Basic Clock Design

[Martin KyteParticipant @martinkyte99762]

Going back the the oily pallets issue.

Harrison said:

In the case of Mr Graham’s clocks, with a small pendulum amplitude and other poor characteristics described earlier (mainly pallet action at a large fraction of the pendulum length . . . text inserted by me) most especially when the oil is foul, a touch of fresh oil will cause the amplitude to increase and the clock to go faster *. Dr Bradley . . . reported a variation of approximately 2 seconds a day when the escapement was freshly oiled.. When the pendulum amplitude is larger, a touch of oil will still as just described cause an increase in amplitude but the effect would be to cause the clock to run more slowly. This is a more satisfactory outcome being more in accordance with the nature of a pendulum.

The way I read the text is Harrison was complaining about pallet action taking place so far along the pendulum rod making variation in friction a much greater effect than it need be. Withe the Graham Dead beat the pendulum is constrained by the pallets and escape wheel for most of it's swing resulting in the frictional forces of the pallets across the escape wheel teeth damping the oscillation and slowing the period. Reducing the friction, reduces the damping and shortens the period. The comment at * is an observation of what the clock does and not that the amplitude is the cause of the increase in rate. The last two sentences state that the clock behaves as expected when friction is low and then gets slightly lower. Friction has become the less dominant effect at that point.

Just as a thought all this would indicate that Harrison thought a great deal about the effect of drag on the action of his pendulums and although I have no evidence to prove this, maybe thinking about the shortfalls of Graham's clocks lead him to understand the effect sufficiently to use it (as atmospheric drag) balanced out with controlled circular error to create a system which was largely immune to atmospheric changes.

Martin

[Michael GilliganParticipant @michaelgilligan61133]

Agreed, Martin

'CSM' argues the case for Harrison's mechanism being superior to Graham's

1. Geometrically, and
2. For its lack of reliance upon the 'state' of applied oil.

The combination results in something where the pendulum [as he says] "has dominion" whereas [implicitly], the Graham design responds unpredictably to small changes.

… anyone for Chaos Theory ?

MichaelG.

[John HaineParticipant @johnhaine32865]

Thanks for pointing out that link Martin, one I hadn't seen. Yes, it gives a formula for the resonant frequency corrected (effectively) for Q. Applying that with Q values of 3000 and 5000 gives corrections of 3.3 nS and 2.5 nS respectively! The simulation results can't really be relied on to nS periods because of the way it calculates periods, but in mechanical clock terms the difference is irrelevant. The difference is 0.8 ns per 2s, which is 3.5 ms in 100 days.

Somewhere I have seen that the impulse from a deadbeat escapement (such as the Graham) is slightly imbalanced, that is it's slightly off-centre from the pendulum swing. This means that the impulse is slightly out of time phase with the pendulum velocity, resulting in a small time error. If the impulse phase is in advance of the pendulum it speeds it up; if behind it slows it down. The imbalance is geometric, but the amount of resulting phase shift depends on the pendulum amplitude. Suppose the imbalance is slowing the pendulum down. You add a spot of oil, reduce the friction, increase the amplitude, reduce the phase shift, and the pendulum speeds up.

You asked about the circular error at working amplitude. The fractional reduction in rate is just (amplitude in radians)squared/16 assuming no correction. At 1 degree, or about 1/60 radians, this is 1/(3600×16) = about 35 microseconds for a seconds pendulum. This is exactly what the simulation gives as well. You can scale up or down from that for other amplitudes.

Air resistance law has to be specified in advance, linear or square law. For normal amplitudes of a degree or so it seems to be about linear, but at Harrisonian amplitudes of more like 6 degrees it's probably square law.

Your last paragraph –

"Just as a thought all this would indicate that Harrison thought a great deal about the effect of drag on the action of his pendulums and although I have no evidence to prove this, maybe thinking about the shortfalls of Graham's clocks lead him to understand the effect sufficiently to use it (as atmospheric drag) balanced out with controlled circular error to create a system which was largely immune to atmospheric changes."

– there seems to be no doubt that this is exactly what he did, though not just circular error but escapement error too.

[Russell EberhardtParticipant @russelleberhardt48058]

Posted by Martin Kyte on 05/05/2016 10:02:58:Perhaps this link would help. You seem to be better at maths than me.

