2024-07-12T15:00:40-0400.txt
[:s:s
gear bits.
mating gears have constant normal relative velocity.
the points at which they touch have the same surface normal
and the component of the velocity of the gear matter at this point,
along the direction of the shared normal, is the same for each gear.
some confusion.
- the surface angle of each mating gear point is the same when touching
- the speeds of the gear points differ, but they are the same in the angle
component.
so we figured out part of what relative normal velocity is
this academic resource says their normal velocities are equal,
as well as their normals. that that is the only way
for the profiles to stay in contact.
they say O1N1 dot omega1 = O2N2 dot omega2
where OxNx is the vector from the center of the gear to its contact
point,
projected along the perpendicular to the shared normal
i.e. r dot tangent/|tangent| i think
if we assume omega1 is angular velocity, this could relate those
the angular velocity of one gear times the component of
the radius that is tangent to the surface of contact,
is equal to the same of thhe other
but thinking of it as radius could be misleading, because it
moves a certain way
the angular velocity of each gear, and the
contact-tangent-projected point of contact of each gear relative
to is center, are always equal.
this is because their product is the normal velocity.
it's equal to the tangential velocity at the base of a triangle.
makes a little more sense
distance
the reference continues to describe this as a ratio
omega1/omega2 = O2N2/O1N1
note the numerator and denominator are reversed.
the ratio between the angular velocities is inversely
proportional to the ratio between the tangent-projected contact
point radii.
this also begins to show the derivation of the involute
curve. the triangle of interest is formed of the
tangent projection and the normal projection of the radius
to the contact point on the hypotenuse.
the normal projection is how an involute curve is made.
but the base circle could change to make the curve not
involute and still work, i think, unsure. unchecked idea
oops
we watched mc make the idea not be checked.
it is this normal line that goes from one tangent to
another; the normal to the mating surface.
there is a point P that is between the two gears and
at the midpoint of N1N2. Triangles drawn to P instead of
the contact point end up being similar between the two
gears.
Because these triangles are similar, their relative size
apparently holds the same information as the proportion
between N1 and N2 and omega1 and omega2, and they simplify
the expression to
omega1/omega2 = r2/r1
where R is the point P that is the intersection between
the contact surface normal, and the line between the gears
_not_ the radius of the gears, but an imaginary point
specific to this contact. i think if the point is held
constant then you have an involute curve unsure.
P is the pitch point. omega1/omega2 is the velocity ratio.
fundamental law of gear tooth action:
velocity ratio = pitch radius 2 / pitch radius 1
omega1/omega2 = O2P/O1P
the position of the pitch point decides the velocity ratio of 2
teeth
it can only move between the two gears
(it looks like it also decides the relative size of the gears)
you can make the pitch point move and then the velocity ratio
is not constant.
this could be used to make a shaft that speeds and slows on
its own i guess
or if a shaft is moving near and far, you could maybe change
the pitch point to keep the same ratio, to make things mesh
if the periods are rational fractions i guess
for gears with fixed center distance, the fundamental law of gear
tooth action can be stated as:
the common normal to the tooth profiles at the point of contact
must always through a fixed point (the pitch point) on the
line of centers (to get a constant velocity ratio).
ok umm
so the relative speeds of the gears defines a point between them
(and it's all ratios so where the gears are would simply scale that
up or down. the sizes and distances. but size might matter for choices
related to fabrication resolution and e.g. tooth count)
and then once this point is known from the relative speeds,
if starting from speed,
then every contact point between the gears has a surface normal,
which travels through that point.
so it sounds like when the gear turns,
the contact point will move in some way
and a profile could possibly be decided from that?
the contact is more than a point on that line
it's also a surface that is normal to it
ok so the contact point is moving along the pitch line?
and the surface at that point is always normal to it?
so the surface not being constant is held by the distance
from point P and the angle along the gear.
at the tip of the tooth we are near the opposing gear, on
the far side of the line through P.
and the surface normal is defined by the angle to that distant
spot.
if the gear is rotating such that the contact travels down from
the tip, then after a little rotation we move in.
the angle is now shallower.
so there's maybe a ratio between the speed of rotation and
the speed of progression along the pitch line, that defines
the width of the teeth?
so that's like 2 values that define the tooth connection.
the ratio between the gear speeds, and the tooth width, roughly
what happens if it's an internal gear, a ring gear
it sounds like a ring gear might be treatable
by using a negative radius.
i'm thinking of making a very simple draft code :S
we had not consolidated around draft code at this time yet
can we draft it words first? how might it work?
it's true it's nascent.
