 2014)

Furthermore, molecular scale computing already exists, in various forms (generally not Turing complete). (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; , Sethi et al., “All-Optical Reversible Logic Gates with Optically Controlled Bacteriorhodopsin Protein-Coated Microresonators”, Advances in Optical Technologies, 2012).

In addition to other techniques present in the literature, MLL computational systems and mechanisms could be created at the molecular scale using, e.g. e.g., molecular manufacturing through mechanosynthesis, or the assembly of appropriately functionalized molecules using atomic force microscopy-type equipment. Conventional chemistry or self-assembly (including DNA origami-type techniques) may also be a feasible route to fabricate MLL mechanisms at the molecular scale. Given the very limited number of basic parts required (e.g., links and rotating joints in MLL) for the presented embodiments, the synthesis and assembly of the necessary basic parts and mechanisms are, in many ways, simpler than the complexities of manufacturing a conventional electronic computer or the implementation of previous proposals for mechanical computing.

energy dissipation

As noted, a complete MLL system can be constructed with nothing more than rotating links and joints. Since, particularly at the molecular scale, there is very little energy loss from rotation around a well-designed rotating joint, a complete computational system can be designed that dissipates very little energy. Additional MLL design paradigms (e.g., torque and mass balance to reduce or prevent acoustic radiation) are also discussed herein, and these may help to further reduce power dissipation. In addition to the physical design of the computing system, operating conditions can also affect power dissipation. For example, if an MLL system operates in a vacuum, the acceleration and deceleration of the links occurs smoothly, and the applied forces are small enough that the deformation of the basic parts contributes to the energy dissipation. is insignificant, and energy dissipation can be reduced even further.

The design of the MLL mechanisms and their interaction with the timing system can also influence energy dissipation. For example, MLL systems can be designed in such a way that, by properly utilizing clock phases, no force is applied to mechanisms that are not free to move (e.g., such a system does not attempt to move a locked mechanism without unlocking it). first). This is the MLL version of “dry switching”, a term normally used in the relay field to indicate that switches have no voltage across them when they change state, but here it will be used in the context of MLL. . Note that while it is a novel and important finding of MLL that complete computational systems can be designed with nothing more than rotating links and joints, m Ll systems can incorporate or interact with additional components. For example, it is described herein how cams and cam followers are a way of generating clock signals. However, while cams and cam followers can be designed (as explained herein) to have minimal energy dissipation, such mechanisms are accessory, and not effectively part of MLL. Motors or other ways to power the movement of MLL systems are another example of a function that can be attached to an MLL system, but are not considered part of the MLL, and the same could be said, for example, of input interfaces. /output that act as a bridge, e.g. e.g., in MLL and non-NELL electronic systems or mechanical systems.

Any mechanical system can dissipate a substantial amount of energy if it is run fast enough to excite internal mechanical resonances. To keep power dissipation as low as possible, a proper design can prevent low-frequency vibration modes from coupling to the clock, and the remaining vibration modes can be calculated and avoided by choosing an operating speed slow enough to avoid excite them, as well as a timing waveform that minimizes their excitation. In a molecular-scale mechanical system, such resonance frequencies may be in the gigahertz range, and the limits they impose on the switching speed may therefore be correspondingly high.

The switching speed of an MLL system, such as in electronic computers, is determined by one or more clocks that produce clock signals. If the frequency spectrum of a clock signal has a component of its energy with resonance frequencies equal to or higher than those of the mechanisms to which it is connected, then a larger fraction of the clock energy than necessary could be dissipated.

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 sinusoidal waveform transition between 0 and 1 (potentially with flat areas at 0 and 1 between transitions to allow non-perfect synchronization of mechanisms between different clock phases) allow a clock signal avoid placing greater than necessary stress on the system mechanisms, as the parts accelerate and decelerate more uniformly than if e.g. For example, a square wave will be used.

There are many ways to generate clock signals. One way to generate a gradually changing clock signal is to use a rotating mass whose rotational motion is converted to linear or near-linear motion. This is, conceptually, the equivalent of a flywheel and crank, and such a device can be made with only rotating links and joints. Some embodiments of the MI,L systems can be coupled to other methods of generating clock signals, such as spring and mass systems, or cams and cam followers, which are described herein.

Several possible sources of energy dissipation were analyzed, including stress-induced thermal imbalance and acoustic radiation. These were not the main limiting factors in the frequency of operation, at least for the illustrative systems analyzed (e.g., diamond-based systems, at the molecular scale). Mechanical resonances and inertia are the main limits on the switching speed for these systems.

Although thermal balance turns out not to be a limiting factor for the illustrative systems analyzed, in some situations it could be, and an objective when seeking to minimize energy dissipation could be to operate the mechanisms in isothermal mode. For this reason short thermal equilibrium times may be desirable. To achieve this, the basic parts of the system are preferably tightly coupled to one or more thermal reservoirs. For example, links are generally attached to a rotary joint that is attached to an anchor block, or to rotary joints that are attached to other links, which in turn are attached to an anchor block. While the exact length of the path may vary based on implementation, this tends to keep the path from any link to an anchor block, which can serve as a thermal reservoir, short.

Note that diamond is used as an illustrative anchor block material (and can also be used for basic parts), among other reasons due to its high rigidity (Young's modulus of approximately 1000 Gpa). Diamond also has good heat conduction, which can be greater than 2000 W/mK in natural diamond, and higher in defect-free and isotopically purified diamond (a principle that also applies to other materials). Many other materials could be used, both for the anchor blocks and for the basic parts, although high rigidity would be preferable for several reasons, including raising the frequency of resonance vibrations, and good heat conduction would be preferable if You want rapid thermal equilibrium. Other illustrative materials include Carbyne (Young's modulus of 32,100 GPa), various fullerenes (e.g., carbon nanotubes can have Young's moduli of more than 1000 GPa, thermal conductivity of 3180-3500 W/mK or higher), silicon carbide (Young's modulus 450 GPa) and silicon (Young's modulus 130-185 GPa, thermal conductivity 148 W/mK). Please note that these values are approximate and generally represent values measured at 300 K (room temperature). Values can vary substantially depending on the atomic structure, purity, isotopic composition, size, shape and temperature of a material. For example, although the thermal conductivity of silicon is 148 W/mK at 300 K, it can exceed 3000 W/mK at temperatures of approximately 20 K.

Also, keep in mind that MLL systems do not need to be composed of a single type of material. Each of the various materials presents different advantages and disadvantages, including not only volumetric properties such as stiffness, thermal conductivity and thermal expansion, but, at the molecular scale, the strength of the individual bonds can be important, as can the exact size of various basic parts and their interatomic separation (e.g., so that they mesh correctly with other basic parts, among other concerns). That said, MLL systems can use a variety of different materials.

The estimated thermal equilibrium time of an illustrative molecular scale embodiment using approximately 20 nm long diamond links is ~0.54 ps. Taking this into account, even a few nanoseconds of thermal equilibrium makes the energy dissipated due to thermal imbalance essentially equal to 0. Therefore, the thermal equilibrium time is not the limiting factor in the switching time for such an embodiment.

In theory, a reversible operation can be carried out with energy equal to 0, as long as the 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 hardware efficiency (Landauer limit). To reduce the power dissipation of a program running on a conventional (irreversible) computer, the logical elements of the hardware can be redesigned to dissipate less power during the computational process. This could result in a significant improvement in energy efficiency, since a conventional computer dissipates much more than ln(2) kBT per bit erased. In fact, even when executing instructions that do not clear any bits, a conventional computer dissipates much more than ln(2) kBT per operation. As a consequence, it is possible to reduce the power dissipation of a conventional computer without paying attention to reversibility.

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 calculations to be carried out under the Landauer limit. Consequently, MLL 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, a single Fredkin gate is reversible. However, reversibility can also be implemented at higher levels, such as when a retractable cascade is used to erase a series of previous calculations. Such techniques are well known in the literature, along with appropriate synchronization schemes, such as Bennett synchronization and Landauer synchronization.

Conventional logic gates

Links and rotating joints not only serve as basic parts for moving data from one place to another, but they 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 rotating links and joints, fixed to an anchor block to hold them in place (and which can also serve as a heatsink).

For example, Figure 3 shows a mechanism that can serve as an AND gate and as a NAND gate. The anchor 301 and the linear slide 302 serve as the first entrance to the door, connecting to the rotary joint 306. The anchor 303 and the linear slide 304 serve as the second entrance to the door, connecting to the rotary joint 307. The joints Anchored rotating joints 305 and 309, plus non-anchored rotating joints 306, 307, 308, 310 and 311 are connected through the appropriate links. And the AND output 310 and NAND output 311 provide the use of the gate as an AND gate or a NAND gate. The operation of this door is as follows. If the linear slider 302 pushes on the rotary joint 306 (an input of “1”, while no movement of the linear slider would be an input of 0) and the linear slider 304 pushes on the rotary joint 307, the effect will be to push forward the AND output 310, producing an output of “1”. If either input (or both) is 0, the AND output 310 terminates at the same position it started, producing an output of “0.” This reproduces the expected truth table of an AND gate.