**LINK**

best regards Martin

Thanks for that link Martin. I'm now beginning to understand what's happening. If his equation for the frequency change with damping factor v is expanded using the binomial theorem we get the frequency being reduced by the damping by a factor of 1- v^2 /8wo plus other higher order terms which are insignificant. As the slowing down depends on the damping factor squared the effect will be very small for low friction cases. So I think Michaels remark about the quality of the oils in Harrison's time makes sense and that the effect Harrison observed may not occur with modern oils.

Russell.

 

 

Edited By Russell Eberhardt on 05/05/2016 20:06:13

[John HaineParticipant @johnhaine32865]

To me it is evident that the effect he observed has nothing to do with the very small influence of damping on resonant frequency (measured in nanoseconds!) but much more to do with escapement error changing as the amplitude increases when oil is applied.

In fact, Rawlings (Science of Clocks and Watches) on pp 110/111 of the 3rd edition confirms that for the Graham dead-beat in practice the impulse has to be slightly late so the pendulum runs slightly slow (but of course this is regulated out). With more pallet friction reducing the effective impulse when the oil is dry, the pendulum amplitude will decrease, and in effect the impulse will be later and the clock run slower. When oil is applied friction reduces amplitude increases impulse gets earlier and pendulum speeds up.

[Michael GilliganParticipant @michaelgilligan61133]

For info.

Here is an article I've not seen before, about 'clock B'

Slightly different slant on the story, and a rather nice picture.

MichaelG.

[Martin KyteParticipant @martinkyte99762]

Hi John and Russel

Russell you are correct. The old oils were animal based and did degrade very quickly.

The point I was making was any damping always acts to slow a pendulum. The example of air resistance was just to illustrate the point although at the time I was not sure of the magnitude of the effect. I'm still not convinced it is as small as you state but that's slightly off the point. With a Graham Dead beat friction will be present in the escapement for virtually the entire swing so increasing the friction at the pallets by virtue of the foul oil increases the damping and slows the clock. Better or newer oil has the opposite effect With very degraded oil this is going to be significant enough to cause the effect as observed. I agree with John re phasing which just makes things worse. With long pallet arms the friction has an excessive effect which is what Harrison was complaining about.

best regards Martin

[AjohnwParticipant @ajohnw51620]

Posted by Michael Gilligan on 05/05/2016 23:57:42:

For info.

Here is an article I've not seen before, about 'clock B'

Slightly different slant on the story, and a rather nice picture.

MichaelG.

Interesting one Michael and a little clearer than some. To me it gives a good clue – the circular suspension cheeks can account for more than what people might generally suppose including barometric air pressure changes. I suspected as much because they must account for the variations from the remontoire he used. Harrison is way past basic clocks and is a pretty deep subject much like Hendrix's guitar and effects pedal there can be many miss interpretations about.

Notices where has basic clocks gone comments – note that there may have been a conclusion that a Brocot escapement would be a good direction to go in as it's easier to make accurately. The main reason it interests me though is that it can be oil free.

The Harrison debate hinges around what pendulums do in practice. Ideally the swing time would be identical irrespective of the angle swung. It isn't so precision clocks may reduce it to as little as 2 degrees. 3 and below is reckoned to have negligible effect, in other words behaves as expected with minimal error from the ideal. Important as there will be minor variations even from the mechanics. Air density raises it's head as well, Usual fix very heavy pendulums.

I mentioned that a Graham must add friction throughout the pendulum swing. It's also generally lightly oiled. It is possible to make the pallets accurately. Rather than cut pallets out of some "turned up tube" it's also possible to turn them directly. This finish up sticking out just like the the version where the "tube" pallets are fastened into a frame. The frame though needs to be in 2 parts. The inner diameter can be measure via a mic with ball attachment usually used for measuring tube wall thickness's.

Here is a shot of an escapement actually made by Brocot. The clock is virtually held together with clock pins but still no sign of a reamer.

Looks like very slight flats on the end of the teeth to me. From the split in the escapement it also looks like the pallet spacing can be adjusted. Probably in part to account for wear over the years..

John

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[Michael GilliganParticipant @michaelgilligan61133]

Posted by Ajohnw on 07/05/2016 17:42:16:

[a] – the circular suspension cheeks

…

[b] Here is a shot of an escapement actually made by Brocot.

