# How to design escapement mechanism and pendulum ?

#### Clockmaker 346

##### Registered User
Hello.

I start making my own design clock.
I fail many times and now I have working mechanism but...
Does not want to work accurately.

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#### Dick Feldman

##### Registered User

Yours is an interesting machine.

The function of the pendulum and escapement is to act as a regulator. Without a pendulum and escapement, the works will speed. A pendulum of a certain length will regulate the mechanism with a shorter pendulum allowing the mechanism to move faster. A longer pendulum the converse.

Your can read about the function and properties of the escapement and pendulum in The Modern Clock, by Ward Goodrich. The book was published over a hundred years ago.

I am curious about the odd shape of your escape wheel. It seems complicated compared to the verge you are using. I do not think you are getting the greatest mechanical advantage with the combination.

In the video below, note where the teeth land on the verge and note the impulse surfaces as the escape wheel pushes the verge. With this deadbeat escapement the escape wheel moves only in one direction because of the angle the teeth meet the verge surfaces.

Best Regards,

Dick

*******I also noticed that the pivot on the escape wheel is loose and jumping around. It needs a bushing!********

[/video]

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#### Ralph

NAWCC Member
I'd say your suspension and drive to the pendulum is loaded with friction. Even the way it is, if I understand the drawing, if the pivot point of the pendulum was changed to be on the same axis as the pivot of the anchor, it might have a chance of running. A pivot used in the suspending of the pendulum would not be recommended in my opinion. A knife edge or a suspension spring would be a better choice.

This is all assuming that I understand your video and drawing.

Ralph

#### Tinker Dwight

##### Registered User
It'd be better if you made the lock surfaces of the pallets deat,
as in a deadbeat. Draw a circle with its center on the anchors
arc.
Also, what is it driving that has so much flex sideways to allow
the impulse to wiggle sideways so much?
Fix those things and it should do better.
I might flatten the ends of the pallets to match
closer the ends of the clubs on the escapement.
Surprisingly, a pointed surface or a slightly larger
area have about the same amount of friction with
the same normal force on them. Making it a sharp
point just increase wear without reducing friction.
If you widened the inpulse face of the pallets to not
be a point, you might have to compensate the
clubs on the escapement a little.
Tinker Dwight

#### soaringjoy

##### Registered User
Welcome to the MB, and thanks for sharing your project.
You are not getting adaquate responses, so I'm moving this to the Clock Construction forum.

#### Clockmaker 346

##### Registered User
I do not understand> "one-half a tooth space" what is it?
How to found that on pictures ?
I drew a circle but I do not know why it has such dimensions?
Why there should be such angles?

There is no mathematical formula to calculate, no proportion.
I do not know why the wheel has to have 15 teeth.
Can I do 20,30, 40 How to that counts?

#### Tinker Dwight

##### Registered User
The half tooth makes sense when you think about it.
Each pallet only interfaces with a tooth for half a
tooth spacing and then goes to the next tooth.
This is true for recoils as well. Half tooth rotation of
the escapement on one side and the other half on the other.
The picture shows an extreme case of a dead beat.
Most dead beats are for larger number of teeth ( yes
you can use any number of teeth ). With a larger
number of teeth, the assemetry of the pallets is usually
ignored for ease of manufacture. Still, when there are just
a few teeth and you want them to push right, they are offset.
Tinker Dwight

#### Tinker Dwight

##### Registered User
I should clearify the statement on tooth count.
Tooth count on the escapement is part of the total
ratio between the pendulum and the minute hand.
I am a little surprised that you could build a clock
without knowing this??
lets say you wanted to do a 40 tooth escapement
and uses a pendulum with a 1 second beat. It would
do one tooth every 2 seconds or 80 seconds to do
one rotation. An hour has 3600 seconds. That means
the ratio of the gears between the minute hand and the
escapement need to be a 45:1 ratio. Other ratios could
be used with the 40 tooth escapement but would require
a different pendulum rate.
The angles of the impulse faces are what determines the
impulse angle of the pendulum. The general rule is 2 degrees.
This is a compromise. Smaller angles would be more accurate
but harder to do with slop in pivots and such.
Larger angles allow too much swing that increase circular
errors and loss do to air friction.
Tinker Dwight

#### harold bain

NAWCC Member
Deceased
You might want to read Ward Goodrich's The Modern Clock. Although written over 100 years ago, the information still applies as to how to design a clock escapement. With a dead beat escapement, the anchor should encompass 25 % of the teeth on the escapewheel for optimum performance.

#### Clockmaker 346

##### Registered User
Hello.

I make little mistake, this is counter clock movement on picture.

I make 30 teeth escapement wheel > teeth space = 360/30 = 12 degrees ( Pendlum lenght should be 100cm ?)
2,5 teeth space is 30 degrees.
Ratio of the gears between the minute hand and the escapement 60:1
And I cant change this. It would ruined symmetry and appearance.