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 direction opposite to the AND output 310, no movement at the NAND output 311 represents an output of “1” and movement to the left represents a “0”. Of course, for use as an AND gate only, the NAND output 311 does not need to be present. And, for use as a NAND gate only, AND output 310 can be ignored. The two are combined for illustrative purposes; they would not necessarily be combined like this in actual use. Since NAND is known to be a universal gate (meaning that all other gates can be created with the appropriate combination of NAND gates), this mechanism alone would be enough to create any combinatorial logic. However, it may be more efficient to build other types of gates directly, rather than through the combination of NAND gates, and to demonstrate other types of gates, including alternative realizations of the NAND gate, additional logic gates are described later.

Figure 4 shows a NOR gate made with only rotating links and joints. Input 1 comprises the linear sliding anchor 401 and is connected through a rotary joint to the inverter 405. Input 2 comprises the linear sliding anchor 403 and the linear slide 404 and is connected through a rotary joint to the inverter 406. As In all of these figures, the linear slides are present as a schematic or programmatic convenience and should be considered as representing some proper connection when these individual mechanisms are combined into a higher-level assembly. Inverters 405 and 406 invert a leftward signal into a rightward signal and vice versa and are connected via rotary joints to the upper right portion of mechanism 407 and the lower right portion of mechanism 408, respectively. Because of the inverters, when either input pushes to the right, the motion is reversed into a counterclockwise motion at the top right of mechanism 407 and the bottom right of mechanism 408. The position of output 409 replicates the predicted 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 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 mechanism 407 and the lower right portion of mechanism 408 therefore show an alternative implementation of an AND gate, with an inverter connected to each input to create an NOR gate instead. Removing the inverters and connecting the inputs directly to the appropriate locations on the top and bottom right portion of the mechanism would result in an AND gate. Furthermore, as shown in Figure 3, this mechanism could 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 is inverted, the NOR gate becomes an OR gate.

Finally, Figure 5 shows an XOR gate implemented using only rotating links and joints. Inlet 1 comprises an anchored rotary joint 501 and a linear slider 502, while inlet 2 comprises an anchored rotary joint 504 and a linear slider 503. Inlet 1 and inlet 2 couple to outlet 505 through a series of links, anchored rotating joints and unanchored rotating joints. The movement, or lack thereof, at output 505 replicates the truth table intended for XOR.

The above shows that any logic gate can be directly implemented using only rotating links and joints. Note that by transferring input data along with the intended output of a logic gate so that no data is lost during the calculation, logic gates that are traditionally considered irreversible can be made reversible. There are also well-known logic gates that are inherently reversible, such as the Toffoli gate and the Fredkin gate, which can also be implemented in many ways using MLL.

Reversible logic gates

Figure 6 shows a Fredkin gate (also called CSWAP gate), a well-known universal reversible gate. The three gate inputs 601, 602 and 603 connect, through a series of links, anchored rotating joints and unanchored rotating joints, to the outputs 604, 605 and 606. It may be interesting to note that this particular implementation of a Fredkin gate is made up of three XOR gates and one AND gate, plus some branched data lines used to replicate data so that it can be used in more than one place within the gate. This demonstrates not only more sophisticated data routing compared to previous gates, but that reversible logic can be built from irreversible logic. A Fredkin gate does not erase any data and therefore does not need to be subject to the Landauer limit.

Given the logic gate examples above, it will be obvious that any type of logic gate needed to implement a complete general-purpose computing system, reversible or irreversible, can be implemented within MLL design paradigms, using only links and joints. rotary. Note that each of the logic gate examples above are coplanar mechanisms. This means that they operate in one or more parallel planes, and movement occurs parallel to the image plane. One of the advantages of coplanar 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 MLL mechanism, and mechanisms that move in more than one plane are also discussed here. Note also that in coplanar mechanisms, hidden or dotted lines are generally not used to show which links are behind which other links. This is because it is largely unimportant. In most cases, a given link could be above or below some other link, and the function of the mechanism would not be affected, subject to considerations such as the links not colliding with each other during movement. You may also want to consider issues such as arranging the links in a way that minimizes the distance to a heat sink, or maximizes the strength or rigidity of the mechanism, but these illustrative designs are intended to be didactic, not to provide a guide. optimal implementation. Optimized implementations could differ depending on the requirements of a particular computing system, including the types of calculations 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

Several ways in which multiple links or lines of data can interact have already been described. For example, they can share data by linking their physical movements to each other around a common rotating joint. And data links or lines can provide input/output for a logic gate (not to mention use within a logic gate). However, additional methods of interaction can be useful to implement a complete computing system.

Another way that multiple links or lines can interact is through a mechanism that causes the links to interfere with each other's movements. That is, the position of a first link can allow or prevent one or more 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, one of the inputs could become 1, but when one of the inputs is 1, the another is locked in place and must therefore remain at 0. In this example, more than one input cannot become 1 at a time, although other designs are possible. This mechanism is called a lock. It is common for a lock to have inputs and outputs, just like a logic gate. For example, a 2-input lock has 2 inputs, and can have 0, 1, or 2 outputs. Each input line to the lock can continue as an output line, or it can end at the lock.

One of the uses of a lock is to create a conditional anchor point. As already explained, a rotary joint can be anchored or unanchored, often depending on whether the rotary joint is secured to an anchor block. However, securing a rotating joint to an anchor block is not the only way to make it immobile. Rather, a rotating joint may be connected to one or more links that, due to the configuration of the one or more links (whether this configuration is permanent or temporary), does not allow movement of the rotating joint. For example, consider a triangle made up of three links. Each link is attached to the other two links by rotating joints at each end. If two of these rotating joints are also connected to an anchor block, even if the third rotating joint is not connected to an anchor block, it is effectively anchored, since the entire triangle is rigid. None of the links of the triangle can move with respect to each other, or with respect to the anchor block. In this simple example, assuming it is not possible to change the link configuration, the third rotary joint is effectively anchored. There are situations where it is useful to have a rotating joint that is sometimes anchored and sometimes not anchored. Locks allow this: The side of the lock that is locked cannot move, so as long as it is locked, it can effectively act as an anchor point. The usefulness of conditional anchor points will be explained later. Another useful aspect of some lock embodiments is that, for example, a binary lock with two inputs can have three states: (0,0), also called "blank", (0,1) and (1,0). The blank state can be useful for saving state and allowing reversible computation, as can be seen herein in the description of how an illustrative shift register can be implemented.

As with all embodiments of MLL, there are several ways to implement locks using only links and rotating joints. Figure 7 and Figure 8 depict a two-input coplanar lock in two different states. Figure 7 shows the position of the lock where both inputs are 0, while Figure 8 shows the position of the lock when one of the inputs is 1. The upper input 701 and the lower input 702 are connected through rotating joints to the upper and lower halves of the lock, respectively. Each half of the lock comprises a 4-bar linkage, comprising links 703, 705 and 712 in the upper half, and links 704, 706 and 713 in the lower half. Additionally, four diagonal links 707, 708, 710 and 711, hold an additional link 709, which connects to the two 4-bar links through unanchored rotary joints. The operation of the mechanism is as follows: When one of the inputs 701 or 702 moves from 0 to 1, the respective 4-bar linkage moves. Movement of the 4-bar linkage, through links 707 and 710 for the upper half, or links 708 and 711 for the lower half, causes rotation of link 709. Link 709, having the same length as the links 703, 704, 712 and 713, and being initially at the same angle, allows any of the inputs to assume a value of 1 when rotating through the same arc that the 4-bar linkage must follow when moved by an input.

However, once an input has moved the upper or lower 4-bar linkage, along with link 709, the other 4-bar linkage (and therefore its associated input/output) is no longer free to move. . The reason is that link 709 is now not parallel, depending on which input was set to 1, to links 703 and 712, or to links 704 and 713. Because of this, the rotation of link 709 will not follow that of the second link of 4 bars, in case it tries to move. Essentially, one of the links (link 705 for the top, if it hasn't moved yet, or link 706 for the bottom, if it hasn't moved yet) will attempt to move through two different arcs at once, causing the mechanism to lock. This is essentially a coplanar version of rotary joints that are not coaxial (described elsewhere herein), but instead of the rotating joint axes changing (which they do, but these axes were never coaxial 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 movement allowed is to set that input back to 0 so that either side (but not both simultaneously) are again free to move to position “1”.

The lock design in Figure 7 has the property that it locks quickly and unlocks slowly. For example, virtually any movement of one input blocks the other input. And, once an input has been set to 1, locking the mechanism, that input must essentially return to 0 before the lock will unlock. It may be desirable to design locks that have more gradual locking properties, and this may have advantages including smoother changes in entropy (resulting in reduced energy dissipation), reduced maximum force on the mechanisms at a given speed of switching, and a reduced time between lock/unlock cycles, as there is less concern that one input must be able to be set to almost exactly 0 before the other input can start moving. The inclusion of springs in the connections to a lock can also aid in the operation of a lock, as the mechanism can then be actuated as desired even in the presence of small positional errors that would otherwise block a locking mechanism. almost instantly when it is 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) that has a properly chosen spring constant. If link 709 is, or incorporates, a very stiff spring, the lock will only allow small positional errors. If link 709 is, or incorporates, a more flexible spring, the lock will allow larger position errors.

