Another Arduino-controlled pendulum clock

[Joseph Noci 1Participant @josephnoci1]

Perhaps the Smart Folk here can assist..

If the period of the pendulum depends only on the length, what is the physics behind correcting the pendulum timing by pulsing more or less often, or regularly with more or less energy?

Does the pulse not just add to the current velocity , 'speeding' the pendulum up?

If that is all that happens, then according to conservation of energy, the pendulum should just go higher since kinetic E has increased. If it goes higher, it will accelerate more on the downstroke, due to the increased potential E – so the pendulum swings faster now, but also higher, so the period remains the same.

What have we actually changed here, other than total mechanical energy?

Since some objectives appear to be to alter the timing electronically, or alter the period electronically, so as to be able to compensate for environmental changes – How does retarding or advancing the pulse change the pendulum period in order to 'correct' its time if only length does this?

Edited By Joseph Noci 1 on 06/09/2023 15:07:01

[John HaineParticipant @johnhaine32865]

Ah, Joe, deeper waters here…

A pendulum's period depends on its amplitude, the fractional rate being given by (angle^2)/16 where angle is in radians. For small angles this is nearly negligible but gets more significant as the amplitude gets larger. Remember that 1s per day is nigh on 1 in 100,000. A pendulum designed for exactly 1 second period would lose 1 second per day at an amplitude of only 0.7 degrees. This is why we want to control the amplitude. Traditional "regulators" also use rather small swings because that also reduces the sensitivity because of the square law.  This is called "circular deviation" or sometimes "circular error". (CD)

If you impulse the pendulum exactly at the centre of its swing that has no effect on its period. If you apply the impulse early (or advance the phase of your sine wave drive) it makes the pendulum period slightly less; if late it makes it longer.  This is "escapement deviation". (ED)  Its magnitude depends on the phase shift and pendulum Q and for small errors the fractional change is (phase error)/2Q. (Strictly tan(phase error)/2Q.)

What one generally does is control the amplitude to keep it constant so the CD is constant and can be "adjusted out".  Likewise one tries to keep the impulse phase constant so ED can be adjusted out.

Many clocks have non-central impulses and when the impulse strength changes (for example because the spring unwinds), the amplitude reduces so it runs faster and the phase angle changes.  If the impulse lags and gets later it slows the pendulum down and if you're lucky the two will cancel out.  

The ultimate is Clock B which plays these effects off against Q changes due to varying barometric pressure to compensate for that too.

There have been designs that deliberately change the amplitude to adjust the clock, event to regulate it to an external reference.  A problem with this is that the amplitude, and hence period, responds only slowly to impulse changes so the loop is very slow.

What a few people (well certainly me and Dave I think) are proposing is to have the pendulum running as stably as possible with controlled amplitude (and in has case eventually in a vacuum), accumulate the phase of the pendulum then digitally correct this "post hoc" based on environmental observations before displaying the "time".

 

Edited By John Haine on 06/09/2023 15:44:59

Edited By John Haine on 06/09/2023 16:21:52

[duncan webster 1Participant @duncanwebster1]

I'm sure cleverer people than me will be along, but here's my take on it. Period depends strongly on length, and to a smaller degree on amplitude. If you keep the amplitude constant, then you only (only?) need worry about length. Clocks have been made where the amplitude is deliberately varied to keep the balance wheel in the case of which I'm aware in synch with a processor driven by a xtal. This to my mind is cheating!

Pulsing the pendulum also changes it's period, theory says the minimum disturbance is by pulsing right at the centre. Mine pulses as the pendulum approaches centre, Fedchenko type pulse just after, by repulsion

Edited By duncan webster on 06/09/2023 15:34:21

[Joseph Noci 1Participant @josephnoci1]

Posted by John Haine on 06/09/2023 15:29:30:

Ah, Joe, deeper waters here…

If you impulse the pendulum exactly at the centre of its swing that has no effect on its period. If you apply the impulse early (or advance the phase of your sine wave drive) it makes the pendulum period slightly less; if late it makes it longer. This is "escapement deviation". (ED) Its magnitude depends on the phase shift and pendulum Q and for small errors the fractional change is phase/2Q.

…………………..

