Gear layout options

Layout 1, the Minimalist Clock

Layout 2

Here we have 7 arbors. The escape wheel to minute layout is the same as above. The minute to hour is similar as above, but does not carry the clock power. The drum to minute is now an additional gear train and can be customized to fit the power reverve needed

At the left:

The escapement  with a 1 second pendulum and a 30 teeth escape wheel, the escape wheel does one rotation per minute and carry a second hand

In the middle:

The minute gear and hand. There is 60 minutes in an hour, so the ratio is 1/60 between the second and the minute hand. 

Then going down is the going train, with the drum on the lowest shft powering the clock

At the right:

The hour gear and hand, there a 1/12 ration between the hour and the minute arbor

It is worth noting that the hour hand can rotate on the minute arbor

Note: For this illustration to be to scale, the gears are module 1

The gears for the ration can be as follow

1/60 = 1/7.5 x 1/8 Gears teeth number can be: 12/90 and 12/96

1/12 = 1/4 x 1/3 Gears teeth number can be: 24/96 and 30/90 ( 24 + 96 = 30 + 90)

1/20 = 1/5 x 1/4 Gears teeth number can be: 20/100 and 25/100

The total ratio between the escape wheel and the hour gear is 1/60 x 1/20 = 1/1200

For one rotation of the drum, the escape wheel will rotate 1200 times that is 1200 minutes, that is 20 hours. (1200 / 60 = 20)

Another way to see it:

In 24 hours the escape wheel will do (24 hours x 60 minute in a hour) 24 x 60 = 1440 rotation

Since the ratio is 1/1200, 1440 rotation X 1/1200 = 1.2, the drum will do 1.2 rotation in 24 hours

With a drum of a diameter of 50 mm, the drop in 24 hours would be:

Drum diameter x Pi x number of rotation in 24 hours 

50 x 3.14 x 1.2 = 188.4 mm of drop for 24 hours. That is 1507 mm for 8 days

Layout 3

The main characteristique here is that the hands are outside the going train

The power is transmitted from the drum to the escape wheel by 4 set of gears with a 1/6 ratio. This allows for smaller wheels

The motion for the hands is picked up by an appropriate gear at a convenient location to get the 1/ 60 ratio

From the minute arbor, there is a 1/12 ratio to the hour hand

Escape wheel to Minute hand ratio: 1/6 x 1/6 x 3/5 = 1/60

The wheel between the pinion of 12 and the pinion of 20 can be omitted see below:

12/72 x 12/72 x 12/72 x 72/ 20  =   12 x 12 x 12 x 72 / 72 x 72 x 72 x 20 = 124416 / 7464960 = 1/60 

Is the same as  1/6 x 1/6 x 3/5 = 1/ 60  OR 12/72 x 12/72 x 12/20 = 12 x12 x12 / 72 x 72 x 20 = 1728 / 103680 = 1/60

Drum to escape wheel ratio: 1/6 x 1/6 x 1/6 x 1/6 = 1/1296

Number of drum rotation for 24 hours or 1440 minutes

Since the ratio is 1/1296, 1440 rotation X 1/1296 = 1.2, the drum will do 1.111 rotation in 24 hours

With the same 50 mm drum diameter, the drop in 24 hours will be: 50 x 3.14 x 1. 11 = 189 mm. That is 1511 mm for 8 days

Layout 4

Very similar to the one above, the difference is the addditon of a "pick up" arbor with 3 gears, z = 20, z = 39 and z = 6

There is the same 1/60 ratio from the escape wheel to the "pick up" arbor

From there, 1/1 (39/39) ratio to the minute hand and 1/12 (6/72) ration to the hour hand

Drum to escape wheel ratio: 1/6 x 1/6 x 1/6 x 1/6 = 1/1296

Number of drum rotation for 24 hours or 1440 minutes

Since the ratio is 1/1296, 1440 rotation X 1/1296 = 1.2, the drum will do 1.111 rotation in 24 hours

With the same 50 mm drum diameter, the drop in 24 hours will be: 50 x 3.14 x 1. 11 = 189 mm. That is 1511 mm for 8 days

And there is more variation

Types of gear and design

Involute gears

Cycloid gears