Figure 9 and Figure 10 depict a lock where, due to the gradual change in torque as the mechanism goes from unlocked to locked, the locking action is more gradual. Figure 9 shows blocking when inputs 901 and 902 are at 0, while Figure 10 shows the blocking status after input 901 has been set to 1 while input 902 is still at 0. Inputs 901 and 902 are connected to the rest of the mechanism through unanchored rotating joints. Note that setting one input to 1 results in the other input moving back slightly in this layout. The overall system can be designed to allow this, or the rearward movement could be maintained within the mechanism, such as by using springs that absorb such movement rather than transmitting it directly to other links.

Being made of the same basic parts, all MLL mechanisms tend to share similar problems. The concepts of sudden versus gradual entropy changes, limiting maximum forces, and designing mechanisms to allow reduced latency between clock phases can be applied to any MLL mechanism, not just locks.

Non-coplanar mechanisms

Many of the mechanisms herein are of coplanar design. While preference is given to coplanar designs for clarity of presentation, MLL mechanisms do not need to be coplanar. Any m Ll mechanism can be implemented in a way that is not coplanar. For example, Figure 11 represents a lock, constructed with links and rotary joints, that is not coplanar. Rather, as will be explained later, rotating joints allow the links to move perpendicular, rather than parallel, to the face of the anchor block.

In Figure 11 and subsequent views of the same mechanism, link 1101 will be referred to as Link1, link 1102 as Link2, link 1103 as Link3, space 1104 as OpenJoint4, space 1105 as OpenJoint5, space 1106 as OpenJoint6. , to space 1107 as OpenJoint7, to rotary joint 1108 as Joint1, to rotary joint 1109 as Joint2, to rotary joint 1110 as Joint3, to rotary joint 1111 as Joint4, and to anchor block 1112 as Anchor Block. The anchor block provides anchor points for the Joint1 and Joint4 rotary joints, which connect to Link1 and Link2, respectively. Link1 connects to Link2 through Joint2, and Link3 connects to Link2 through Joint3. All joints and Link1, Link2 and Link3 are shown in the unlocked position.

In the unlocked position, which may be referred to as “(0,0)”, the axis of Joint3 is aligned with the axis of Joint1, and the axis of Joint2 is aligned with the axis of Joint4. Therefore, Joint1 and Joint3 can be called coaxial, as can Joint2 and Joint4. If Link1 or Link3 were rotated, one of their rotating joints would move out of its current plane and therefore, depending on which link was rotated, some of the joints would no longer be coaxial with each other (a condition called “non-coaxial”). ). The concepts of coaxial and non-coaxial are important since, in this embodiment, these conditions are what define the locked versus unlocked position. The reason for this is that in the unlocked position, Link1 and Link3 each have an axis around which they can rotate. For Link1, this is the axis defined by Joint1 and Joint3 when they are coaxial. For Link3, this is the axis defined by Joint2 and Joint4 when they are coaxial. When these joint assemblies are not in the coaxial position, the lack of alignment between the two axes prevents rotation, since a rigid object with one degree of freedom cannot rotate simultaneously around two different axes. As a result, when Joint1 and Joint3 are not coaxial, or Joint2 and Joint4 are not coaxial, the lock is locked and the only movement allowed is to return to the unlocked position.

Note that technically, virtually any amount of Link1 or Link3 turning would create a locked condition. However, for explanation purposes, the later figures show approximately 30 degrees of rotation. This is arbitrary, and any amount of twist could be used that allows the system to act reliably (just like any other angle, as opposed to an angle perfectly perpendicular to the face of the anchor block). Analogously to the coplanar lock, if Link2 were replaced by a spring of similar length, the lock's tolerance for positional errors could be increased at its inputs to the extent deemed appropriate. Given this explanation, it will be obvious that if Link1 or Link3 were to rotate an appropriate amount, any link that had not rotated would be prevented from doing so until the rotated link returned to the unlocked position.

To achieve this twist, 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 Link1. These other links can serve as entrances for the lock. Link1 and Link3 each have a pair of connections (OpenJoint5 and OpenJoint7, and OpenJoint4 and OpenJoint6, respectively) so as not to allow four inputs (although that is possible, that is not the intention of this particular design), but rather to allow one entry line continue past the lock if desired. For example, OpenJoint5 can be considered a continuation of OpenJoint7 (or vice versa) and OpenJoint4 can be considered a continuation of OpenJoint6 (or vice versa).

Figure 12 shows a top view of the same mechanism as Figure 11, with only the link 1101 and the anchor block 1112 being visible in this view.

Figure 13 shows the same mechanism as Figure 11, but in a locked position that could be called “(1,0)”. In this state, 1101 has rotated, through the rotary joints 1108 and 1110, making the rotary joints 1109 and 1111 non-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 achieved by other links (not shown) connected to 1105 and/or 1107.

Figure 14 shows a top view of the state of the mechanism in Figure 13. In this top view, it can be seen that 1101 has rotated approximately 30 degrees counterclockwise. 1102 cannot be seen in this view, but it would rotate with 1101 in this case, revealing 1103 below it. Note that the direction of rotation is arbitrary. Both clockwise and counterclockwise would have the same effect of locking the lock. This is also true for 1103.

Figure 15 shows the same mechanism as Figure 13, but in a locked position due to the rotation of 1103 instead of 1102. This position could be called “(0,1)” In this state, 1103 has rotated, through the rotating joints 1109 and 1111, making the rotating joints 1108 and 1110 non-coaxial, thus locking 1101. The rotation of 1103 would be caused by other links (not shown) connected to one or more of the OpenJoints, 1104 and 1106, of 1103.

Figure 16 shows a top view of the state of the mechanism in Figure 15. In this top view it can be seen that 1103 has rotated approximately 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 operation of the lock, and one or both could be used.

Given these examples and the principles of MLL, many other designs (for locks and all other MLL mechanisms) will become obvious. The specific implementations that work most efficiently may depend on the case, and the illustrative embodiments herein are not provided as examples of optimized mechanisms, but rather to demonstrate how all the elements necessary for a generalizable computational system can be created using only rotating links and joints, and that even within the restrictions of only using rotating links and joints, many different logical and mechanical options are available, including virtually any type of logic gates, reversible and irreversible, and mechanisms that operate in large measured in two dimensions (“coplanar”), or three dimensions (non-coplanar), complete with robust data routing, at any angle desired.

Balances

Force and motion can be transmitted from one end of a link to the other end using a rotating joint around which the link rotates. Such a mechanism will be called a “balance”, since the entrance is often 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 design of the mechanism, and the state of the system.

A simple balance is represented in two different states in Figure 17 (showing an input of 0, with the input linear slide 1701 being retracted) and Figure 18 (showing the same mechanism with an input of 1, with the slide being extended). linear input 1701). In these figures, inlet 1701 is connected to link 1702 via rotary joint 1703. Upper rotary joint 1704 and lower rotary joint 1705 are connected via links to upper outlet 1706 and lower outlet 1707, respectively. The upper rotary joint 1704 is anchored in these representations, preventing the upper outlet 1706 from moving, while the lower rotary joint 1705 is not anchored, allowing the lower outlet 1707 to move if the inlet 1701 moves.

Figure 19 represents what would happen if the upper rotary joint 1704 and the lower rotary joint 1705 were reversed (i.e., if the upper rotary joint 1704 was unpinned and the lower rotary joint 1705 was anchored), given an input of 1. The Output motion would occur at the upper outlet 1706 instead of the lower outlet 1707. One of the interesting properties of scales is that they can be designed to preserve the sum of their inputs. In the example above, if the input is 0, the output is 0. If the input is 1, the output is 1. This would also be true for a simple line, but complex scales can be built with multiple inputs that still add up. Departures.

Another advantage of scales is that they can route data differently depending on another input. Another input, for example, can control the status of locks connected to a scale. The locks act as conditional anchors, routing data down one line or another depending on the state of the locks and allowing a scale to function as a switch or “switching gate.” For example, a single scale with conditional anchors could be placed on any of the configurations shown in Figure 17, Figure 18 and Figure 19, as the anchor points can be changed (this concept is demonstrated in subsequent figures).

Figure 20 and Figure 21 illustrate one way multi-input scales can be used to preserve the sum of inputs and to route data. Two states of the same mechanism are represented, which are formed by connecting two 2-input scales together (a “double binary scale”). Inlets 2001 and 2002 are connected to link 2005 by rotating joints. Link 2005 connects to link 2007 through a rotating joint. Link 2007 connects to link 2006 through a rotating joint. Link 2006 connects to outputs 2003 and 2004 through their respective rotating joints. The fixed length of link 2007 causes the sum of the entries to be preserved. Since link 2007 cannot change length, if input 2001 or 2002 moves, a corresponding movement must take place at output 2003 or 2004. Figure 20 shows the state of the mechanism when input 2001 is 1, and input 2002 is 0. Figure 21 shows the state of the mechanism when input 2001 and input 2002 are both 1. Note that the mechanism in these figures (as is often the case due to the complexity of more complete systems and the need for clear illustrations of the basic underlying mechanisms of MLL) does not bind to other mechanisms as it would in a real MLL system. In this particular case, without additional restrictions 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 indicate whether the outputs will be (0,1) or (1,0), or even something similar (0,5,0,5). In a real system, one way to solve this problem is with locks. By conditionally blocking one of the outputs, the other output is forced to move in a predictable manner.