[c] The clock is virtually held together with clock pins but still no sign of a reamer.

.

John,

[a] … forgive the pedantry, but at this level it's important: The cheeks are cycloidal, not circular … If you haven't already done so, I recommend reading Huygens' Horologium Oscillatorium. [thankfully, there is an excellent English translation available, by Dr Ian Bruce.]

[b] … Thanks for the Brocot photo.

[c] … I really don't think you will find a commercial reamer for Clock Pins; if a broached hole isn't good enough for you, I would suggest making your own reamer from a steel clock-pin.

Welcome back, by the way.

MichaelG.

.

P.S. … The anchor on a Brocot escapement is almost always adjustable in some way … There's not much chance of re-shaping the jewell pins to make fine adjustments, so it's much simpler to change the distance between their centres.

Edited By Michael Gilligan on 07/05/2016 18:33:10

[AjohnwParticipant @ajohnw51620]

You mean T=4pi sqrt(a/g) where a is the rad of the curve used to generate the cycloid and is 1/4 the length of a simple pendulum and T is the period and etc Michael?

He didn't use it in his subsequent clock, He used a link arrangement instead. No chops as they are usually called. The pivot point of the crutch didn't coincide with the pendulum pivot. He later went back to chops again – on paper.

In Harrison's case it's probably safer to say curved chops that were adjustable anyway.

John

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Edited By Ajohnw on 07/05/2016 19:17:29

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Ajohnw on 07/05/2016 19:17:01:

You mean T=4pi sqrt(a/g) where a is the rad of the curve used to generate the cycloid and is 1/4 the length of a simple pendulum and T is the period and etc Michael?

.

John,

What I meant was "I recommend reading Huygens' Horologium Oscillatorium." …. For several reasons, but mostly because Huygens was not only a genius, but also a great communicator.

MichaelG.

[John HaineParticipant @johnhaine32865]

Harrison, and Clock B, used circular cheeks, not cycloidal. This is quite explicit. Anyway real pendulums, which are compound so they have their mass distributed, are not made isochronous by cycloidal cheeks. It seems that Harrison knew this.

[AjohnwParticipant @ajohnw51620]

I just doubt if Harrison's chops were cycloids Michael. On the other hand they might be. Huygen's aims was to correct the swing of a pendulum and it seems very little actual use was made of the idea despite lots of work. Harrison#s protractors would be well aware of Huygen's work as well.

The best ever pendulum is often reckoned to be down to this bloke. Change of subject but again not in any way a basic clock.

**LINK**

However note the need for a microscope to set the swing and other factors. That one it seems could detect changes in gravity due to the position of the sun and moon.

John

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[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 07/05/2016 22:41:27:

Harrison, and Clock B, used circular cheeks, not cycloidal. This is quite explicit. Anyway real pendulums, which are compound so they have their mass distributed, are not made isochronous by cycloidal cheeks.

.

Indeed … 'twas my error

Cycloid only works for a 'simple' pendulum.

MichaelG.

[John HaineParticipant @johnhaine32865]

John, that link doesn't seem to work for me. Was it the Loomis and Brown article on the Shortt clock tests?

[James AlfordParticipant @jamesalford67616]

I am currently drawing up plans for a Brocot escapement for this clock, rather than my original design. I have read that the diameter of the pallets should the same as the gap between the tips of the escape wheel teeth, less the drop. What would be the consequences of using smaller sized pallets than this? The main thing that I can see is that it may run out of "operating" surface if the pendulum were to swing too far, so the cut-out part of the pallet tries to engage, rather than the curved face.

Can anyone please advise?

Thank you.

James.

[AjohnwParticipant @ajohnw51620]

It looks like the data base is off line John. Perhaps best to try again in a few days. Odd it's one I have made a lot of use of at times and I hope that mentioning it on the web hasn't caused them to restrict usage. When it's back on line you could try searching Astronomical Clock. The paper was written by F M Fedchenko. It is mostly of academic interest though.

You would be increasing the recoil James if you mess about with the other face so best stick to the design. The other curved face just provides clearance for the pallets and could be replaced by the other form that has a straight angled line instead. The curved form provides stronger teeth. It's possible to cut that with a curved form tool first and then a suitable slitting saw. I'm stuck for a suitable linux cad package that will draw one easily so will have to do it on paper.

