A bit hypothetical but, assuming two identical gears, the driver has
100mm pitch circle and the driven has a 100mm pitch circle, they are
spaced at 100mm centres. The driven is attached to a rubber wheel.
Correctly meshed, for one revolution of one gear the other will turn one
revolution, which is a distance of 100mm x pi = 314.15mm
If the gears centres are then altered to 102mm without altering the
pitch of either (or anything else) will the driven gear travel further
or less per revolution? Is there a formula to work it out?
What will happen is that you will have an effective PCD of 102mm,
but the teeth will now be the wrong shape for that PCD, the effect
of which is that you will hear more noise from the train (assuming it is
transmitting power and not movement as with clocks).
The noise arises because of stress in the teeth, with the teeth
themselves bending backwards and forwards.
This, incidentally is one of the reasons for using involute teeth
in power trains - the broad base of each tooth gives additional
strength compared to the cycloidal teeth used in horology.
The driver/driven gears will still turn in the same ratio as before.
Could you please disambiguate that last bit please?
"transmitting power and not movement as with clocks"
Is this some special physical process you have invented? Is it reliant
on some special rare lubricant, perhaps made from the hide of virgin
sheep? Is this lubricant Down and Out Systems latest product?
Do tell us. When you have, maybe you can also revisit NMR and nuclear
That is just "colloquial usage", the sort of thing someone who doesn't
really understand physics would say.
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Nah! It is a well known fact that clocks are driven by time. Any
springs, weights or other apparent driving source are put there to fool
the over-curious. A bit like God putting fossils in the rocks as a
practical joke against Darwinists.
Read Richard Dawkins 'The Blind Watchmaker' if you don't believe me.
Swim? Naturally with MADNAT <http://www.madnat.org/
You wrote on Wed, 21 Apr 2004 20:25:46 +0100:
MH> Read Richard Dawkins 'The Blind Watchmaker' if you don't believe me.
Shouldn't that be: Read William Paley "Evidence of Christianity"
With best regards, g1lvn Gareth (William Paley).
Replace "mycallsign" to reply by E-mail
Complete crap - 0/10 (How does the power get from the spring/weight to the
Partially true but mainly crap - 2/10 (The noise mainly emanates from the
contact of tooth on tooth which is minimised if the tooth 'depthing' is
An almost completely misinformed opinion - 1/10 (The tooth base is dependent
upon module or DP and in most cases cycloidal and involute have similar base
dimensions - although cycloidal *could* have a narrower base. You will also
find that involute tooth forms *are* used in modern horology, partly because
the depthing is less critical and is therefore suited to mass-production
Correct - 10/10
That's only 23 out of 50 - Must do better!
I think that, perhaps, you need to adopt a mature attitude to debate
rather than the rather silly and infantile stance that you exhibit below.
Grow up, OM.
The purpose of the going train in a clock is to transmit movement
and not power. The going train is stationary for most of the time,
and the concept of power, as a rate of doing work is meaningless.
If you want to show yourself up to be a childish fool by arguing
that some energy must come from the spring or the weights, then
that is your prerogative.
If you want to show yourself up to be a childish fool by arguing
that malformed teeth are not subject to bending stresses, then
that is your prerogative; text books on gear theory disagree with you.
On Fri, 23 Apr 2004 20:50:29 +0100, "Airy R. Bean"
What utter rubbish you utter. Maybe you might help us all out by
telling us what the SI unit for the transmission of movement might be?
The Bean perhaps?
It has clearly escaped (sic) your attention that the primary purpose
of the going train is, as the name usefully prompts you, to keep the
clock "going" - i.e., to supply the energy to the pendulum that is
lost through friction, viscous drag, hysteresis in the suspension
spring, .... etc., and thereby to keep the pendulum swinging at a
(near) constant frequency. Remarkably, it supplies this energy at the
same (average) rate as it is dissipated. As your elementary physics
will tell you, power is energy per unit time. So the train very
clearly transmits power.
Whether or not the transmission of power is continuous or
discontinuous is massively irrelevant.
The transmission of movement (to the hands) is an incidental
convenience - it saves the user from the significant inconvenience of
having to count pendulum oscillations himself in order to tell the
It depends on what accuracy you're looking for. The AVERAGE
ratio between a pair of spur gears is uniquely defined by the ratio of
the numbers of teeth in the wheels and is independent of variations in
centre distance or errors in tooth shape provided sequential tooth
contact is maintained.
In your case the average ratio will remain at 1:1 and will
not change as the centre distance changes.
If you are looking for an accurate instantaneous velocity
ratio life gets more complicated. Perfectly cut involute teeth have
the interesting property that small changes in centre distance
slightly change the effective pressure angle but the velocity ratio
Cycloidal teeth (mainly used in clocks) do not have this
property and will only produce constant velocity when meshed at the
correct centre distance. Centre distance errors will produce velocity
errors at tooth frequency.
In either case eccentricity will result in instantaneus
velocity errors at rotation frequency. 1% eccentricity in one of the
two gears will produce 1% velocity variation. Eccentricity in the
mating gear has a similar effect but this may add or subtract to the
driving gear error.
Hang on fellars!
It depends on which bit of the gear you are considering.
A point on the pitch circle, i.e at 100mm diameter, travels 314.15mm
The tip of a tooth goes further and the axis goes nowhere.
What happened to the rubber wheel?
I'll hazard a guess that it is driving something.
It will rotate once for every turn of the driver.
How far its rim will travel depends on its diameter.
e.g. If 100 mm then it travels 314.15mm.
Remove the 'bait' from the 'trap' to catch the Dragon
Leave the trap.
OK, time to come clean :-)
The driven gear is attached to the back of a plastic wheel with a rubber
tyre of about 200mm dia. The driver is attached to an electric motor.
The driver is engaged with the driven gear by means of a very rudimentry
hand lever with no fixed positon to marry the two pitch circles
together, therefore the teeth can be engaged anywhere from the top of
the tooth to the bottom of the tooth. This is what prompted the
original post, I assumed that if the teeth were only just contacting on
their tops then the contact would be on a larger diameter than that of
the correct pitch circle thus making the gears travel a greater distance
for one revolution than if they were meshing correctly at their
respective pitch circles.
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