Switching doors

As described above, scales, along with locks, are one way in which a switching door can be implemented. Figure 22 shows a switching door with an upper input 2201, a lower input 2202 and a central input 2203. The middle input is connected, via a scale, to the upper output 2204 and the lower output 2205. The upper and lower inputs control whether the intermediate input is routed to the upper output or the lower output. For example, if top input 2201 is set to 1, then the top lock that top input 2201 connects to is locked. Since that means that the line leading to the upper output 2204 cannot move, when an input of 1 is provided to the middle input 2203, the scale to which the middle input 2203 is connected must move the line leading to the bottom output 2205. The top and bottom inputs would generally never be 1 at the same time, so they could actually be condensed into one input that controls both locks, e.g. e.g., an input of 0 that locks the top lock, and an input of 1 that locks the bottom lock, or vice versa.

Binary double scales attached to locks can also be used as switching doors. Given a binary double scale, one input is permanently locked, while one input is permanently unlocked and connected to one 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 scale. In essence, the clock input is routed through the dual scale to one or the other “input” via the single line that controls the two complementary locks. Note that switching gates (and other MLL mechanisms that have locked states) can be used even when dry switching is desired. In the case of a switching gate like the one in Figure 22, the clock force is applied through a balance connecting two locks. Since the system can be designed so that both locks are never locked simultaneously when 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 can conditionally always move in one direction or another.

Logic gates using locks and scales

An interesting property of locks and scales is that they can be used to create all traditional logic gates (as well as other mechanisms), reversible and irreversible. Before describing one way in which this can be realized, it will facilitate the understanding of the illustrative lock-based logic gate to discuss an alternative method of providing an input to a mechanism (in this case, a lock). It is typical to think of a binary input as a single connection to a line. For example, in the logic gates described above, such as AND, NAND, NOR and XOR, each of these logic gates took two inputs, often represented as two linear actuators, but which in a real MLL system would be e.g. e.g., two connections to data lines. The Fredkin gate takes three inputs, and thus had three locations where data lines could be connected. Each of the inputs to these illustrative logic gates was binary, that is, 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 in that entry, while an entry of 1 was represented by some forward or rightward movement.

However, there are other ways to represent the input. For example, instead of a binary input using a connection that 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, a of connections to an input would always move: Line 0 would move if the input were 0, and line 1 would move if the input were 1. This contrasts with the fact that 0 was previously represented by no movement of an entry. This strategy of using two lines per binary input is useful with locks because it allows any value, 0 or 1, to create a locked state. An input of 0 locks one side of the lock, while an input of 1 locks the other. An advantage of having both 0 and 1 resulting in a locked state on different sides is that this allows one lock to act as two different conditional anchor points. This can be used, for example, to control which side of a scale moves when input is entered onto the scale. The following example shows a mechanism that illustrates how this property of locks can be combined with scales to create logic gates.

Figure 23 represents one way a NAND gate can be constructed using scales and links. The clock input 2301 is connected to the scale 2302, which in turn is connected to the scale 2303, which in turn is connected to the scale 2304. Through a series of locks and lines, the clock input is directed to the scales 2305 and 2306, and finally results in the movement of the upper output 2312 or the lower output 2311. Inputs 2307 to 2310 provide inputs to the gate, with four input lines used to represent two binary inputs, as shown. described above. Specifically, entry 2307 will be indicated as “A0” (meaning it is associated with entry “A”, and will be moved if entry “A” is 0), entry 2308 as “B0”, entry 2309 as “A1” and input 2310 as “B1” 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 branched using simple rod-shaped links, or connected to a single link providing multiple connection points. The representation in Figure 23 was chosen for reasons of clarity, not because it should be exactly how the mechanism is actually implemented (which is generally valid for all mechanisms described herein). The mechanism works as follows: If actuated, inputs 2307 to 2310 move the side of the door they are connected to and lock the door. In other words, if the input (A,B) is (0,1), lines A0 will move, and lines B1 will move. Since A is not 1, lines A1 will not move, and since B is not 0, lines B0 will not move. Obviously, input (0,0), (0,1), (1,0) or (1,1) is allowed. Entries establish a pattern of which doors are locked and which are not. This pattern in turn determines which side of each scale is free to move. The clock input then activates the scales, with the end result being that either the lower output 2311, representing (A NAND B)0, will move, or the upper output 2312, representing (A NAND B)1, will move . The resulting output generates the NAND truth table:

As already mentioned, NAND is a universal gate. Therefore, it follows from this example that a system of locks and scales could be used to design any other desired logic gate, 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-scale-based mechanisms can be used to implement any other logic gate directly, including AND, OR, NOR, XOR, XNOR, NOT, Cn OT , Toffoli and others.

An implementation of a Fredkin gate has already been described. Locks and scales can also be used to build a Fredkin gate. A Fredkin gate has three entrances and three exits. The three inputs will be named A, B and C, and the three outputs will be named X, Y and Z. Input A is always connected to output X. If input A is 0, then input B is connected 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 noted above, Fredkin gates are universal gates , meaning that any logical or arithmetic operation can be computed with just Fredkin gates. This is not to say that a practical MLL computing system should be composed solely of Fredkin gates, as this would not necessarily be the most efficient configuration for many computational tasks. As will be obvious from the teachings herein, many other types of gates can be implemented using MLL. Fredkin doors are used as an illustrative embodiment because they are universal and reversible.

Figure 24 represents a Fredkin door made using locks and scales. Due to the complexity of the mechanism, a simplified notation is used where the anchored rotary joints are not shown explicitly, but are assumed to be at the unconnected ends of appropriate links. The input or clock signal (actuator not shown, as with all inputs to this mechanism) would be attached to rotary joint 2401. The input for input A1, A0, B1, B0, C1 and C0 would be attached to rotary joints 2402, 2403, 2404, 2405, 2406 and 2407, respectively. Inputs B1, B0, C1, and C0 would also connect to rotating joints 2408, 2409, 2410, and 2411, respectively. The signal and clock inputs are connected through a series of links and locks, and for some outputs, scales, to output X12412, output X02413, output Y12414, output Y02415, output Z12416 and output Z02417. Note that outputs X1 and X0 are not shown on the right side next to the other outputs to reduce the complexity of the figure. In reality, they could obviously head to any desired location. Please note that links 2418 and 2419 are part of 4-bar linkages, not scales, which forces these links to remain vertical when moving. The black triangles 2420 and 2421 illustrate rigid linkages (a straight line is not used to avoid a representation with excessive lines crossing each other, and this representation is only schematic, the actual mechanisms could be implemented in many ways).

The blank state is depicted in Figure 24. Conceptually, from this state, inputs A, B, and C are set during one clock phase. During a subsequent clock phase, the clock signal connected to rotating joint 2401 is set to “1”, which causes the various scales within the mechanism to move, resulting in outputs X, Y and Z being set. as appropriate. While a simple approach to building a system would be to use Fredkin gates everywhere, and use three-phase Landauer synchronization, other approaches are feasible. As will be obvious from the various known synchronization schemes, there may be additional clock phases and, when using Bennet synchronization, the number of clock signals will depend on the number of stages you wish to allow in a retractable cascade.

Shift registers

Shift registers can be used as a basis for implementing sequential logic in a computer system. For example, two numbers to be added, subtracted, ANDed, or ORed are stored in two shift registers and synchronized in an arithmetic and logic unit consisting of a handful of gates, with the result sent to the input of a third shift register. displacement 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 synchronized 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; the data (0,1, or b) at the input is shifted in while the data at the end of the array is shifted out. Binary synchronized shift registers can be implemented using only the clocks and rotating joints connected by links (creating locks and scales) described above. Shift registers are simple, but when combined with appropriate combinatorial logic, they contain all the fundamental elements required for a computing system.

A shift register can be constructed by combining locks and balances, and assuming the presence of a clock system, so that each cell (which could be seen as a flip-flop, and which can also be considered 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 depending on an earlier or later clock phase, as appropriate. This allows data to be copied and shifted through the shift register, rather than deterministically setting the contents of the entire shift register simultaneously.

Figure 25, Figure 26 and Figure 27 represent a single cell of a shift register, in three different states. In these figures, input 02501 is connected through a rotary joint to one side of lock 2505. Input 12502 is connected through a rotary joint to one side of lock 2506. Clock signal 2503 (although schematized differently to provide a mechanism that is more complete when independent, in a real system it would be a connection to the clock system) joins the scale 2504. The locks 2505 and 2506 determine which of the outputs 2507 or 2508 are moves when the clock signal becomes 1. The lock containing outputs 2507 and 2508 can be considered as the output lock for the entire cell, while locks 2505 and 2506 are holding area locks. The importance of this concept will become clear when connecting multiple cells in series.

Figure 25 represents the cell in its blank state, before any input has been provided, and while the clock signal is low or at 0. Figure 26 represents the cell after input 2501 has been set to 1, but before the clock signal has moved to high or 1. This results in blocking the lock 2505.