So far I have found that a 60T one will be about 95mm dia and a 120T one about 190mm dia. Irksome as I would prefer 120T.

John

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Edited By Ajohnw on 08/05/2016 10:05:58

[AjohnwParticipant @ajohnw51620]

This is the first of 13 video's "describing" the making of a replica Harrison's RAS regulator I mentioned earlier.

**LINK**

Personally I have always wondered if his grass hoper escapements needed power applying with a lot of care to prevent them from running away. He also made wooden ones for probably rather high end domestic use. There is also a youtube video showing some shots of a  replica some one made. It's called Harrison's Wooden Clocks.

John

–

Edited By Ajohnw on 08/05/2016 12:17:43

Edited By Ajohnw on 08/05/2016 12:18:26

[James AlfordParticipant @jamesalford67616]

John,

Thank you for your reply. It took me ages to work out why it would increase recoil. To my logic, it seemed that a smaller pallet would reduce the recoil, after studying some videos and thinking about it, I think that I can see the reason.

I shall carry on drawing.

Have you tried Onshape CAD? It is an online system and sketches or drawings can be exported in dxf and dwg formats, amongst others.

Regards,

James.

[Russell EberhardtParticipant @russelleberhardt48058]

Posted by Ajohnw on 08/05/2016 10:04:16:I'm stuck for a suitable linux cad package that will draw one easily so will have to do it on paper.

Draftsight is a comprehensive 2D package produce by the Solidworks people. It is available for Ubuntu and its derivatives. I find the current version works fine on Linux Mint.

Russell.

[AjohnwParticipant @ajohnw51620]

I'll see if I can find some images that give the main aspects of the design James. The size of the pallet given that the active face is set at the correct angle shouldn't make any difference to recoil. Altering the angle will.

I've just had 1/2 hr + on my knees, huddled up praying to my PC with a vacuum cleaner. HP make wonderful workstations that even have a blow through heatsink on the cpu – pity they don't assume that some one will need to clean it one day. I had to undo 4 screws with a 15mm long phillips bit as no room for anything else. I've even got sore fingers now. As the cpu was running rather hot it became extremely slow.

I'll have a look at the cad package suggestions. I had looked at LibreCAD which is a spin off from Qcad. It will do it but it's cumbersome to use purely with a mouse so I have made some suggestions as to how they might improve it. I might load Qcad but it isn't clear as to what remains after the 15mins of pro sample disappears.

John

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[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 08/05/2016 06:46:14:

John, that link doesn't seem to work for me. …

.

The adsabs link is working fine this morning, John

MichaelG.

[AjohnwParticipant @ajohnw51620]

As things tend to interrelate there doesn't seem to be much "do this" and all will be ok design information on Brocot escapements. It seems that there may be a list of ideal designs about some where but I can't find it. Best I could pull together is this.

What it really doesn't cover is the rake on the active face – the flat side of the tooth as other factors such as the number of teeth spanned and the length of the escapement arms alter it.

The best way to view that seems to be looking at what happens at the start of lock when the pendulum carries on swinging, Left hand pallet in the view on the top left. The rake at that point needs to be tangential to the curve of the pallet swing. As it's a curved path it can't be precisely replaced with a straight line so there is a need to play with escapement arm length and the number of teeth spanned to flatten the curve as much as possible.

It can work as the video clearly shows. The drop, 0.1 pitch clearance can be altered by rotating the pallets slightly and as De Carle points out the impulse angle can be reduced by moving the pallet up a touch but not by so much that it can run unlocked.

Well this is how I see if, If anyone knows better or can think of other aspects now would be the time to mention it.

When I ran through the design verbally I suspect I had the tooth pitch incorrect. The graphic design starts with twice the number of teeth sectors. One thought that struck me was what would happen if the flat raked side of the tooth was given a suitable rad but as most things will have been thought about long ago I suspect there is a catch.

John

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[James AlfordParticipant @jamesalford67616]

John,

Thank you for this information which I shall need to study carefully, I am working on my design of the escapement slowly and shall update this thread once I have something completed.

Regards,

James.

[Martin KyteParticipant @martinkyte99762]

AJohnW

Belated response to your question. The grasshopper does need to be 'powered' at all times. If you remove the drive both arms detach from the scape wheel and the train runs uncontrollably. Grasshopper escapements really need maintaining power mechanisms.

regards Martin

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