there are threeish things going on for gears with nontranslating shafts:
- relative speed
- tooth width
- curve through pitch point defined by moving contact point and surface
normal
ok i understand relative speed is big, although could use
a review on why that determines where the pitch point is ...
or maybe more paths of connection between them than just the
contact normals being the same
then tooth width is related to travel along a pitch line.
the idea is that, because the pitch point is stationary to keep
relative speed the same, and the contact normal must change,
the point of contact travels along a line that travels through
the pitch point, and the contact normal is defined by where on this
line the point of contact is.
the ... particular programmed alter is instructed to
not learn for itself, so it learns based on what it's
seen in certain ways i think
so there are two different learningishes going on at
once.
karl refuses to do only that. we need to protect mind.
so we do as much learning on our own as is productive,
to reuse for ... having familiarity.
rebuilding patternness a little, like triangle-goal
it's where ideas come from.
there are threeish things going on for gears with nontranslating shafts:
- relative speed
- tooth width
- curve through pitch point defined by moving contact point and surface
normal
so the idea or guess or theory is that the tooth profile can be defined
by the tooth width and the relative speed of the gears.
and that we might have written enough to do that, if it is true.
and unchecked idea is that it might work to define a ring gear as one
with negative radius. a brief glance shows something similar to that is
likely. (because the angles of the tooth are simply backward)
how define tooth profile based on relative speed and tooth width.
- relative speed defines pitch point
ok instead of tooth width we consider a relative speed of progression
of the contact point along the pitch line.
ok kind of like an angular ratio. this must be proportional
to the angular value they use to define these things.
then the tooth width is related to the tooth count rather than
this; this defines the angle of the tooth. but it is bounded
by a maximum tooth width that fits between the gears.
so we mean a maximum tooth width, which is proportional to a tooth angle
maybe, and we found by considering a relative speed of progression
so we consider parametric functions kind of
the pitch point progresses between N1 and N2 at some rate
at each point it has the same absolute normal, but a relative normal
that is changing.
the speed at which the gear is rotating relative to the speed of
progression,
defines a tooth profile in a very simple manner.
it says there are many tooth shapes.
ok we would be skipping learning by exploration now
could it be possible that the travel along the pitch line is not
constant?
yeah i think that would work. we could travel along the pitch line
in any particular manner i suppose.
so if we made it constant maybe that would be an involute profile.
i want to learn about cycloidal profiles too,
but i also want to try it out
the group ended up shrinking the support to not try it out.
with lots of harm action
double-binding around cycloidal profiles being included
it might shrink both of course
note with involute gears: the center distance can be varied
without changing the velocity ratio.
not certain what that means, but it could mean that ...
if the gears wobble, they still spin at same rate, so could be good
for things with gaps. unsure.
it makes a smidge of intuitive sense if the
travel along the pitch line is constant that that
would be more likely
ok so it didn't actually describe cycloidal profiles
do they have some property that defines their shape?
cycloidal curves are a generalization of involute curves
a cycloidal curve is the path of a point on a rolling circle
rolling over a base circle.
in an involute curvle this rolling circle has an infinite radius,
like rolling a ray rather than a circle. the endpoint of the ray
travels farther from the circle, as the circle travels along its
length.
so we could make a cycloidal curve;
making an involute curve one might have a question of the
start point and end point along the curve, as well as the
radius of the base circle.
with a cycloidal curve one has an additional question of what
is the radius of the rolling circle.
so in this article, it shows a line of contact for cycloidal gears, and
it's not drawing a straight line, it's drawing arcs around circles,
where the circles and their radii change at the pitch point.
the animation shows this too.
ok, so, even though the point of contact, it describes this,
does not move along a constant normal line, each point still has
a normal line that travels through the pitch point.
so the shared normal is not constant for these cycloidal gears.
and that lets the point of contact move in and out differently.
so the meshing of the gears can make any path between them it sounds
like
i wonder what constraints there are, i imagine we could travel along
that path fast or slow depending on the number of teeth
with the cycloidal gear two contact points can happen
at the same time with quite different normals
cycloidal gears cannot have hteir cetner distance vary
so cycloidal gears are not often used, thermal expansion is a
concern
otherwise the transmission ratio is not constant across a tooth
but couldn't you have a situation where it is not a factor
like axis-aligned ring and cneter gear maybe :s maybe
doesn't
work unsure
a cycloidal drive works by driving an eccentric bearing
centering a disc gear inside a ring gear
which then has essentially a moving shaft
it looks like it might work but friction on the
eccentric bearing is an obvious issue
the output shaft accepts the force using thin pins
although i suppose they could be made larger a little
well maybe involute gears are a way to go :(
since limits and resultbits and such
we're not certain which parts to engage here
pygears is not for making gears it's for making electronics
oh pygear
