Unusual Escapement

**LINK**

https://en.wikipedia.org/wiki/Riefler_escapement

I still don't see this Duncan - if the bob is stationary relative to the suspension point but the latter is moving, the bob has momentum at least as it passes through the mid position, and therefore kinetic energy - where does that go for it to be stationary when it reaches an extreme?

Re simulations - the article I wrote for HSN described these as well as the analysis.

The bob isn't stationary relative to the suspension point, it is swinging at its resonant frequency. The suspension point is moving relative to the rest of the world sinudoidally with the same amplitude but 180 degrees out of phase. Add the two together and the bob has no sideways motion relative to the rest of the world.

Back again, David.

Duncan and John's input, have added more food-for-thought!

Contemplating the effects of shifting the pendulum suspension horizontally in sync with its time constant can, to say the least, be tricky. The conical pendulum system demands even more concentration.

With reference to Michael’s Farcot/Carrier-Belleuse Conical Mystery Clock link …

**LINK**

… although difficult to follow; between 0:56 – 1:00 of the video, and also the wheel and its speed variation briefly visible between 1:10 – 1:14, it appears that the bob of the conical pendulum is tracing an ellipse. Since the contact point of the pendulum tip visibly slides back and forth a short distance along the ‘torque arm’, the effective torque transfer varies.

The suspension of the pendulum appears to be a ‘twin’ gimbal, similar in principle to Hook’s universal joint.

Q1. Does this form of suspension have little x/y influence?

Q2. Would it be safe to assume that the elliptical trace results from not only the varying torque, but also the earth’s rotation?

Sam

Edited By Sam Stones on 27/05/2022 23:35:48

Hello Sam,

Yes I did notice the wheel speed variation that you mention. I thought, that as the speed of the wheel is varying, the radius that the pendulum is describing would also vary. Therefor tracing an ellipse.

Or, there is something causing the pendulum to trace an ellipse which in turn slows the clock.

Or, 'radical thought' is there a normal escapement hidden inside and the conical pendulum is for show? 

David

Edited By David Noble on 28/05/2022 08:10:23

But "the rest of the world" - or the "fixed stars" - is what determines that the bob has mass, inertia, and momentum. If it's stationary relative to the these then when the suspension point moves it will exert a gravitational force on the bob (times the sine of the instantaneous angle) causing it to accelerate and start swinging at its resonant frequency with respect to "the rest of the world". You can make relative motions disappear by transforming to other reference frames for constant velocity but not when acceleration and gravity are concerned.

If the suspension point is a twin gimbal then the pendulum will have two resonant frequencies in orthogonal directions, rather like the "solar sidereal" clock I mentioned earlier. These will be very close together and it wouldn't be surprising if the pendulum swung in a slight ellipse as a result. I don't think this would be due to an "Foucault" effect, it's hard enough to show effects of the earth's rotation even with very long precision pendulums! But a fascinating lock - it seems to be the only example of a clock actually using a conical pendulum for timekeeping there is.

Also, at the end of the train there must be a wheel rotating at the speed of the pendulum driving the "pallet" - it's unlikely this will be dead true so there could easily be a varying drive torque every rotation. The short sequence showing the movement around 1:13 in aren't showing very even rotation either.

Edited By John Haine on 28/05/2022 12:23:15

By the way David, where is this clock, you said a "stately home", please?

Would it be Cliffe Hall, Keighley?

seeing as someone mentioned lego clock escapement I thought you might find this interesting.

**LINK**

Spot on John. We were in the area for a 1940s dance weekend in Haworth.

David

Pendulum works equally well in a speeding train. Momentum is all about relative velocity surely. If I'm travelling at 100 mph and a hammer is travelling at 101mph, both relative to whatever we decide is fixed, it won't hurt when it hits me. The Earth isn't a fixed point anyway, it's travelling 66,627 mph relative to the sun, which itself is travelling at 200 km/sec (sorry about the mixed units) relative to the galaxy centre. I'm on the lookout for a slow motor!