Figure 27 represents the mechanism of the previous state once the clock signal has been moved high. As the clock signal 2503 pushes the scale 2504, because the lock 2505 is locked, only one side of the scale 2504 is free to move. Therefore, the clock signal moving high is transmitted through the lock 2506 and to the output 2508. Note that movements between states such as those illustrated in Figure 25, Figure 26 and Figure 27 do not have place simultaneously but are governed by the clock signals and the data inputs (which can be linked to the 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 perform and well known in electrical implementations, but more complicated in a mechanical implementation.

Figure 28a, comprising the left half, and Figure 28b, comprising the right half, collectively represent 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. following. In Figure 28a, cell 12801, and in Figure 28b, cell 22802, are each equivalent to the mechanism depicted in Figure 25. In Figure 28a, cell 1 2801 has a connection to a clock signal through of link 2803 (represented as a partial link to indicate connection to a clock system not shown), and in Figure 28b, cell 22802 has a connection to a clock signal through link 2806. Links 2804 and 2805 connect cell 12801 and cell 22802.

As in Figure 25, Figure 26 and Figure 27, it is assumed that a multiphase clock signal is present, and links 2803 and 2806, and the data inputs associated with each cell would preferably operate in 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 12801 passes data to cell 22802 may be instructive. The sequence of events is as follows: (1) In clock phase 1, the clock for cell 12801 was already at 0, and the data inputs are set for cell 12801. Either the upper or lower lock of cell 12801 is blocked, depending on which entry was set to 1; (2) In clock phase 2, the clock signal for cell 12801 is set to 1. This results in unlocking the side of the balance present in moving cell 12801, which in turn moves already either link 2804 or link 2805. This locks one of the locks in the holding area of cell 22802, copying the data in cell 12801 to the holding area of cell 22802. Note that the output lock of cell 22802 has not yet been moved; (3) In clock phase 3, the clock signal for cell 22802 is set to 1. This copies the data of the holding area locks to the output lock of cell 2 2802. In detail, one of The locks holding area of cell 22802 was already locked, so when the clock signal for cell 22802 changes from 0 to 1, only the unlocked line could move. When this unlocked line moved, the exit lock of cell 22802 was blocked. The second of the two holding area locks of cell 22802 was also blocked; and (4) the clock signal for cell 1 is set to 0. This removes the data of cell 12801 from cell 22802 unlocking only the hold area lock of cell 2 2802 that was initially locked when the clock cell 12801 was set to 1, as the other lock had just been locked by the clock signal to cell 22802. This cycle is then repeated as new data is entered into cell 1. In step 2 above , it is observed that the exit lock of cell 2 2802 has not yet been moved. This allows these illustrative shift register cells to store previous data, while mechanisms such as some of the logic gates described herein have their state completely determined by 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.

From this description it will be evident that if reversibility is desired at the level of the shift register cell (or other mechanism), all that needs to be done is to execute the clock phases in the opposite order. If a retractable cascade is desired, then a scheme such as Bennett's synchronization can be used, along with the appropriate hardware design (e.g. the ability to store 'garbage' bits so that no information is lost, thereby which allows the calculation to be reversible for as many depth levels as desired). In the current example, the shift register is only 2 cells long, only 2 numbers can be stored. In a real system, such a shift register can be arbitrarily long. Furthermore, while this particular implementation is a serial input/serial output design, it will be obvious from this example that MLL can be used to implement any other type of shift register desired, such as parallel input/parallel output. serial input/parallel output, and others.

Impulse cancellation

It may be useful to perform calculations without altering either the center of mass or the moment of inertia of a group of computational structures, so that the forces that these changes would cause are not coupled to the entire system, thus potentially contributing to energy dissipation. This can be achieved by using sets of structures whose movements cancel changes in center of mass or torque around any axis (a “cancellation group”). Such techniques can be applied to any structure, such as links, locks, logic gates, scales, clocks, and larger aggregate structures. For example, consider a link or line that is used to transmit data from one place to another. This structure can be replaced by four parallel structures, conceptually grouped as two pairs. Each element of a pair moves in the opposite direction, canceling changes in center of mass and linear momentum. However, each pair could still create a torque. Therefore, the direction of motion 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 therefore such cancellation groups can be used to transmit data while reducing the energy coupled to the rest of the structure.

Figure 29 illustrates this concept using groups 2901 and 2902, each of which contains two members, 2903 and 2904, and 2905 and 2906, respectively. Within a group, each member moves in the opposite direction with respect to the other member (although each member is not connected to the others in the diagram, in a real system the movements would be synchronized, e.g., by signal signals). clock). For example, as shown, member 2903 has moved to the right, while member 2904 has moved to the left. The accelerations that occur 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 net torque on the anchor block. The addition of 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 to the torque of group 2901, allows for complete cancellation.

Obviously, many other designs could be used either to cancel the boost, or to reduce the need to do so in the first place (e.g., by reducing mass or reducing radii to centers of rotations). Given this, momentum cancellation is not limited to any particular arrangement. Cancellation groups are also not limited to a specific number of members. Odd numbers could be used, such as where the members of a cancellation group do not have the same masses or momentum. For example, two members could be used to cancel another member that generates twice the boost. And impulse cancellation need not be complete. Furthermore, forces along any axis can be directed in a similar way. For example, in real designs, it may also be necessary to cancel forces that cause torque along the Z axis, which is defined for this example as perpendicular to the plane of the figure. The complexity and increase in mass of a full cancellation may outweigh the benefits, and the appropriate amount of cancellation (if any), and what force components to cancel, if any, will vary from case to case.

Watches

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 computer 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 more clocks that create a plurality of clock signals. These signals could take the form of reciprocating motion transmitted through mechanisms, such as through lines, or the use of rigid frames (which are actually simply links of specialized shape; for example, a rigid frame could be connected to a clock). in a single location and then branch out, potentially in multiple directions or dimensions) to connect to many doors or other mechanisms), supported by support links as needed. The optimal number of mechanisms connected to a single clock or clock signal will be implementation-specific, depending on factors such as the mass being driven, system rigidity, and 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.

Clock signals could be generated in several ways. For example, rotating masses, harmonic oscillators, or cams and cam followers can 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 rotating joints, could be used to drive each clock signal back and forth and required no parts beyond links and rotating joints. A flywheel could be kept in constant motion by some type of power source or motor, which replenishes the energy lost in the dissipative mechanisms of the system. A discussion of exactly how such a power source or motor could be implemented is beyond the limits of the invention. It is obvious from the literature, which contains substantial work on both macroscale motors and molecular scale motors, including biomotors (e.g., ATPases, flagella) and synthetic motors, that there are many ways to implement such motors. and many ways to power such motors, including external chemical, light, direct current, and electrical fields.

Other watch designs introduce parts beyond links and rotating joints, so they are not technically in the definition of m Ll. However, since the use of alternative timing systems connected to an MLL system can be useful, we describe how such alternative clock implementations can be designed for minimal power dissipation. Furthermore, since a single clock can drive many logic elements, even if the clock itself were somewhat dissipative, overall the computation could still be quite efficient.

An alternative timing 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 synchronization frequency would be used, and that the synchronization frequency would be provided by a very simple mechanism. Using such an oscillator, the components would preferably be designed to use sinusoidal-type clock signals (including signals with sinusoidal-type transitions between 0 and 1 with flat areas in between for timing purposes), and would be designed in such a way that they do not generate overtones of significantly higher frequency during operation (such as if a moving part collides with another moving part). Alternatively, a simple oscillator sum could be used, the sum approximating the desired clock signal. Using a sufficient number of oscillators could, in principle, approximate the desired clock signal with the maximum desired precision, at the expense of additional parts. One way to implement a harmonic oscillator is with a spring (including 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. .

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 described later. 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 rotating joints at each end. The link thus forms an axle that can be used as a camshaft. The cam would be attached to the camshaft (or the camshaft could actually be the cam, assuming it has the appropriate cross-sectional shape). A cam follower can be constructed, for example, using a wheel connected to two rotating joints, connected to a lever arm. Rotation of the camshaft would rotate the cam. The cam follower wheel would ride up and down on the cam, causing the lever arm to rise and fall 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 with an eccentric rotor and stator, as well as variations in types of motion. that the cam performs, such as designs where the cam simply rocks back and forth, or moves in a way that is itself under programmatic control, as well as combinations of the above and obvious variations.

While it may not be obvious how smooth curves can be made at the molecular level, since angles and distances are quantified by the nature of chemical bonds, this problem can be overcome. For example, in diamond, buried Lomer dislocations could be used to create smooth curves on the surface of a Lonsdaleite cam (hexagonal diamond). Similarly, gradual changes could be achieved with diamond and other materials, using changes in bonding patterns, the incorporation of elements of varying atomic radii, using tension to slightly displace an atom or atoms, or using naturally curved structures, such as the nanotubes. Using these strategies, a molecular implementation of cams and cam followers (and indeed any part of such a system) could be realized to almost arbitrarily precise tolerances, even at distances below a single atomic diameter.