There have been designs that deliberately change the amplitude to adjust the clock, event to regulate it to an external reference. A problem with this is that the amplitude, and hence period, responds only slowly to impulse changes so the loop is very slow.

………………………..

What a few people (well certainly me and Dave I think) are proposing is to have the pendulum running as stably as possible with controlled amplitude (and in has case eventually in a vacuum), accumulate the phase of the pendulum then digitally correct this "post hoc" based on environmental observations before displaying the "time".

Thanks John:

I wrestle with the distinction between a few of your statements..

If you impulse the pendulum exactly at the centre of its swing that has no effect on its period

I presume this holds only if the impulse amplitude is a constant – will higher impulse amplitude decrease the period? Velocity is max at this point and a higher impulse will add to that? Or is this as I first stated – that all we are then doing is increasing the swing, not the period?

Impulsing Early – Is that before BDC, and late , after BDC?

Why would a late impulse increase the period? Are we not increasing the velocity just after the point the bob begins slowing down?

There have been designs that deliberately change the amplitude to adjust the clock, event to regulate it to an external reference. A problem with this is that the amplitude, and hence period, responds only slowly to impulse changes so the loop is very slow.

Intuitively I grasp why the response is slow in this mode – Reducing the pulse energy input does not in itself slow the pendulum – it has to run itself down – but pulsing with higher amplitude – would that not increase the pendulum amplitude in the same way and at the same rate as a phase shifted pulse ( the 'early pulse' )

What a few people (well certainly me and Dave I think) are proposing is to have the pendulum running as stably as possible with controlled amplitude (and in has case eventually in a vacuum), accumulate the phase of the pendulum then digitally correct this "post hoc" based on environmental observations before displaying the "time".

If i understand this correctly, then this is what I am trying to do as well…..Use my amplitude control loop to try fix the amplitude as hard as possible, use the adjusters to get close to 2sec at an environmental 'norm' (room temp, midway Baro reading, etc) and then let it run – the shift from that timing reference is then measured and used to correct computer time ( not pendulum timing) against the environmental changes.

What worries me though is that from what you say, it would seem I am would be wasting my time trying to perform timing adjustments on the pendulum, such as your early/late impulses would do, by changing only the amplitude of my sine wave drive, and not its phase….

edit – smileys…

Edited By Joseph Noci 1 on 06/09/2023 16:15:17

[SillyOldDufferModerator @sillyoldduffer]

Now the clever people have answered, here's my take.

The curve followed by a pendulum bob isn't isochronous, so its period varies with amplitude. The bob's curve is nearly isochronous at small amplitudes, so most pendulum clocks operate with amplitude less than 5°. This reduces amplitude error considerably.

I can use the effect to decide when more energy is needed. Measuring period with high resolution allows small changes of amplitude to be detected, and used to govern impulses. The goal is to keep amplitude constant whilst minimising any disturbance of the bob. (Over impulsing is causes many problems!) I've tried two strategies:

• Impulsing on every beat, but reducing impulse power until the pendulum just runs reliably. Graphing period at high resolution shows both over and under-impulsing. I have not found it possible to eliminate impulse disturbance entirely.
• Impulsing whenever amplitude drops below a set value. Allowing the pendulum to swing freely for 'n' beats minimises impulse disturbance, but the cost is the extra disturbance caused by the powerful impulse needed to increase amplitude enough to beat free 'n' times.

My first clock ran best with impulse every beat. The second runs better with n about 3. My hypothesis is that:

• the first clock needed plenty of energy to keep it going because it was low Q and crudely built. Amplitude fell so quickly that the best strategy was to impulse it little and often.
• the current clock being better made and higher Q loses amplitude relatively slowly, allowing it to maintain a governed amplitude with less frequent pulses. The best strategy is a moderately powerful impulse every so often.

If I'm right there is no instantly obvious physical law because how best to achieve constant amplitude with minimum disturbance depends on how the pendulum is constructed and what it is running in. A pendulum suspended in air inside a tight box is very different to the same pendulum swinging in a hard vacuum. I guess a well-made pendulum in a vacuum will perform better with 'n' beats per impulse, whilst a competently made pendulum swinging in air might do better with 1 impulse per beat.

I have a notion of applying graduated impulses. When more energy is needed, do a succession of weak impulses rather than one big one. Not done it yet – I'm already up to my armpits in pendulum problems!

