Building the pendulum demonstrator

"Couldn't help it come apart in my hands"

The story from many a youngster :-)

I tell the story in the video, but basically it has a very fiddly bearing in there. I got it working and glued it in place, but had to break the glue joint for the tear-down. Then I failed to fiddle it back into working again.

:(

Maybe I'll replace the ball bearing with a flexure, as I recommend in the video. Or, maybe I'll just put the damned thing on the shelf and cook up another video!!

Why not use a knife edge bearing like the big boys? A couple pieces of crossed wedge-shaped hardwood is easier to make than metal and less hazardous if you get a finger in the wrong place.

Mark L. Fergerson

Not sure who the "big boys" are, but some of the finest pendulum clocks made, including the Short clock use a flat spring for flexure. In fact, a later clock with essentially the same degree of accuracy and precision uses a three piece spring to correct for the squared term in the pendulum equation which helps to make the period constant for a small range of angle (the largest cause of error).

That's what I know about, and what I suggested in the video -- to use flat flex cable for the wiring and flexure both.

The design that I've seen uses a flexure operating between rollers machined to a cycloid -- IIRC this does the same correction as the three- spring thing that you're talking about.

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I was thinking of a school field trip when I saw the big Foucault pendulu m (that used to be?) at Griffith Park Observatory. The guide touted the kni fe-edge (which that pendulum didn't use) as having the lowest possible fric tion and damping available. Easiest to maintain and repair, too.

Maybe it has too *little* damping for precision clocks?

Mark L. Fergerson

The less damping the better. The most accurate time pieces in the world before quartz were pendulum clocks where the master pendulum was operating in a vacuum, driven by blipping an electromagnet and whose phase and amplitude was sensed by photosensors.

As far as the lowest-loss hinge, I'm not sure if a knife-edge is better than a flexure or not. I know that a well-designed flexure is one of the best ways to make a precision, limited-travel hinge. But then -- knife edges are supposed to be pretty cool, too.

With aluminum and (I think) steel, the loss is very low as long as you're not getting close to enough stress to permanently deform the part. Any energy put into the thing by bending it is given back as it relaxes.

I think the longevity of the knife edge leaves something to be desired.

I'm not familiar with those. The Shortt clock used a vacuum pendulum with a gravity lever for providing the impulse as well as the sync to an external pendulum which drove the clockworks. I believe that was still the penultimate clock when quartz was introduced. At least they were still in use in observatories..

The sharper the knife edge, the less friction, but the quicker the wear. As it rounds off it creates a curve that affects the center of rotation of the pendulum and therefore its period.

Aluminum springs???

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Flexures can be very good indeed--very low loss, very repeatable.

The two main residual problems with them AFAIK are both connected with the temperature coefficient of Young's modulus. The first is that the restoring force is a fairly strong function of temperature. There are materials (All oy 42 is one iirc) where this effect is much smaller, but they aren't the o nes with super low CTE.

The second is that the effective location of the hinge varies due to the st rength of the various materials having different tempcos, even if the whole thing is made of super-low CTE materials such as Super Invar or fused sili ca.

An Alloy-42 flexure would probably make a pretty good pendulum hinge.

Cheers

Phil Hobbs

There was a Scientific American article in the '80s that described a way of toughening clay-based ceramics using a polymer additive that made the microscopic flakes of the clay arrange themselves in stacks.

Their demo was a coil spring made of Portland cement. IIRC their material had about the fracture toughness of aluminum.

Pretty cool

Cheers

Phil Hobbs

I don't know that the restorative force varying would cause a change in the period. A temperature change would be slow so the pendulum swing would have many cycles to adjust. I believe that would the length of the swing would change with temperature, so the second order effect would kick in. That is why another clock was designed with three springs, two outside springs with one length and an inner spring with a slightly shorter length which bent differently counteracting the second order term in the period equation.

I'm not sure what parts you are talking about, the pendulum I expect rather than the spring. Yes, the pendulum must be constructed of good materials and kept at constant temperature as much as possible.

My understanding is that Invar has good thermal properties, but is not as stable as one might desire. The properties can change with time. I think they use other materials in combination to get a very low CTE overall.

The aluminum flexures I've seen were designed to deflect less than a degree. But aluminum is a very low-loss metal, and makes high-Q resonators (which can be a bitch sometimes, in control loops).

So, this is a very old memory, from a book that was loaned to me by a clock-fanatic friend of my dad's, when I was in my teens.

You support the pendulum from a strip of thin brass, and the strip is constrained between two drums (dowels? pins?). As it moves it wraps around one drum or the other, and stays straight from the drum to the pendulum rod.

The drums are a special shape (which may just be circular -- it has been about 40 years), which tends to correct for the period getting longer with increasing amplitude.

And -- that's what I know about that!

the period.

It does. For small amplitudes, the restoring force due to gravity is

F_g = -k theta

and the flexure stiffness contributes at the same order in theta.

Cheers

Phil Hobbs

I remember that too.

IIRC it's a cycloid, but when somebody famous like Huyghens tried it, the additional friction contribution made it worse rather than better. I think that Vannevar Bush / John Early Jackson article from SciAm has the story.

An old friend of mine, Hunt Curtis, was into clocks. He used to organize meetings, and said that he got some funny reactions when booking venues for horologists' meetings. ;)

Cheers

Phil Hobbs

This is only approximation, no? I seem to recall the formula uses a sin(theta) factor which is expanded as a power series and the second term becomes important for the more accurate clocks. That is why the amplitude of the swing is held as constant as possible.

d^2?/dt^2 = ?(g/L)sin ?

How approximate is this?

Too many toys and too much free time :)

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Now that you mention it, that was mentioned; the heavier pendulums don't use knife bearings because there isn't anything hard enough and cheap enoug h to make the edges out of that won't deform appreciably. For small ones as in the demo, I'd think synthetic ruby, like they used to make Tandy leathe r swivel knives out of, should last quite a while. Mohs hardness of 9, give or take a fraction. I used to see them at a surplus store in AZ but I woul dn't know where to look now. Maybe silicon carbide milling inserts? They're cheap and even harder.

Mark L. Fergerson