Using a rotating mass to generate clock signals only requires rotating joints and links, the basic parts of MLL systems. If a cam and a cam follower were used, the rotating joints that connect the lever arm of the cam follower to the wheel, and those that allow the cam to rotate, have already been described again. However, in a cam-based system, there is rotating contact between the cam and the cam follower wheel surfaces, a situation that does not arise when considering the basic MLL parts. While this may seem like a mechanism that creates unwanted sliding friction, this is not necessarily the case. The two surfaces do not have to slide over each other, but rather rotate synchronously. The analysis indicates that, especially in the case of a molecular-scale and atomically precise (or nearly so) implementation, the energy dissipation of such a mechanism would be very low.

In such a molecular scale mechanism, the very slight distortion in the shape of the wheel and the very slight variation in the attractive force (van der Waals) between the surface and the wheel could cause a very slight generation of phonons. Viewed in the frame of reference of the cam follower, the wheel and surface would be static, except for the displacement at a very high frequency of the crystalline structures within them. As a consequence, there should be no generation of low frequency phonons. And the inertia and positional uncertainties caused by thermal noise will prevent the mechanism from being able to reproduce the higher frequency components in the cam signal, even in the absence of a low-pass filter at the output (which could be used if desired. , and could be implemented, e.g., as a simple spring and mass device).

Additionally, various cancellation methods could be used to minimize the high frequency signal component that is encoded on the cam surface. This can 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 a certain distance. By attaching each cam follower wheel to the cam follower, their outputs would be effectively summed or averaged, canceling out 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 cancellation signals could be encoded in each track), resulting in arbitrary precision of the aggregated signal. Another method of reducing high frequency noise would be to rotate the crystalline shaft of the material the cam is made of, and perform a corresponding rotation of the crystalline structure of the wheel that meshes with them. By properly choosing the crystal rotation and width of the cam and cam follower, other high frequency signals can be eliminated due to the change in timing and atomic spacing when the cam contacts the cam follower wheel. Yet another method to reduce the transmission of high frequency signals is to reduce the rigidity of the cam and cam follower coupling to the rest of the system. For example, reducing the spring constant of the cam follower arm, or reducing the stiffness of the joints on which the cam follower mounts, would help filter out high frequency signals.

Considering these examples, it will become 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 makes it possible in particular to minimize such signals. As the cam follower moves up and down 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 cam surface. 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 the power dissipation caused by the coupling of the high-frequency components of the clock signal to the mechanical vibration modes is below the desired levels. Note that the cam follower mechanism described can exert a relatively strong force when the cam is pushing 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 necessary, for example by using two cam followers and two cams (with the coded signals rotated appropriately relative 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.

Illustrative analysis of switching time

The basic constitutive equations of simple Newtonian motion and assumptions about the size and physical strength of the links can be applied to an analysis of switching time, mass, force, and resonance 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 make an estimate of a possible operating speed of an illustrative molecular size system. The links are assumed to be ~20 nm in length and approximately 0.5 nm to 0.7 nm in diameter. The links are supposed to be made of diamond or similar material, and can be braced to increase their rigidity (e.g., a triangularly braced beam, rather than just a straight beam). The positional difference between “0” and “1” is assumed to be ~2 nm. The rotating unions are assumed to be similar to those shown in Figure 1, and the system is assumed to operate at room temperature. These assumptions allow the stiffness of the link and the rotating joint to be calculated. To determine the resonant frequency, the mass must be determined.

The mass of a typical mechanism can vary widely. Even using a given link type, the mass will be quite different depending on whether the mechanism is a 4-bar single link, a lock, a scale, a logic gate, etc., and the exact implementations of those structures. To use round figures, the moving mass of a link may be approximately 8 x 10-23 kg, while the moving mass of a mechanism made of several links could be of the order of 10-21 kg. Using these assumptions, the resonance frequency for an illustrative molecular scale mechanism may be approximately 13 GHz. A square wave clock signal would lead to substantially higher power dissipation than necessary. Therefore, the clock waveform is assumed to be generated as a sine wave, convolved with a Gaussian to reduce unwanted high-frequency components, or optimized using standard linear systems theory to minimize the generation of non-resonances. desired. Additionally, for reasons of restraint, the clock can operate at a frequency well below the calculated 13 GHz resonance frequency. Depending on various assumptions, such as how much power dissipation is acceptable and with how much margin of error, this results in switching times in the range of 1 ns to 10 ns. Obviously, this is just an example. Larger structures would likely operate at slower speeds, while smaller structures, more rigid structures, designs that move shorter distances between “0” and “1”, lower operating temperatures, or relaxation of some of the Assumed conservative design, would result in faster switching times.

MLL Overview

MLL has been shown to be capable of creating mechanisms including lines, logic gates, locks, scales, switching gates and shift registers, using only rotating joints and links. MLL provides any combinatorial logic using various combinations of logic gates that, alone (e.g., NAND or Fredkin gates) or together, are universal. Sequential logic, and therefore memory, can be provided by flip-flops or cells, which can be combined into shift registers.

Considering the availability of combinatorial logic and sequential logic, it will be obvious that a complete computational system can be built using MLL. For example, the Von Neumann architecture, a well-known Turing complete architecture, requires three main components: A control unit, an arithmetic logic unit, and a memory. Using combinatorial and flip-flop logic, a finite state machine can be created that can be used as a control unit. Combinatorial logic can be used to create an arithmetic logical unit. And, flip-flops can be used to create memory. Everything you need for a complete computer system. Of course, such a system need not be based on the Von Neumann architecture; This is simply an example to illustrate the fact that all the necessary components of a complete Turing system can be provided using MLL. Depending on the exact mechanisms used and the synchronization scheme employed, an MI,L-based computational system can be irreversible, reversible, or a combination of the two. The ability to create mechanical computing mechanisms and complete computational systems, using only rotating links and joints, can provide advantages including reduction of friction (and therefore energy consumption and waste heat generation), design simplification and device manufacturing, and device robustness (e.g., operation at more extreme temperatures than permitted by many other known computing systems, since the mechanical logic could operate up to near the melting point of its constituent parts, while that electronic computing suffers from bandgap problems at extreme temperatures).

Mechanical bending logic

Flexures can take the place of rotating joints used in MLL, resulting in Mechanical Bending Logic (“MFL”). With the replacement of rotating joints by bending, all MLL mechanisms have analogous MFL mechanisms. For example, Figure 30 shows the MFL version of the MLL lock depicted in Figure 7. Link ends 3001 and 3002 of links 3003 and 3004, respectively, are a location where input mechanisms could be connected. The anchored link ends 3007 and 3008 of the links 3003 and 3004 act analogously to the anchored rotary joints. Please note that there are no actual rotating joints present in the MFL version of a lock. Rather, the flexures, illustrated by semicircular cutouts 3005 and 3006, provide flexible points between various parts of the structure. These flexures allow force, which may be introduced into link ends 3001 or 3002, to be transmitted through triangular links 3010 or 3011, respectively, and into link ends 3012 or 3013 (which may be considered outputs), respectively. . Link 3009 serves the same purpose as link 709 in the coplanar MLL lock of Figure 7. The entire mechanism of Figure 30 can be made (but need not be) from a single piece of material, where the different links They are monolithic, but logically separable because they are bounded by inflections.

In general, the movement and function of MFL and MLL locks are completely analogous, but changes in the relative angle between links in MFL are facilitated by flexures rather than rotary joints. Although locks are used to demonstrate the analogy between MFL and MLL, it will be evident that the same analogies can be made between any mechanism and therefore, by replacing the rotating joints with flexures, a complete T uring system can be realized using MFL. Of course, bends require suitable materials, which may differ from those of the links, and the geometry of the bends does not necessarily have to be just that depicted in Figure 30. Bends are known in the mechanical arts, and the Suitable designs and materials could be adapted for almost any degree of movement, size, operating temperature or other parameters.

Mechanical wiring logic

Another method of implementing mechanisms and computing systems that are analogous to MLL (and therefore also MFL) is to replace rotating links and joints with cables, pulleys, and handles. This design paradigm will be referred to as Mechanical Wiring Logic (“MCL”). With respect to basic, or primitive, parts, MCL cables are analogous to MLL links, and MCL pulleys are analogous to MLL rotating joints. Handles are an additional primitive that do not have a direct counterpart in MLL or MFL. Handles are used to assist in the interaction of wires, for example to create locks, and in that sense, they assist in the construction of mechanisms with analogous logical functions, even if the part itself has no direct analogue. Taking into account the teachings herein, it will be obvious that by applying force to a cable, the movement can be transmitted through the cable and to other mechanisms as desired (hence its analogy with links). Similarly, it will become apparent that pulleys can be used, among other purposes, to allow cables to bend so that movement can be directed in any desired direction (hence their analogy with rotating joints).

MCL primitives can be used to create, among others, structures, scales, and locks. While MCL implementations of scales and locks may appear different from their counterparts in MLL, viewed from a “black box” perspective, MCL scales and locks can be implemented to be logically equivalent to the respective mechanisms in m Ll. That said, MCL also provides Turing complete systems.

