Multi V-groove self-centering
Up: Scale agnostic design principles, Self centering
This is about the general mechanical design principle of self centering with
using multiple (two or more) female V-shaped grooves and opposing male shapes.
The principle can be generalized to (three or more) pyramid and cone shaped structures.
▒▒〕＞▒▒ █🭬🭨█ ▒▒〕＞▒▒ █🭬🭨█
Motivations
- Allowing for lower accuracy and precision needs in the assembly process. And thus also …
- Allowing for higher speed assembly while still keeping error rates low (or FAPP zero).
FAPP zero means that other damage effects start to dominate. - Minimizing accumulation of small errors in the assembled structures. (Or for AP structures preventing it all together.)
- Preventing irreversible slip that is not restored when the load is causing (over)load is gone.
This relates to depending on friction to hold things in place. Which we want to avoid and which this principle can help to avoid. - Making assembly processes, disassembly processes, part recomposition processes in general
into an enjoyable oddly satisfying experience.
More abstractly: Correcting for lack of accuracy and or precision in the assembling process.
This can benefit both fully automated assembly and manual assembly remote controlled and direct by hand.
Single V groove
A single linear female V shaped groove in a part combined with
a single linear male V shaped protrusion on a mating part
can serve as a basic self centering element.
Undesired sideward wiggle/rotation:
⚠ Chamfering off the edge of the male protrusion can help prevent only the tip hitting the bottom,
which would defeat the purpouse of the V-groove.
⚠ Fundamental limitation A single V-groove:
It does not pose much resistance against rotational forces (moments) around its axis.
A bigger V-groove can only slightly improve on that.
And that at the huge cost of the self-cenetring V-groove structure becoming similar size as the mating parts.
better to keep the groove small but go for at least two grooves (parallel spaced of roughly orthogonaly crossing).
Same considerations hold for n-sided pyramids and in the limit cones.
Just that there is wiggle in more two axes now with just one pyramid and still wiggle in one axis with two pyramids.
Related is the idea of kinematic coupling.
https://en.wikipedia.org/wiki/Kinematic_coupling
Related unicode characters.
Also ones for the culled off trapezoidal side:
- ⏠ U+23E0 ︹ U+FE39 ︿ U+203F
- ⏡ U+23E1 ︺ U+FE3A ﹀ U+203E
- 〔 U+3014 ＜ U+FF1C 〈 U+3008 〈 U+2329 ⦑ U+2991
- 〕 U+3015 ＞ U+FF1E 〉 U+3009 〉 U+232A ⦒ U+2992
Multi V-groove
At least two grooves are needed to avert the aforementioned wiggle issue.
Note that this also hold for concentric tangential V-grooves that can serve as rotational slide bearings.
(wiki-TODO: Add a photo of the circular V-groove bearing experiment and discuss the outcome.)
Ultimate load capacity limit
In case of …
– big forces shall be transmitted through the interface and
– as much of the base material strength shall be retained as possible
it is better to densely cover the surfaces densely with V-grooves
rather than using just two small ones far apart to merely counter the wiggle.
Size of the V-grooves and amount of the tip cutoff becomes a trade-off.
This is related to fir tree joints being a generalization to
dovetail joints optimizing maximal retention of base material strength.
Too much manufacturing errors and too stiff material to mate properly by acceptable pressure
Due to manufacturing errors (in accuracy and precision)
it may be that not all surfaces that are intended to be in contact are actually in contact.
Increasing clamping force/pressure may be able to make all the surfaces contact but then
- … load may turn out distributed badly putting local spots above the fatigue limit.
- … depending on the amount of errors and the stiffness of the material things may even brak right away before they contact
These issues can be compensated by …
- … going to slightly softer materials that allow fur just enough sufficient flex
- … decreasing manufacturing errors so far that is possible (at all and with acceptable trade-offs) of course.
Noat that even in the in the limit of atomically precise manufacturing there is still the systematic known error in accuracy
that comes form the atomic granularity of matter. There is plenty of flexibility though. See Superelasticity of fully defect devoid gemstones at the nanoscale.
Related: manufacturing error / material stiffness / parallel spring competition
Concrete example in FFF 3D printing:
Small V-grooves in FFF-3D-printing can incur quite a huge relative errors.
(including elephants foot, lack of cooling warping, corner speed ringing, z-axis-wobbel, and whatnot)
Many cheap & easy to print 3D printing materials are to stiff to compensate by flex for these errors.
PLA is especially stiff and thus bad for this. Not to mention that it can't cope with high permanent loads.
It will flow and/or microcrack till catastrophic failure in months to weeks.
Author of these lines advises to stay away from PLA and variants for
anything beyond throwaway shape testing prototypes.
Nanoscale specific considerations
The former was all scale-agnostic.
The multi V-grooves self centering principle can
provide a specific benefit that only applies to nanoscale systems.
Constraints on angles of the grooves
Due to the atomistic lattice only the main crystallographic planes offer reasonably smooth surfaces at the lowest scales.
This the angles of v-grooves and are pretty much very limited in options and pre given.
Fine tuning sliding rods in channels
Specifically the atomistic lattice (of diamond silicon or whatever gemstone used)
does not allow for fine tuningly matching the size of a channel to a rod that is meant to slide within.
The next best thing that one can do though (so lone one does not go fro absolute mimimal size)
is to gently press the rod in a v-groove like corner of a channel.
This van be done fine tuningly by leaf springs also situated in the channel.
Related here is crystolecule based rod-logic
that should work well at MHz frequencies.
Mating v-protrusions edge chamfering (tip culling)
Due to atomic perfect accuracy an precision in AP mechanosynthesized structures
it often may not be necessary to chamfer the edge of the mating V protrusion.
This has to be looked at at a case by case basis.