But we are talking about accelerations not uniform velocity. It's true that the earth is moving around the sun etc but these have negligible effects locally on something the size of the clock. In your thought experiment the suspension is oscillating above an initially stationary bob, and except when it's vertically above it it will exert a sideways force that will start it swinging. The suspension is local to the bob.

David, thanks for the confirmation! I'm planning a few days up north so will try to take in the museum. The only references to actual conical pendulum clocks I can find in HJ and the AHS journal are to ones by this French maker Farcot.

There is a useful Wikipedia page about Farcot : **LINK**

https://en.wikipedia.org/wiki/Eugène_Farcot

MichaelG.

**LINK**

Sorry Michael, your link got corrupted.

Edited By John Haine on 29/05/2022 11:03:54

John, we'll have to agree to differ, it's a fairly academic point anyway as the challenge of moving the suspension point at exactly the correct amplitude and frequency is not trivial.

.

Possibly because of the è 

Good job I also posted the text then

Thanks, John

MichaelG.

Edited By Michael Gilligan on 29/05/2022 15:26:28

Did anyone notice the picture of a clock with the message 'Watch later' ?

Tim

Well I swung by the museum yesterday on my way home from the Lakes and had a good look at the clock, which is really interesting. From some videos I took of the wire on the pivot that drives the pendulum through its finial the pendulum period seems to be 2 seconds though the pendulum must be at least 1.5 - 2 metres long. I suspect that there is a lot of mass in the pendulum rod and the globe near the bottom is not as massive as it looks, so the pendulum is distinctly "compound". Also being a conical type it will have a shorter period as its amplitude gets bigger. It was running about 5 minutes slow and the small number of staff seemed to have no knowledge about it. It certainly looked like the pendulum was running in an ellipse though hard to confirm as I couldn't get a camera angle reasonably normal to the plane of swing. Interesting that the pendulum was suspended through a rather rusty looking coil spring! The finial was quite darkly patinated except for the end where it bears on the driving wire, and interestingly that seemed to be polished by the friction as you can just about see in David's photo.  Yesterday it was running with the wire near the top of the polished part but the latter extended nearly to the point, so I wonder if there is a temperature effect?  Yesterday was very warm so the pendulum would be at its longest.

I've done some more reading up on what should really be called "spherical pendulums" and they are a lot more complicated than they look! They are very prone to swing in elliptical paths even if perfectly aligned and driven.  I think the way this works is that the clock movement applies a reasonably constant torque to the pendulum causing it to swing out further as it accelerates.  As it gets to its resonant frequency the amplitude gets rather large so the air resistance increases rapidly until the energy lost through drag equals the torque x speed, when it stabilises.  All kinds of things could cause inaccuracy, I'm not surprised these didn't catch on!

Edited By John Haine on 18/06/2022 18:28:08

Contributors have rightly pointed out that the period of a conical pendulum is dependant on the angle of the cone. However, the period of a plane pendulum is also dependant on the angle of swing, it's just that for small angles this error is very small. Using the formula for a conical pendulum I found in a previous post, and one for plane pendulum with greater amplitude found at large amp I have plotted the attached curve. I actually only used the first 2 terms in the equation, which is slightly cheating as the conical uses the cos() term. There isn't a lot to choose. I don't know how you control the amplitude of a conical pendulum, it feels like a trickier job than a normal escapement.

With distractions like this it's no wonder progress o real world stuff is slow

Edited By duncan webster on 20/06/2022 13:16:46

I might have attached the wrong picture but I'm away from the computer, wait till this evening before shooting me down in flames

Yup, wrong attachment, here's the right one. The blue line is the first three terms of the link as in

sqrt(1+a^2/16+a^4*11/3072) where a is the half amplitude

the red line is sqrt(cos(a))

the plane pendulum appears a lot better on this basis, so apart from novelty value why use conical?