Tracks and channels

Like MLL rotating joints, MCL pulleys can be anchored or non-anchored. However, in MLL the links are rigid and this helps restrict the movement of unanchored rotating joints. In MCL, the cables are not rigid, so appropriate geometric constraints must be provided in a different way. One way to do this would be to maintain tension on the appropriate cables (e.g. clock cables) so that the pulleys connected to those lines cannot move unless, in this example, the clock lines move, in which case the movement of the pulley is limited to the path defined by the clock wires. Another way to approach this problem would be to mount pulleys on links where such a constraint would be necessary (although another primitive would then be required, and since this blurs the distinction between MLL and MCL, such an implementation is not discussed below). Yet another way is the use of channels, tracks or other guiding means in the anchor block. By virtue of the sliding attachment to the guide means, the movement of unanchored pulleys is appropriately restricted.

Figure 31 and Figure 32 show a top view and a side view, respectively, of a pulley that can slide in a channel. The anchor block 3101 contains the channel 3104. The pulley 3102 is monolithic with, or connected to (fixed or rotating), the shaft 3103. The shaft 3103 connects itself and the pulley 3102 to the channel 3104 in a sliding manner. . Drive cable 3105 is attached to shaft 3103 and allows movement of the pulley in the channel (e.g., driving using a watch line). Please note that this is only one way of driving and guiding pulley movement and of securing a pulley to a track, channel or other guiding means. Many other designs would be obvious, such as a pulley with a shaft extending through the anchor block with an expanded bottom protruding so that it cannot exit the channel, a beveled channel and shaft (e.g. similar to a profile dovetail joint) that could achieve the same goal, or adding another shaft structure on top of the pulley, along with another anchor block, holding the pulley between the two.

Another way of providing guide means would be to mount rails to the anchor block, the pulley being secured to the rails by any one of many known means. The point is not the exact mechanical implementation, but rather to provide some means of guidance, preferably with low friction, taking into account the flexibility of the cables; Any of the many known means of guidance could be used.

By now understanding how the movement of the pulley can be restricted without the need for links, the analogies between MLL, MFL and MCL become easier to describe. Since it has already been shown that, in MLL, locks and scales are sufficient (although not the only way) to create Turing complete systems, it follows that if analogous mechanisms exist in MCL, MCL can also be used to create Turing complete systems. Turing complete. It has already been indicated that, with respect to basic primitives, MLL links can be compared to MCL cables, and MLL rotary joints can be compared to MCL pulleys. To demonstrate 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 scale is described.

MCL Locks

Locks can be created in MCL using handles that are an integral part of, or attached to, cables or other structures. With the proper design, these handles allow the reproduction of the characteristics of an MLL lock. Specifically, with respect to a binary implementation with two inputs, from the unlocked state (0,0), there are two allowed moves, and they are those from the unlocked state (0,0) to one of the locked states, (0,1 ) or (1,0). From any of the locked states, the only movement allowed is to return to the unlocked state. Please note that there is no reason why handles cannot be attached to virtually any structure as appropriate, and lock construction is not the only use for handles.

One way to implement the desired logic is depicted in Figures 33a-c. In Figure 33a, a first cable 3301 is traversed by a second cable 3302. Two handles 3303 and 3304, and 3305 and 3306, respectively, are fixed to each cable. Figure 33a shows the lock in position (0,0), where any wire is free to move. Figure 33b shows the lock in position (0,1), the second cable having moved, thus locking the first cable by virtue of the fact that one of the handles 3305 of the second cable is between the handles 3303 and 3304 of the first cable , preventing its movement in any direction. Figure 33c shows the lock in position (1,0), the first cable having moved, thus locking the second cable.

Many other designs are possible that allow the handles to act as locks. Figure 34, Figure 35, Figure 36 and Figure 37 represent an illustrative handle design that may also impose the constraint that the only movement allowed in a lock from the (0,1) or (1,0) state is towards (0,0). This handle design is more complex, but requires only two handles (one on each cable) instead of four, to create the desired locking logic.

Figure 34 shows a single 3401 handle. Generally, a cable would be attached to either end (not shown), but such handles could be used in other scenarios as well, such as connected to MLL links.

Figure 35 shows how two of said handles 3501 and 3502 mesh together to form a lock. In this figure, the lock is shown in the blank state (which means, neither handle is positioned to block the movement of the other).

Figure 36 and Figure 37 represent the same handles 3501 and 3502 in the state (0,1) and (1,0) (or vice versa; since the mechanism is symmetrical, the crank that is defined as handle 0 and the which is defined as handle 1 is arbitrary).

It can be seen, by inspecting the shape of these handles and their relative positions in the blank states, (0,1) and (1,0), that if two cables or other structures interact through the appropriate movement of said handles, this The restriction that the only movement allowed from state (0,1) or (1,0) is to state (0,0) applies.

MCL Ovals

Conceptually, it may be useful to define a structure in MCL called an “oval”, as this arrangement of basic parts is a way to create more complex mechanisms such as scales and shift registers.

As depicted in Figure 39, one way to implement an oval uses a closed loop of wire 3801 (referred to as a “logic wire” to distinguish it from wires that serve as inputs/outputs, including those that provide clock signals, although this distinction is just for clarity of description, as logic wires can also provide input/output, as in the case of crossed ovals that can be used to form cells and shift registers), which may include one or more structures, such as the handle 3802, and passing around one or more pulleys 3803 (two pulleys are represented, but other numbers can be used to change the shape, length, vibration and entropic characteristics, or other characteristics other than the oval, which despite the name , they do not necessarily have to be oval in shape). If one or more of the pulleys may be unanchored, guide means such as rail 3804 may be included. The unanchored pulleys may be driven (moved along their guide means) by cable 3805, which may be, e.g. . e.g., linked to a clock signal.

One or more cable housings such as those illustrated by housing 3806 may be included to reduce power loss, as described elsewhere herein. The handles facilitate interaction with other structures and can be connected to one or more input/output cables 3807 and 3808. By itself and in its simplest form, an oval simply takes an input and can (but does not have to) transmit it as an output. For example, if cable 3807 is moved and the pulleys are anchored, the opposite side of the logical cable must also move, causing cable 3808 to move. Therefore, the oval can relay data, but no substantial calculation takes place. However, ovals can be designed to perform calculations by interacting with other structures (including, e.g., other ovals or cables). When combined with locks, this is a way to build a scale through MCL.

MCL Balances

Figure 39 represents a scale as part of an oval. Scales and ovals can also serve as part of a shift register. The scale includes pulley 3902 and the left side of logic cable 3901. Figure 39 depicts an oval with unanchored pulleys and two crossover cables providing data input, the two crossover cables coming from, e.g. e.g., data cables or other oval. Optional structures such as cable housings are omitted for clarity and, as usual, an anchor block is assumed to be present but is not depicted. Logic wire 3901 passes around pulley 3902 (and its partner, not labeled). Both pulleys are mounted on tracks, illustrated by 3903. Clock line 3904 drives the mechanism by pulling on the pulleys, which will cause them to slide on their tracks. The logic cable has two pairs of handles 3905 and 3906 and 3907 and 3908. Wires 03909 and wire 13910 provide an input to the oval. Each crossover cable has a pair of handles 3911 and 3912, and 3913 and 3914, respectively. As they cross the oval (at right angles in this diagram, but other angles and layouts can be used), wires 0 and 1 can position their handles to interact with the oval's handles. The triangular handles 3915 and 3916 (shown as triangular only to visually distinguish them from the other handles; this shape is not significant) connect to the output line 13917 and the output line 03918, respectively. This configuration is for example only. The starting lines could easily e.g. e.g., positioned differently, or connected to the appropriate lock handles instead of using separate handles.

Figure 39, Figure 40 and Figure 41 differ only in the position of the input cable handles. In Figure 39, both locks are in the blank position; meaning that the input cable handles and logic cable handles would not interact if the mechanism were actuated. In Figure 40, cable 3909 has movable handles 3911 and 3912 so that handle 3911 is now between two of the handles on the logic cable, 3905 and 3906. This can be considered an input of 0, since the input line zero has moved. If the mechanism were activated in this state, the upper side of the oval would be prevented from moving, since the handles 3905, 3906, 3911 and 3912 form a lock that is then locked.

In Figure 41, cable 3909 has not moved, but instead cable 3910 has moved. This can be considered an input of 1, since wire 1 has moved. The effect is to lock the opposite side of the oval by placing handle 3913 between handles 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 on an MLL scale. The operation of the oval based balance is as follows: Assuming that the initial position of the pulleys is on the left side of their respective tracks. When inputs are established, the input wires block either the top or bottom side of the oval. Next, the clock line moves the pulleys from left to right. The lateral movement of the pulleys is the same regardless of the inputs. However, which side of the logic cable moves is determined by the inputs. Whichever side of the logic cable is blocked, it is forced to remain stationary. Therefore, when the pulleys move, only the unlocked side of the logic cable moves. This results in movement of output line 0 if an input of 0 was given, and movement of output line 1 if an input of 1 was given.

