Connection method

In the context of APM locking mechanisms are the simplest most compact physical structures that one can built that hold things together.
Reversible ones are needed to build recyclable AP systems and products. They can be split into three classes:

• energy barrier locks
• hierarchical locks
• friction locks

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The different methods to lock building blocks into place

Energy barrier locking (soft)

In the macro-scale springs, magnets, gravitation, and almost unused electrostatic attraction belong to this class.
In the nano-scale springs, VdW-force (Van der Walls attraction), chemical bonds and in some cases electrostatic attraction are well usable.

There thermal movement can knock a lock open by probabilistic chance which must be taken under consideration in system design. Energy barriers high enough to effectively prevent opening by chance can be easily reached. [Todo: add VdW math example; add more details]

All other locking methods do too display energy barriers but have other more predominant traits.

Van der Waals locking

Two coplanar atomically flat surfaces attract each other quite a lot.

• ~1nN per square nm this equates to around ~10,000 bar.
  Original Source: (Nanosystems 9.7.1.)
  indirect source: [1] (beware: the noted binding energy is mistakenly taken from a covalent interface - Nanosystems 9.7.3.)
  double indirect source: [2]
• ~2.7nN per square Nm 1/20 the tensile strength of diamond
  Source: (Nanosystems 3.5.1.b) (more than titanium and low grade steel)

They can still slide effortlessly along each other (possibly superlubricating) so depending on the use indents may be needed to prevent that. (intuitive feel)

Van der Waals forces can be used to do self assisted assembly (which is a weaker form of self assembly aka brownian assembly). When assembling a hinge one does not need to plug the axle in actively and fix it in place with e.g. a locking snap-ring. Instead the axle gets sucked in as soon as its hold over its sleeve. One gets it out again by pushing with a blunt tool. This simplifies assembly a lot. Less manipulator complexity and less positioning resolution (and thus stiffness) is needed.

For the tiniest assemblies counting only a handful atoms locking will be necessary since there are an Avogadro number (~6*10^23) of parts so some will thermally self disassemble if the probability for this is extremely but not astronomically low. The probability P for thermal self disassemly of parts sicking together with energy E quickly becomes astronomically low as can be seen by the formula: P = e^-(E/(kT)).

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Comparing the VdW interaction with covalent bonds can give a better intuitive feel for VdW interaction forces.

Form locking

Main article: Form locking

Hierarchical locking

Something is hierarchical locked when one has to remove a part such that a locking part can be removed. The structure can be disassembled only in a specific order. Hierarchically locked structures can have tree shaped topologies.

Related: Expanding ridge joint

Friction

Nails and screws base their locking ability on friction but in AP products one usually finds super-lubrication between surfaces.

One can design surfaces such that they perfectly intermesh but this would effectively create a series of energy barriers (energy barrier locking) in which the barrier after the first one won't have much use (linear instead of exponential decrease of accidental disassembly probability). Furthermore the energy might be not well recoverable (non-stiff hydrogen bonds dissipate power) leading to unnecessary waste heat. Thus the classical nail and screw design probably makes no sense at the nanocosm (To investigate: in-how-far is this statement true?)

Kinds of connection mechanisms tat are typical for a specific scale

• <1nm - single covalent bonds
• <1nm...typical:32nm...<1µm -- matching surfaces full of open radicals (densely packed -> irreversible connection)
• >32µm...typical:1µm...open-end -- reversible interlocking structures
• >1µm...typical:1mm...open-end -- high level self aligning and dirt expulsing interfaces

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The locking nature of screws

• mechanical advantage
• self-retention by friction

Examples for various combinations of locking types

• snap buckles: pure energy barrier locking - zero hierarchical levels
• snap ring: hierarchical locking of at least one but most of the time two layer
• door handle mechanism: hierarchical locking of one layer (with retention of the locking part)
• ...

Related

• Combination lock stones as a safety measure against malicious disassebly attacks are mentioned here.

External references

• further information: Nanosystems chapter 9.7 Adhesive interfaces