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# How do I make a chain rotating around 2 gears complete a single rotation in exactly 60 seconds? Answered

Hello everyone,

I'd like to start off by declaring I am new to this website and have little understanding of technology as of yet. If my question has been answered before I apologize, but I haven't been able to find it in the forum.

I've recently started tinkering with 3D printing as a bit of a hobby and am trying to make items that are more than just odd looking. One of the things I'd like to create is the following clock found on youtube: http://www.youtube.com/watch?v=4S2DSteBLDY

Now this clock is made with Lego and its creator has labeled it as a 'proof of concept' as the 'lift' that delivers the ball, which should represent a minute, actually only counts ~55 seconds. For an actual clock I'd like it to have 60 seconds per minute and I am wondering if I can calulate the specs before I spend money on printed prototypes that dissapoint..

So using 2 Cogwheels/gears with a Chain that picks up a ball every 60 seconds (so a full chain rotation) based on an electric motor. I've found several 3-9v electric motors, but all seem to have rotations in the thousands whereas I'd expect to need like a few dozen rotations per minute(?). The clock I am trying to make is smaller than 20cm and I'd like for the chain to span a max 16cm in the final clock.

Summed up:
1) How do I decide the right Gear? size/teeth?
2) What Electric motor/power source would suit a very low amount of rotations?
3) How can I time the motor/gears to complete a cycle in exactly 1 minute?

Thanks in advance for taking a look ;)

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## Discussions

The standard for frequency regulation of AC power in the power grid (US) is 60 +/- 0.05 Hz.

Therefore, although using a synchronous motor does produce a line-correlated period (the motor tracks the variations in the line frequency), it does not technically produce an "exact" 60 second rotational period.

The link below shows the realities of the grid for a 50Hz country.http://wwwhome.cs.utwente.nl/~ptdeboer/misc/mains....

One would need to produce their own power system driven from a precisionclock to produce something close to exact.

Thanks a lot for the replies, all very helpfull! It makes life a lot easier knowing a bit of basic terminology - such as [stepper/synchronous motor]. With the calculation following later in this post I'm aiming at 3 RPM from the motor but when looking up Synchronous motors on Ebay they often have settings like 2,5-3 or 1-3 RPM. Does this mean their accuracy varies or can you set its RPM in that range? Also - is there such a thing as resistance/torque (if that's a correct label) affecting the RPM that I should be calculating for with something this small/these motors?

So I've made an attempt at understanding all the info shared and made a calculation (included in the paint file image) based on the rough setup I had in mind and how it would work out timewise. Any feedback about how well I understood this/ any possible errors spotted would be magical ^^

First an explanation on what I was thinking during the math:
I'm calculating that the finest settings for 3D printers available to me print with a 0,01cm/0,1mm max. accuracy, and the distance between the centers of the pulleys/gears can therefor only be printed to that accuracy. Since π hes endless decimals, the difference between π of the gears and the distance [centerpulley=>centerpulley] would result in a slight inaccuracy of the 60 second rotation (?).

4.01 as a diameter was the closest quick find that results in a π value that can be rounded up to 2 (printable) decimals for the distance between gears with a minimum loss in time accuracy. ((I later found that 3.88 as a diameter would cut the time loss to a third of this calculation = 10+ sec a day))

4.01π = 12,5978 = 12,60
12,60+12,60+12,5978 = 37,7978 = ~3RPM for a ~60 sec Cycle
http://www.ebay.com/bhp/3-rpm-motor

Difference in Time/Accuracy
A. (12,60+12,60+(4.01π))-((4,01π)*3) = 0,0044269182

B. (4,01π)*3 | 0,0044269182
-------------------------------------------
100% | 0,0351404446% inaccuracy in a rotation

C. 60(sec)*0,000351404446{%} = 0,02108426676 Sec/Min Too Slow

D. 0,02108426676*(60*24) {Minutes*Hrs} = 30,36 Sec/Day Too Slow

As I previously mentioned there are 2 decimal diameters that according to this calc. would result in more favorable π outcomes for an accurate 1 min cycle, so I am mainly interested in how applicable/correct the calculation is.

Finally: Also; a <10 sec/day inaccuracy could be acceptable perhaps, as I'd have to put a note with the clock that people have to adjust its time on a weekly basis. I may consider also making a more accurate version of the clock with just 1 very large gear so I can use a 1RPM motor as an alternative version.

Thanks again for thinking with me ;)

Use an ac syncronous motor like I used in my star tracker, its very accurate with its 1 rpm rate and uses mains power, plain and simple hookup.

https://www.instructables.com/id/Build-a-Motorized-...

Keep your gearing 1:1, ie both gears have the same diameter and number of teeth, then the top mechanism will always rotate at 1rpm too. So basically whatever gears and chain you have available, obviously smaller in line with your example video would be more practical.

Chain length passing per minute= Pi x pulley diameter x RPM.

Chain length = centre to centre distance of pulleys + Pi x Diameter of pulleys.

Most geared motors will have the output defined in RPM.

HOWEVER to be accurate your going to want a motor that is synchronised somehow.

A synchronous motor uses the mains frequency to keep time.

Other ways would be to use a stepper motor and a microprocessor to drive the motor this could be very accurate.

A standred motor could be used if it had a sensor to mark the start point. The every minuit it could be triggered to dleiver a ball. Microprocessor or even 555 timer could do this.