Figure 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 handle 3913 had moved between handles 3907 and 3908, the underside of the oval was blocked. Therefore, when the pulleys move to the right, the logic cable must follow in the only possible way: by winding the logic cable so that the handle 3915, and therefore the output line 13917, move to the right. right. Note that data cables such as 3909 and 3910 are not the only way to provide input to an oval, and output cables such as 3917 and 3918 are not the only way to obtain output from an oval. For example, crossed ovals can interact directly, with the logic wire of one oval serving as an input to a neighboring oval. Since, when combined with locks, an input can be used to control which side of an oval is moved, this is analogous to the operation of an MLL or MFL scale. And, since Turing-complete systems were shown to be possible using only MLL locks and scales, it follows that MCL can also implement Turing-complete systems.

moving mass

An advantage of some MCL embodiments is a reduced moving mass compared to some MLL or MFL embodiments. Because the cables are not required to be rigid, they can have a smaller cross section and a correspondingly lower mass than links<m>L<l>of equivalent length. A conventional example of this principle is comparing the mass of a cable with the mass of a beam-type structure. In general, a structure that only has to support tensile forces can be made less massive than a structure that must also support, e.g. e.g., compression or bending forces. On a molecular scale, examples of strong but flexible structures that could be used as wire include carbyne (linear acetylenic carbon), polyacenes, polyethylene, and polyiceanes, although many other structures could be used.

A potential disadvantage of using cables is that the flexibility may allow modes of vibration that would not exist in a more rigid structure. Additionally, these vibration modes can change as the length of a given section of cable changes. For example, if the distance between two pulleys changes, thus changing the length of the cable segment between them, the allowed vibration modes may change, much like plucking a guitar string in different positions. This also results in entropic changes in the system. Any of these effects can lead to energy dissipation.

However, these vibration and entropic problems can be solved by keeping the moving mass of the mechanisms low. This can be achieved by restraining the cables in such a way as to prevent them from vibrating freely. One embodiment of this concept would be for the cables to be located in trenches in the anchor block. If such trenches are considered to have a rectangular cross section (although this is not necessarily the case), they would restrict the cable on three sides, with the fourth side being open to facilitate routing the cable out of the trench to interact with the pulleys. It's also possible to constrain a cable on all sides, such as the way Bowden wraps its internal cable in a sleeve or casing. If this sheath is relatively rigid, and the internal space of the sheath is appropriately sized compared to the cable, essentially no vibration will be allowed within the sheath. A molecular example of this would be a polyyne wire in a (9,0) SWNT (single-walled nanotube), but obviously many structures could be used, preferably those that are rigid, fit closely to the wire and sheath, and that allow that the cable slides freely in the sheath (but without substantially vibrating).

While short segments of cable may be exposed between trenches, sleeves or other types of casing, and where the cable contacts a pulley, these segments will be relatively short compared to the total length of the cable, thus marginalizing energy loss. by cable vibrations and entropic changes. Since the cable housings do not need to move with the cable, the moving mass is kept low, potentially enabling systems with higher switching frequencies compared to systems that require more solid rigid links instead of flexible cables.

Additionally, a cable system could be implemented with fluids inside the housings. A solid plug at one end of the casing would push on the fluid, which in turn would push another plug at the opposite end of the casing. Like a closed loop of cable, by actuating either end, this can effectively provide a “cable” (albeit made of a fluid, including a gas) that can be pushed or pulled by actuating the appropriate end. Such designs could also be used to implement scales and locks, moving the parts hydraulically rather than via a solid link or cable. Although a hydraulic system would not traditionally be called a cable, it is considered a cable system herein because the logical and mechanical operation is almost identical to that of a solid cable.

Type 1-4 systems

As mentioned above, due to the use of pawls and triggers, detents, springs, or other mechanisms that store and then release potential energy in a manner not directly linked to the system's computational degrees of freedom, all pre-existing Turing complete systems for computing mechanical systems can be classified as type 1. Due to the potential energy savings, all other things being equal, type 2-4 systems would be preferred over type 1 systems, with type 4 systems being the most preferred. MLL, MFL and MCL are all capable of creating type 2-4 systems. In fact, most of the embodiments described herein would result in type 4 systems, while the addition of e.g. e.g., of springs to some mechanisms (such as between the gradual lock depicted in Figure 9 and other mechanisms, to allow for clearance) could result in a type 2 system, and some designs that, e.g. e.g., they 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; leaving the locks in the (0,0) state ) does not necessarily mean that the parts are free to move, as can be seen in the mechanism described herein).

It may not be immediately apparent that MFL can be used to create type 3-4 systems, as it may appear that push-ups store potential energy by their very nature. In fact, some flexure-based designs, if they use flexures to store potential energy and then release it with some effect on the system, would be classified as type 1 or type 2. However, in MFL, it is not necessary to use flexures for a potential energy storage. Rather, its function may be solely to provide kinematic restraint, as does the analogous structure in MLL, the rotary joint. As such, the force required to bend a bend can be arbitrarily small, as long as the bend still provides the necessary stiffness with respect to the relevant degrees of freedom. This leads to the conclusion that the potential energy storage of bending may be trivial, as is the potential energy stored in the stretching of MCL cables, or the stretching, bending, or compression of<m>L links. <l>.

Furthermore, even if the force required to bend a flexion were substantial, since flexions are not used to drive movement in a type 3-4 system, systems can be designed where the net potential energy of the flexions is essentially 0. For For example, a pair of flexures connected to a link could be prestressed in opposite directions. Moving the link in one direction would increase the potential energy of one of the bends, while decreasing the potential energy of the other bend, resulting in no net change (and therefore no net increase in the force required to move the link) over some range of permitted motion.

Summary

Three illustrative paradigms have been described for mechanical computing, MLL, MFL and MCL. Each of these paradigms is 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 computation, and simulations of a molecular-scale mechanism indicate that properly designed realizations of MLL can compute with energy dissipation levels below the Landauer limit. There is no reason to think that MFL and MCL cannot provide similar efficiency.

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 computing system previously enabled. MLL, MFL and MCL share physical and logical parallels, in some sense they are three realizations of the same concepts. Each is capable of not only Turing-complete computing, but also providing Type 2, Type 3, and Type 4 systems (alone or in combination with each other), allowing for lower power dissipation. Each also has a very low number of required primitive types, with MLL and MFL requiring only two basic parts and MCL requiring three, which reduces the complexity of system design, manufacturing, and assembly. Furthermore, not only are a very small number of basic parts required, but none of the basic parts include gears, pawls and pawls, detents, or many other common mechanisms that are widely used in other systems, but which likely dissipate excessive energy through friction or vibration. Finally, each is capable of creating computing systems that use dry switching; There is no need to waste energy applying force to a basic part or mechanism, only to find that it will not move due to its logical state.

Considering the teachings herein, including multiple embodiments demonstrating the general design principles of being able to provide Turing-complete computation, reversible if desired, across type 2-4 systems, with very few types of primitives, that lend themselves to the creation of energy-efficient mechanisms, both because of the nature of the mechanisms themselves and because such mechanisms and systems can be designed to use dry switching, it will be evident that variations can be created using different mechanisms or primitives.

Claims (11)

i.A binary mechanical computing mechanism comprising: an anchor block (301, 303); The binary mechanical computing mechanism is characterized by comprising a set, configured to perform a combinatorial logic operation and/or a sequential logic operation with only mechanical link logic primitives, mechanical bending logic primitives and/or mechanical wiring logic primitives to carry out the combinatorial logical operation and/or the sequential logical operation; where one or more of said primitives define one or more inputs (302, 304) for data, encoded by the physical position of the inputs (302, 304), one or more of said primitives define one or more outputs (310, 311) for data, encoded by the physical position of the outputs (310, 311), where The primitives are connected to each other to selectively allow or prevent the movement of other primitives with respect to the anchor block (301, 303) based on the physical position of the one or more inputs (302, 304), so that one or more Outputs (310, 311) are the result of logical operation on the one or more inputs (302, 304). 2. The mechanical computing mechanism of claim 1, wherein the assembly requires only a combination of links (202, 204, 207), rotary joints (201,203, 206, 208), flexes, cables (3301), handles (3303 , 3304, 3305, 3306) and pulleys (3102) to carry out the combinatorial logic operation and/or the sequential logic operation. 3. The mechanical computing mechanism of claim 1, wherein the assembly requires only a combination of links (202, 204, 207) and rotary joints (201, 203, 206, 208), a combination of links (202, 204 , 207) and bending, or a combination of cables (3301, 3302), handles (3303, 3304, 3305, 3306) and pulleys (3102) to carry out the combinatorial logic operation and/or the sequential logic operation. 4. The mechanical computing mechanism of claim 1, wherein the assembly requires only links (202, 204, 207) and rotary joints (201, 203, 206, 208) to carry out the combinatorial logic operation and/or the sequential logical operation. 5. The mechanical computing mechanism of claim 1, wherein said mechanism is a logic gate or a shift register. 6. The mechanical computing mechanism of claim 1, wherein said mechanism is a shift register consisting of locks and scales. 7. The mechanical computing mechanism of claim 1, wherein said mechanism is a logic gate consisting of locks and scales. 8. The mechanical computing mechanism of claim 7, wherein the logic gate comprises a reversible logic gate. 9. The mechanical computing mechanism of claim 1, comprising means for dry switching. 10. The mechanical computing mechanism of claim 1, wherein the mechanism is micron to nanoscale. 11. The mechanical computing mechanism of claim 1, wherein the mechanism is a molecular scale mechanism.