Dave

[Joseph Noci 1Participant @josephnoci1]

Posted by SillyOldDuffer on 06/09/2023 16:45:48:

Now the clever people have answered, here's my take.

The curve followed by a pendulum bob isn't isochronous, so its period varies with amplitude. The bob's curve is nearly isochronous at small amplitudes, so most pendulum clocks operate with amplitude less than 5°. This reduces amplitude error considerably.

I can use the effect to decide when more energy is needed. Measuring period with high resolution allows small changes of amplitude to be detected, and used to govern impulses. The goal is to keep amplitude constant whilst minimising any disturbance of the bob.

But you are trying to keep amplitude constant by varying the period which you said will not vary if length is constant, and if the swing angle is small…

Your method would seem to reduce to spreading impulse energy over time to get the required amount of impetus, ie, 1 pulse every few swings..and not where the impulse is applied.

This does not seem to be in line with John's concept of changing phase of the pulse, ie, its position relative to the bob zero. Will you concept therefore also suffer from the slow response time issue? In fact you confirm that – 

I can use the effect to decide when more energy is needed

and not where in time energy is needed…

 

Edited By Joseph Noci 1 on 06/09/2023 16:58:47

[John HaineParticipant @johnhaine32865]

Posted by Joseph Noci 1 on 06/09/2023 16:13:19:

Posted by John Haine on 06/09/2023 15:29:30:

Ah, Joe, deeper waters here…

………………………..

Thanks John:

I wrestle with the distinction between a few of your statements..

If you impulse the pendulum exactly at the centre of its swing that has no effect on its period

I presume this holds only if the impulse amplitude is a constant – will higher impulse amplitude decrease the period? Velocity is max at this point and a higher impulse will add to that? Or is this as I first stated – that all we are then doing is increasing the swing, not the period?

Sorry I wasn't clear. Impulsing at the centre does not change the pendulum's phase instantaneously. If the impulse is just strong enough to make up for the lost energy then there is no net change to period.

Impulsing Early – Is that before BDC, and late , after BDC?

Correct.

Why would a late impulse increase the period? Are we not increasing the velocity just after the point the bob begins slowing down?

Again, if we are impulsing each period and just replacing the lost energy, the late impulse causes a phase jump that lengthens the period. Similarly an impulse that is early shortens the period.

There have been designs that deliberately change the amplitude to adjust the clock, event to regulate it to an external reference. A problem with this is that the amplitude, and hence period, responds only slowly to impulse changes so the loop is very slow.

Intuitively I grasp why the response is slow in this mode – Reducing the pulse energy input does not in itself slow the pendulum – it has to run itself down – but pulsing with higher amplitude – would that not increase the pendulum amplitude in the same way and at the same rate as a phase shifted pulse ( the 'early pulse' )

No, the same time constant determined by Q applies, and anyway the impulse will be applied at BDC.

What a few people (well certainly me and Dave I think) are proposing is to have the pendulum running as stably as possible with controlled amplitude (and in has case eventually in a vacuum), accumulate the phase of the pendulum then digitally correct this "post hoc" based on environmental observations before displaying the "time".

If i understand this correctly, then this is what I am trying to do as well…..Use my amplitude control loop to try fix the amplitude as hard as possible, use the adjusters to get close to 2sec at an environmental 'norm' (room temp, midway Baro reading, etc) and then let it run – the shift from that timing reference is then measured and used to correct computer time ( not pendulum timing) against the environmental changes.

What worries me though is that from what you say, it would seem I am would be wasting my time trying to perform timing adjustments on the pendulum, such as your early/late impulses would do, by changing only the amplitude of my sine wave drive, and not its phase….

You could use amplitude to adjust its mean rate. But my approach is to have the pendulum deliberately running fast and not to adjust it to a particular period, and deal with the "rating" in code.

edit – smileys…

Edited By Joseph Noci 1 on 06/09/2023 16:15:17

[Joseph Noci 1Participant @josephnoci1]

Posted by John Haine on 06/09/2023 19:07:59:

Posted by Joseph Noci 1 on 06/09/2023 16:13:19:

Posted by John Haine on 06/09/2023 15:29:30:

You could use amplitude to adjust its mean rate. But my approach is to have the pendulum deliberately running fast and not to adjust it to a particular period, and deal with the "rating" in code.

