Periodic table of gearbearings
One way to potentially reduce friction in Atomically precise bearings is to use roller bearings.
But as static friction is absent and there are no truly flat surfaces in positionally atomically precise crystolecule bearings
the rollers need gear teeth to ensure reliable rolling.
For gearbearings at or near the lower possible physical size limit individual rows of atoms can make up the teeth.
For larger (still atomically precise) gearbearings some conventional tooth flank can be approximated (see kaehler brackets and Graphene sheet lining).
Contents
Why full cycloids are a good tooth profile for atomically precise bearings
It turns out that a profile of alternating full epicycloids and full hypocycloids has several advantages over involute profiles.
Gears with full cycloid tooth profiles like to be pressed together to the ideal distance whereas
involute gears like to be constrained by axles to a to some degree choosable axial distance.
Gearbearings with involute profiles need a very high pressure angle to allow presstogether which ...
- introduces friction
- prevents gearbearings with very low tooth numbers
Contrary to that with full cycloid profiled much lower tooth numbers are possible.
Also full cycloids profiles feature no harsh edges. Thus they are ...
- probably better approximable with Graphene sheet lining.
- more similar to soft single rows of atoms as tooth profile than involute profiles are.
In general full cycloid profiles tend to run smoother with lower friction.
The pulsating pressure angles that full cycloids profiled suffer from can be compensated by herringbone tooth trajectory twists.
For mechanosynthesis there manufacturing constraints of metal working do not apply so
the more complex geometry is no more problem than involute profiles.
Same applies for various kinds of today's (2023) 3D printing and casting.
Periodic table to get more options for the smallest bearings
There are certain mathematical constraints that must be upheld to
get a gear-bearing with the teeth of the sun ring and planets all fitting together.
It turns out that when allowing unequal spacing for the planets then
one gets much more options for the smallest possible gearbearings.
Thus allowing different spacing is desirable. But we still want as much symmetry as possible.
Thus we make groups of planets with one kind of planet spacing within the groups and
an other kind of spacing between the groups of planets.
One gets a set of three defining numbers like so:
gcd_ = 3; // number of planet groups - greatest common divisor of gears mplanet_ = 2; // number of planet teeth per planet group msun_ = 4; // number of sun teeth per planet group
All spacings between planets along the relevant secants must be greater than
the two times the planets pitch radius plus four times the cycloid rolling radius.
Some combinations of numbers violate that condition and must be filtered out.
