# Overall Gear Train Calcs Plus Hour Hand Question

#### devils4ever

##### Registered User
I'm in the process of designing a clock and I'm having trouble understanding the way the hour hand is concentric with the minute hand. Plus, I'd like someone to check my overall calculations. I'm using "Making Clocks" by Stan Bray as a reference. See below.

Great wheel is 96T, center wheel is 96T, third wheel is 90T. All pinions as 12T. The escapement wheel has 30T with a 39.14" long pendulum giving a 2 second period . So, the escapement wheel turns once per minute. The third wheel rotates at 90:12 = 7.5:1 ratio or 60 sec * 7.5 = 450 sec/rev. The center wheel rotates at 96:12 = 8:1 ratio = 450 sec/rev * 8 = 3600 sec/rev (once per hour). Finally, the great wheel rotates at 96:12 = 8:1 ratio = 3600 sec/rev * 8 = 28,800 sec/rev or 8 hrs/rev.

I think I got this part correct, but tell me if I'm wrong. All these wheels and pinions are vertical in the pic below.

Now, I'm not sure how to get the hour hand connected to this. I need to reduce the minute hand on the center wheel by a factor of 12. So, I'm thinking of using a 48:12 ratio and a 36:1 ratio to get this. The wheel on the right is 48T and mates with a 12T pinion on the center wheel. This wheel has a 12T pinion and mates with the 36T wheel. This gives the proper rate and direction of rotation, but obviously the bore in this wheel doesn't line up with the center wheel's bore because the 48T wheel has a difference pitch diameter than the 36T wheel.

How does this get resolved?

Thanks!

#### Richard Cedar

NAWCC Member
Devils4ever,

Welcome to the fascinating world of clock design and construction. I have reviewed your calculations for the tooth count for your "going train" (from escapement to winding wheel), and they look good to me. Note that from my experience, there does not appear to be a universal agreement on a wheel naming convention which can be confusing.

You ask a good question about the teeth count for the hour train to ensure that both the minute and hour hand arbors are concentric. The key is to ensure that the addition of the tooth count on the two mating wheels and pinions is the same. For example, suppose you choose to choose 12 teeth on the pinion that rotates with the minute hand and 48 teeth on what you call the "wheel to the right" giving a ratio of 4:1; then, you need to find tooth counts for the meshing wheel and pinion that give a ratio of 3:1 and add to (48+12) 60. The obvious choice is 45 teeth on the wheel and 15 teeth on the pinion, which also adds to 60. There are other ratios for these wheels and pinions that work, but I always use 48:12 and 45:15.

Happy to attempt to answer any other questions you have on clock design.

Richard Cedar
Cedar Clocks
www.CedarClocks.com

#### devils4ever

##### Registered User
Devils4ever,

Welcome to the fascinating world of clock design and construction. I have reviewed your calculations for the tooth count for your "going train" (from escapement to winding wheel), and they look good to me. Note that from my experience, there does not appear to be a universal agreement on a wheel naming convention which can be confusing.

You ask a good question about the teeth count for the hour train to ensure that both the minute and hour hand arbors are concentric. The key is to ensure that the addition of the tooth count on the two mating wheels and pinions is the same. For example, suppose you choose to choose 12 teeth on the pinion that rotates with the minute hand and 48 teeth on what you call the "wheel to the right" giving a ratio of 4:1; then, you need to find tooth counts for the meshing wheel and pinion that give a ratio of 3:1 and add to (48+12) 60. The obvious choice is 45 teeth on the wheel and 15 teeth on the pinion, which also adds to 60. There are other ratios for these wheels and pinions that work, but I always use 48:12 and 45:15.

Happy to attempt to answer any other questions you have on clock design.

Richard Cedar
Cedar Clocks
www.CedarClocks.com

Thanks, Richard.

I was using the terminology for the wheels from the book. I thought that was universal. From the bottom up, the author calls the wheels: great wheel, center wheel, 3rd wheel and escape wheel on top.

Interesting about the teeth counts. Yes, that makes sense. It's like solving simultaneous equations. First, the overall ratio has to be 12:1 and then the sum of each pair has to be equal to each other. I was thinking to myself that maybe changing the module of the gear would work. But, this solution is better. I can use the same module on all the gears.

#### John MacArthur

NAWCC Member
Cannon pinion 15 t, intermediate wheel 45 t. (3 to 1), intermediate pinion 12 t , hour pipe wheel 48 t (4 to 1). Centers are right, the module cutter for the 12 t. pinion will do a fine job on the 15 t. pinion. 3-to-1 plus 4-to-1 equals 12-to1. For the record, I use exactly that terminology, probably it's British. Best of luck, and keep us informed of your progress.
Johnny

#### devils4ever

##### Registered User
Okay, here's the updated version using 12:48 for the first reduction and 15:45 for the second reduction.

#### John MacArthur

NAWCC Member
Looks like you got it right. What module are you considering? Do you have a style of case in mind? When you get started, take plenty of pictures so we can watch your "build".

Johnny

#### devils4ever

##### Registered User
Module = 1. That seems to give the size of wheels that seem about right.

I'm thinking of an open type of style similar to what clickspring did. I haven't thought too much about the case yet.

I plan on starting slow and build some prototypes first. The escapement worries me the most. I'm starting with that.

#### John MacArthur

NAWCC Member
The escapement is the biggie, for sure, especially the Graham. Penman "Practical Clock Escapements, and Goodrich "The Modern Clock" both have pretty good material on Graham design/execution. It looks like you're using a capable CAD which helps a lot.
Johnny

#### devils4ever

##### Registered User

I drew this using "Drawing Cock and Watch Escapement: Distance Learning Course" by British Horological Institute as a guide.

#### devils4ever

##### Registered User
That book "Practical Clock Escapements" book by Penman looks like it's just what I need. Not inexpensive. Order placed! Thanks.

#### devils4ever

##### Registered User
Oops. I just realized I can't get 96 teeth on my dividing head. So, instead of using 96:12 ratio, I'm using 104/13 ratio. I can do 104 and 13 teeth on my dividing head.

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