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This is an idea for a device to split rotary power
(torque) in a manner similar to an Epicyclic gear
(planetary gear), but without the need for an Annulus
(ring gear). All of the gears have their teeth on the
outside. This allows the device to be more compact,
and potentially less costly
to manufacture.
The concept is fairly simple... it's not very different
from a compound planetary gear [link].
In the middle of the mechanism, we have the planet
carrier.
Then, on one side of the planetary carrier, there's a
primary sun gear, and on the other side of the planetary
carrier, there's a secondary sun gear.
On one side of the planet carrier, there are some
number of primary planet gears, each touching the
primary sun gear.
On the other side of the planet carrier, there are the
same number of secondary planet gears as there are
primary planet gears.
Each secondary planet gear is touching the secondary
sun, and is connected, axle-to-axle, with a primary
planet gear. Naturally, the axles pass through the planet
carrier.
And, that's it!
If there are two or more planets on each side of the
planet carrier, and they are equally spaced around the
suns, then no bearing is necessary to hold the planet
carrier in it's place; the sun gears provide the necessary
support.
When the planet carrier is kept stationary, it's very easy
to calculate the gear ratios between the two different
sun gears.
If the primary sun gear has M teeth, and the primary
planets have N teeth each, and the secondary planets
have P teeth each, and the secondary sun has Q teeth,
then the gear ratio is MP/NQ. Note that if M/N equals
Q/P, then the gear ratio between the two suns is 1:1,
which is rather silly.
When the planet carrier is not kept stationary... well,
my math skills aren't up to the task (thinking about the
problem makes smoke come out of my ears), but I'm
certain that the system is mathematically equivalent to
an ordinary epicyclic gear, with an annulus whose size
can be calculated from M, N, P, and Q.
(?) Compound Planetary Gears
http://en.wikipedia...und_planetary_gears
[goldbb, Nov 07 2012]
(?) Prototype Annulus-less Epicyclic Gear (ALEG)
http://www.yogile.com/k6fz74nj#41m
Also a differential made from all straight gears [scad mientist, Nov 08 2012]
Baked!
http://lego.roerei....ar-calculations.htm
Last Image on page seems to be this idea [goldbb, Nov 16 2012]
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Annotation:
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If you happen to like Legos... |
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It should be easier to construct an instance of this
epicycle gear variation out of Lego Technic parts than
to construct a normal planetary gear, since there are
few Lego parts suitable for use as a ring gear, and
they're all fairly uncommon pieces, and awkwardly
large. |
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If we were building this out of Lego Technic parts, we
might choose to use a 5-hole beam as the planet
carrier, 8-tooth gears for the primary sun and secondary
planet gears, and 24-tooth gears for the secondary sun
and primary planet gears. |
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The ratio between the two suns is 1:9, obviously. |
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Turning the planet carrier once, with the large sun held
stationary, turns the small sun eight times. I think. |
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Turning the planet carrier nine times, with the small
sun held stationary, turns the large sun eight times. I
think. |
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(I no longer own legos, or I would actually build this and
test it, instead of trying to visualize, so my ratios might
be off). |
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Before anyone asks how this linkage might be useful
with Legos, since we wouldn't be able to rotate the
planet carrier in a full circle (since there's no gear teeth
on it)... |
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If you were to oscillate the planet carrier with a motor-
driven crank and connecting rod, and put a wheel
(acting as a flywheel) on the small sun, and connect the
large sun to an indexing gear (double-acting ratchet),
you would have built yourself a Constantinescu Torque
converter. |
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Also, there *might* be a way to use a 40-tooth gear as a
planet carrier, with the axles connecting primary and
secondary planets going through the holes in it... but
I'm not sure there exist lego gears which could mesh at
these distances. |
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// Concave Gears only //
I think you meant convex? |
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I always just used a Lego differencial when I need this sort of gearing, but I had never considered such a configuration before, and it's rather interesting. [+] You really would benefit from having a good diagram though. |
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Also it made me realize that it woud be possible to create a differential with no 90 degree gears. Rather than have the idler at 90 degrees, just have your gear with matching sun gears but have the planets on opposite sides of your carrier offset from each other and geared together so they turn in opposite directions when the carrier is stationary. |
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I don't think your idea, or my derivative differential, would be as efficient as current standard gears (more forces on bearings and more gears meshing), but they could be easier to build in some situations. |
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I added some photos of Lego prototypes. I didn't have a really good panet carrier, so the one shown would have to be belt driven. |
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In some of the photos, it looks like the sun gear is on the same axle as the planet carrier. What is seen in the pictures is actually a short piece of rod through the carrier to keep it from sliding left or right. The carrier is supported only by the gears. Better support could be made, but then it would be harder to see. |
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I don't have a good place set up to share photos so those will expire in 14 day. [goldbb], feel free to download those and/or find a more prmanent home for those. |
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scad mientist,
Thanks, I meant convex, not concave. |
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And, great prototypes, and thanks for putting the
pictures up! |
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If the planet carrier were only one brick thick, the
whole differential would be 4 bricks thick, excluding the
enclosure. |
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Or if you left out the reversing gear, and had it as a sort
of epicyclic gear, it would be only 3 bricks thick. |
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