A little clearer..Thanks.

Why running fast, as opposed to slower, or nearly correct?

[John HaineParticipant @johnhaine32865]

So I only need to skip pendulum pulses, just seemed easier.

[duncan webster 1Participant @duncanwebster1]

I've linked this in another post, but it explains large amplitude penduli, and does the sums for you

My clock is set to run deliberately slow, as I have a button which advances the 30 sec slave every second to set it right. But I'm not a pendulista, as long as it keeps decent time I'm happy

[SillyOldDufferModerator @sillyoldduffer]

Posted by Joseph Noci 1 on 06/09/2023 16:56:24:

Posted by SillyOldDuffer on 06/09/2023 16:45:48:

Now the clever people have answered, here's my take.

The curve followed by a pendulum bob isn't isochronous, so its period varies with amplitude. The bob's curve is nearly isochronous at small amplitudes, so most pendulum clocks operate with amplitude less than 5°. This reduces amplitude error considerably.

I can use the effect to decide when more energy is needed. Measuring period with high resolution allows small changes of amplitude to be detected, and used to govern impulses. The goal is to keep amplitude constant whilst minimising any disturbance of the bob.

But you are trying to keep amplitude constant by varying the period which you said will not vary if length is constant, and if the swing angle is small…

Your method would seem to reduce to spreading impulse energy over time to get the required amount of impetus, ie, 1 pulse every few swings..and not where the impulse is applied.

This does not seem to be in line with John's concept of changing phase of the pulse, ie, its position relative to the bob zero. Will you concept therefore also suffer from the slow response time issue? In fact you confirm that –

I can use the effect to decide when more energy is needed

and not where in time energy is needed…

My electromagnet is mounted side on so I can pulse the bob at any point after the beam is broken. I had the idea that pulsing the electromagnet as the bob approached top of swing (max amplitude) would lift the bob a little higher by it flying into an area of apparently reduced gravity, thus reducing the jolt. As the strength of a magnetic field weakens rapidly with distance, I thought the grab would accelerate the bob softly.

However, George Airey did the maths about 200 years ago and showed least disturbance occurs when the bob is travelling at it's fastest, ie when it passes bottom dead centre. So I measure amplitude, and if it is below an experimentally determined value, I pulse the magnet on the next beam break, with the beam set to trigger at BDC*. Pulse when is easy, I don't know about a timing a sinusoid to energise a bob..

Dave

Due to a build error, the electromagnet fires after BDC at the moment. Hopefully explains why my pendulum is noisy…

[KitwnParticipant @kitwn]

It's very interesting to see this thread burst into life again after a couple of years.
My own developments over the last couple of years have been to greatly simplify the control of the wooden clock. It now uses an Arduino which makes experimenting much easier and allows me to include my interest in writing software in this project.

The original design had three magnets on the rim of the pendulum and a hall sensor on the frame so that measuring the delay between them passing the sensor could measure the linear velocity of the pendulum which is related to the amplitude of the swing. This becomes unnecessary in the new design, who's software has become simpler and simpler over time as I realised what is, and is not, necessary for good control of the clock.

The basic control is as described in my earlier post but the software parameters can more easily be altered to suit the mechanics of the clock and it's response time and variation around exact timing. The Arduino proves a serial output of the pendulum period and relative timing to the 1PPS pulses which is interesting and allows easy fine tuning of the pendulum weight and software parameters. Once settled, the period drifts around +- 5mS and the timing relative to the 1PPS varies about +- 20mS.

My clock is all wood and the mechanism is driven by the pendulum rather than the other way round in more traditional designs, but the basic measurement principle could be used to regulate many types of clock by suitable means.

I know some people consider locking a pendulum to a crystal as 'cheating' but we make these machines as a hobby, don't we? Something for our own amusement, designed to exercise our minds and utilise the particular range of knowledge and skills we have each acquired. It's only cheating if you misrepresent your creation as something it is not by, for example, entering it in a competition for purely mechanically timed machines.

A more reecnt version of the design can be seen at the link below. I'm currently working on a bigger version made from Tasmanian hardwoods.
https://vimeo.com/614929644

[John HaineParticipant @johnhaine32865]

Just as a test a photo of the pendulum bob and sensors

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