big D
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have any of you found a website that has some good plans for an escapement clock?
anything that happens happens.

anything that, in happening causes something else to happen, causes something else to happen.

anything that, in happening,causes itself to happen again, happens again.

it doesn't necessarily do it in chronological order, though.

bkim
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Does anyone have good ideas on how to make a non-electrical clock?

(No, I don't know of a website that has good plans for an escapement clock.)

But I looked at the history of clocks, and water clocks, pendulum clocks, and quartz oscillators come up. Yeah, I think the pendulum (escapement) clock would be the best bet out of the three.

Protestant
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There are Lego escapement videos on Youtube.

Matt77
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### It's About Time; Math Help

Hello all.
I'm in a ditch here so-to-say in finding out the mathematical truth that underlies all projects such as these. I'm trying to build a pendulum that has a period or [ time for one swing back and forth ] of 1.6 seconds. Although I could simply calibrate it with numerous attempts of comparisons in time, I'd rather actually learn how to find the answer mathematically. Every-time I conjure up some answer, it turns out to have the effect of about ~2-10 seconds off my goal at 1.6 second per Period. Can anyone tell my where my faults are made?

Here is what I have:
My Goal ~ 1.6 Seconds per Period
T= Period
L= Length
G= Gravitational acceleration (And yes, I'm using the accepted average of 9.81 m/sec²)
F= Frequency
n= pi

For my Frequency, since my time is already known, I am using the reciprocal (1/1.6) of my time. F= .625 Hz
Since I know both my frequency and time, all I need is the length. That's the problem.

I did the equation L = g/(4n²f²)
So Length= 9.81 m/sec²/ (4*9.869604401*.625) = .397584325 m/sec²
Which converts over to 39.75843246 cm as equal to L

To check my answers, I used these equations for frequency and time:
T= 2π√(L/g)
f= (1/2π)√g/L

I have more than triple checked myself. I've plugged in other number and estimates and tested them all out.
In the end, once I apply the length I obtain through math to my pendulum, the results are far from my predictions.
For the pendulum itself, I am using 7 pretty big washers and for the 'string' I have used both string and dental floss. I've reduced the friction at the fulcrum or top of the pendulum as much as possible. Really though none of these factors except perhaps friction should even effect the outcome! Does anyone see an error in my calculations?

EDIT- I seem to be getting closer! Dental Floss produces the least amount of friction and I am within .01~.2 away from exact timing but this is from calibration. From Math, I am getting closer to 3 seconds off the 'ticker' so to so. A last question, for the length of the 'string' of whatever you want to substitute; Do I include the half inch string that is attached to the hole in the washers? Or do I cut the length at the knot that proceeds to the top?

Like this: O>----- The "O" is the weight, which has a hole in the middle. The ">" is the part of the string that is ties into a knot around the washers (weight), and the "-----" is the main part of the string.

Matt77
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I think the reaction is more or less of a factor depending on how you look at it.

Like somebody in the first few posts mentioned, having a pendulum with a .5 second period would help a lot. The shorter string you have on the pendulum = the less time you have to react = the higher probability that your reaction will not only be taken into account, but have an effect on your educated guess timing. Once an almost perfect to perfect pendulum has been built, it will come down to skill and test scores.
I think almost anyone is capable of having a great reaction in the pendulum's period is 2 seconds or above. I like to focus on the weight and then use my peripheral vision the judge the point where the kinetic energy stops and the potential energy is at its highest.

fleet130
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### Re: It's About Time; Math Help

The length of the pendulum is measured from the "pivot" point to the center of mass of the pendulum.

If your "string" has a relative high mass, compared to the total mass of the pendulum, the center of mass of the pendulum could actually be "outside" of the "weight".

Edit: there are java applets available to demonstrate pendulums and do the calculations for you.
Information expressed here is solely the opinion of the author. Any similarity to that of the management or any official instrument is purely coincidental! Doing Science Olympiad since 1987!

Uncle Fester
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### Re: It's About Time; Math Help

I have a century-old clockmaking reference that makes a passing comment about "making sure the pendulum swings only through the cycloid" for best accuracy. Sorry, but you now know as much about "the cycloid" as I do.

Floss for pendulum? That could be your source of error-- pendulums need to be rigid, since at each end, the direct downwards pull of gravity creates a "bow" in flexible penduli. Since it's a RATIO between end bob and pendulum arm weight, pendulums tend to be rather heavy. I have an 1840 English railroad station clock that keeps near-perfect time (< 1 second/month), and the pendulum bob weighs over ten pounds.

does your pendulum swing freely until it dampens down to zero, or does it refresh with an escape mechanism? if the latter, the shape of the gears and escape is very specific in order to add energy, yet not lengthen the period.
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fleet130
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### Re: It's About Time; Math Help

From Galileo's Theory of the Pendulum was flawed but!
A Cycloid Curve is generated by a point on a circle's circumference rolling on a plane. See figures below. The cycloid posses interesting physical properties. It is brachistochronous and tautochronous: brachistochronous, because it represents the path completed in the shortest time between two points for a given type of motion (such as a fall under the effect of gravity); tautochronous, because a body made to oscillate along a cycloid will always take the same time to cover it, whatever the amplitude of the oscillation. Galileo (1564-1642) mistakenly believed circular oscillations to be tautochronous. The brachistochronous property of the cycloid was demonstrated by Jacques Bernoulli (1654-1705) in 1697, while Christiaan Huygens (1629-1695) proved its tautochronism in 1659.
HUH? What did he say?

Simply, the effective length of the pendulum is shortened in relation to how far the pendulum it is displaced from the center of it's swing. Clock escapements sometimes incorporate a "shorthand" implementation of this in which the arm of the pendulum consists of two separate pieces. The swing of the top, shorter part of the pendulum's arm, is limited so the "pivot" point of the pendulum changes when it swings beyond that point.

Edit: Here's an online book: Clock and Watch Escapement Mechanics I found using Google to search for "escapement design".
Information expressed here is solely the opinion of the author. Any similarity to that of the management or any official instrument is purely coincidental! Doing Science Olympiad since 1987!

binary010101
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### Re: It's About Time; Math Help

Wouldn't it be slightly easier to measure time using a sand clock? Not counting accurately would be a source of error in itself when you measure time using a pendulum, and the pendulum slows down over time due to friction.
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