# Designing a clock, stuck on gear reductions

• jasc15
In summary, the problem is to design a wooden pendulum clock with 2 pair of gears whose final ratio is 12:1, and the sum of the diameter of each pair are the same (so i had 0.4":1.6" and 0.5":1.5", where 0.4"+1.6" = 0.5"+1.5" = 3"). The first set of gears was trial-and-error, but I'm looking for an analytical approach since trial-and-error isn't working here. The ring driven by the pendulum (the escape wheel, which is directly attached to the seconds wheel, shown) is already turning once per minute (by having a pendulum

#### jasc15

A few weeks ago, I decided to challenge myself, and design a wooden pendulum clock. It's been loads of fun, especially the hard parts. One such hard part prompted me to make this thread.

Here is the problem:

Like any regular clock, The hour, minute and second hands are on the same axis, however, most wood clock kits I see don't include a second hand. Placing the hour and minute hand (reduction of 12:1) on the same axis wasn't too difficult. The challenge there was to have 2 pair of gears whose final ratio was 12:1, and the sum of the diameter of each pair were the same (so i had 0.4":1.6" and 0.5":1.5", where 0.4"+1.6" = 0.5"+1.5" = 3"). The problem for the second and minute hand is exactly the same, only with a 60:1 ratio. My approach with the first set was trial-and-error, but I'm looking for an analytical approach since trial-and-error isn't working here. I tried setting up simultaneous equations, but there are only 2 equations with 4 unknown gear diameters.

This problem has obviously been solved many moons ago, but I'm not sure what to call it so I can search for a solution.

Here's the clock so far. You can see the 12:1 gear set on the main face.

http://img189.imageshack.us/img189/8929/1009jc.jpg [Broken]

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Nice job!

Thanks!

Nice avatar.

I forgot to mention. Obviously, there are an infinite number of solutions to this problem, but the gear diameters can't just be any diameter. I've been using a diametric pitch of 10, so the diameters must be a multiple of 0.10". I suppose i could change the tooth pitch if necessary.

I'm afraid that I can't help with your problem, but I've got to tell you that you have one very cool project on the run. We expect photos when you're finished.

Well, I cheated and added several gears in between the second and minute hands. By doing that, I eliminated one constraint (having only 3 wheels) and was able to have the second and minute hands concentric, but it's a bit ugly since I had to add not one, but 2 additional gears (i had to keep an odd number so the direction of both hands was the same). It will work, but I would still rather solve this problem than force it.

http://img684.imageshack.us/img684/586/1055a.jpg [Broken]

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I probably miss something, but if the ring driven by the pendulum (I don't know clockmaker terminology, sorry) rotates n times per minute (with n being an integer) you should be able to get the seconds of that that ring, with a n times reduction gear. If not, then I don't understand how you reduce the ring speed to the minute hand speed in the first place :)

The ring driven by the pendulum (the escape wheel, which is directly attached to the seconds wheel, shown) is already turning once per minute (by having a pendulum with a 2 second period). Then there is a reduction of 60 from the seconds (escape) wheel to the minute wheel. It is simple, unless you want only one gear in between the two. That is the constraint I am having trouble with.

Here is a description of the problem with that constraint:

http://img267.imageshack.us/img267/5757/24332466.png [Broken]

w is my seconds wheel, and z is my minute wheel. x and y are fixed together and rotate at the same speed.

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Ah ok, so it is the initial 1:60 reduction you need. Do you only want to use spur gears (as shown) or would something like worm-gears or planet gears be acceptable?

Well, since I will be cutting the gear teeth out of plywood with a scroll saw, anything more complex than simple spur gears would probably be impossible.

Also, as I mentioned earlier, I solved this problem already for the 12:1 ratio between the minute and hour hands.

Well, you will probably have to fix something in order to arrive at a single result since your description allow solutions at all scales. If for instance you fix the distance of the reduction gear as d = w+y from the handle axis and fix the size of one of the gears, say w, you end up with

$$y = d - w$$
$$x = \frac{d}{1 + 60\frac{w}{d-w}}$$
$$z = x-d$$

If d and w are not useful for you as fixed values you should be able to find two other constraints that will lock the "size" of the problem for you.

It may also be, that you can introduce a constraint by fixing the (integer) number of tooth at one one gear and look for integer solution for y/w and z/x. If you want about the same reduction ratio for the two gears you could use 60 = 6*10 = 4*15 meaning, say y/w is 4, 6, 10 or 15 with z/x made to fit that value.

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whoa, i just stumbled on it. Trial and error took way too long, but it worked.

(108*100)/(10*18)=60

(10.8"*10.0")/(1.0"*1.8")=60

So I've solved the problem, but by brute force not the elegance of an analytical approach. So I am only 75% satisfied.

Here is an update:

I haven't started making it yet, but I have started to practice cutting gears out of some scrap plywood lying around. This is the 'finished' design. Any changes from this point will be minor.

[PLAIN]http://img260.imageshack.us/img260/8991/1071.png [Broken]

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Looks nice! You should consider documenting your build and sharing it on http://www.instructables.com/" [Broken].

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hmm, I had thought about documenting this on the web somewhere, but wasnt sure where. Ill certainly consider it, though I probably won't do it as a work in progress type of thing. It would be after its finished.

It looks very nicely done. May I ask what program you used to model it with and approximately how long it took?

I modeled everything using Solidworks and used the bundled Photoworks for the rendering you see above. The other images are just screen captures. I started designing less than 2 months ago, but it was during my lunchtime and after work so I couldn't say how many hours.

Dude, great job. Bravo!

Many months have passed, but I have some pics of the clock as it is now. It runs, however not in the configuration in these photos.

This is the first design seen in the images above, but it wouldn't run. Too much friction.
[PLAIN]http://img571.imageshack.us/img571/4638/img0023ov.jpg [Broken]

Here is the first revision to the design, and the wheels spin freely with a little impulse. There are some details to iron out, but I'm fairly confident that it will run.
[PLAIN]http://img51.imageshack.us/img51/6918/img0013dq.jpg [Broken]

[PLAIN]http://img828.imageshack.us/img828/6664/img0006sw.jpg [Broken]

[PLAIN]http://img828.imageshack.us/img828/5889/img0010ci.jpg [Broken]

And just in case you didn't believe me, here is a video.

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This is probably too late to be useful unless you still have problems with friction, but on many old clocks, the small gears were made from a "squirrel cage" of two small wheels with metal rods between them acting as the gear teeth.

This makes it possible to use high gear ratios like 10:1 and still have coarse pitch gear teeth. A "wire" pinion can have as few as 6 or 8 teeth and still work efficiently. The friction is more or less independent of the profile of the teeth on the large wheel, which is also useful.

If you had a suitable hardwood, you could maybe even make a "wire" pinion with wooden dowels instead of metal wire.

Hi - thanks to this thread, I was able to complete my electromagnet driven pendulum clock.

A small coil in the base "nudges" a magnet in the end of the pendulum rod, keeping everything running.

Video here:

I needed to implement the 60:1 gear ratio, so I used the 10,108,18,100 gears described here. It's been running successfully for 24 hours now.

Thanks,
Steve

www.stephenhobley.com

Here is a way to solve this problem, it's taken from norton book of design of machinery

#### Attachments

• clock problem.pdf
214.9 KB · Views: 896

## 1. How does gear reduction work in a clock?

Gear reduction in a clock is the process of using multiple gears of different sizes to slow down the rotation of the clock's hands. This is achieved by connecting the gears in a series, with the smaller gear rotating faster and the larger gear rotating slower.

## 2. What is the purpose of gear reduction in a clock?

The main purpose of gear reduction in a clock is to accurately measure and display the passage of time. By slowing down the rotation of the clock's hands, gear reduction allows for more precise timekeeping.

## 3. How do you determine the gear ratio for a clock's gear reduction?

The gear ratio for a clock's gear reduction is determined by the number of teeth on each gear. The ratio is calculated by dividing the number of teeth on the larger gear by the number of teeth on the smaller gear.

## 4. What factors should be considered when designing gear reductions for a clock?

When designing gear reductions for a clock, factors such as the desired speed of the clock's hands, the size and weight of the hands, and the accuracy of timekeeping should be taken into consideration. The gear ratio, as well as the material and quality of the gears, should also be considered.

## 5. How can gear reduction be used to change the speed of a clock's hands?

By using gears of different sizes and connecting them in a series, gear reduction can change the speed of a clock's hands. The larger gear will rotate slower, while the smaller gear will rotate faster, resulting in a slower overall speed for the clock's hands.