Attached my old desingn. I cant only little( max 3-5mm) change those dimensions. Pendulum lenght 50 cm (escapement wheel should have 44 teeth ?)
My upside down escapement

I can make pendulum max lenght 50cm, so escapement wheel should have 44 teth ? > Did not take advantage of pushing
And that dont change gear ratio 60:1 ?

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#### harold bain

NAWCC Member
Deceased
The pendulum length is determined as much by the escapewheel tooth count as it is by the other gear tooth counts leading from the motion works to the escapewheel.

#### Tinker Dwight

##### Registered User
You pendulum length for the 30 tooth is about right. I calculate 99.3 cm ( to the center of the bob ).
For the 44 I get 46.2, not 50.
I also don't like your pallets. If they match what you have in your drawing, I think
you'll have way too much drop. It also looks like the tip spacing is wrong and
I went back and looked at the video. It is suppose to be a deadbeat
but isn't.
Tinker Dwight

#### Tinker Dwight

##### Registered User
One last thing. To minimize the friction, the pendulum should swing from
the center of the anchors pivot, not the escapement wheels. It should
have a longer crutch. It should be at least 15 or 20% of the pendulum
length or you'll not be able to keep the slop in pivots and slot on the
pendulum small enough.
Tinker Dwight

#### Tinker Dwight

##### Registered User
Since you expect to make a new escapement wheel to give you
a shorter pendulum, you need to change the size of the clubs
They should be 40% of the circumference spacing between the teeth if you intend
to keep the pointed pallet ends.They look to be less than 30%.
The lock surfaces should be dead ( following a circle centered on the
pivot of the anchor ).
Tinker Dwight

#### Clockmaker 346

##### Registered User
You pendulum length for the 30 tooth is about right. I calculate 99.3 cm ( to the center of the bob ).
For the 44 I get 46.2, not 50.
I also don't like your pallets.
Pallets is not even sketch.

For calculation I use
gary's wooden clocks-clock gear math
http://garysclocks.sawdustcorner.com/clock-gear-calculations-excel.zip

But I have more gears

Minute wheel has 60 teeth to pinion 15 tetht
next 60 > 15
and final 60 > 16
Ratio
4>1
4>1
3,75>1
Total 60:1
So for this Excel file I use 16>1 and 3,75>1
For the 44 I get 46.2, not 50. >> argh rounding error I need 42 teeth (Please confirm)
Gary use strange excel formula
=9,8*I16/(2*3,14159)*(I16/(2*3,14159))
Its 9,8*a/(2*pi)*(a/(2*pi)) >>> 2,45*a^2 / pi^2 more clear (or not ?)
a is pendulum period

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#### Tinker Dwight

##### Registered User
I use the fancy formula:

39.1" / ( BPS )^2 = Pendulum length.

A 60:1 ratio means the it will have a 1 BPS with a 30 tooth.

2 * 60 * 30 = 3600 BPH

3600 /3600 = 1 BPS.

A 44 tooth will have a BPH of

2 * 60 * 44 = 5280 BPH

5280 / 3600 = 1.4666... BPS

39.1 / ( 1.4666...) ^ 2 = 18.18 inches

18.18 * 2.54 = 46.2 cm.

Also, 39.1 = 9.8 / ( pi ) ^ 2 / 2.54

I should note that the period of a pendulum is 2 times the beat.
Tinker Dwight

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#### Clockmaker 346

##### Registered User
OK.

Finaly I use 45 tooth and 44,13 cm pendulum.

How to calculate tooth angle now mark as 12 and 24 degree?

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#### Tinker Dwight

##### Registered User
The 24 is measured from the tangent of the circle
from the arbor of the anchor, at the contact of the
entrance pallet.
The 12 degrees is added to that.
The picture shows a short span. You should try to
span 10.5 or 11.5 teeth.
By the way, it is OK to use the club end escapement wheel
but you need to use the proper pallet tips with it as well.
You need to split the normal pallet width in 2 and make
half for the pallet end and half for the escapement club.
Tinker Dwight

#### Clockmaker 346

##### Registered User
I do not understand some of the technical terms.
Can someone draw me a sketch and a simple calculation (angle marks as A,B,C,D)?
I use 45 tooth and 44,13 cm pendulum.

#### Tinker Dwight

##### Registered User
The angles C and D should be complimentary ( sum 180 ).
Draw radial lines from the center of the anchors arbor to the
edges of the impulse faces. the angle should be about 2 degrees
and must be equal on each side.
I hope that you don't expect to use those lock surfaces. That will
never work.
Tinker Dwight

#### Clockmaker 346

##### Registered User
I don't get it .

C & D should be 90 degres ? or example 40 + 50 ?

Or I make mistake and angles 78.65 should be 90 > that will change red wheel diameter.

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#### Tinker Dwight

##### Registered User
I'm not sure what I was talking about myself?
Also, you should design a more traditional
Graham deadbeat than this one. The lift angles
shown would not be normal for longer pendulum as well.
Typical would be 2 degrees and not 8.5 degrees.
Tinker Dwight

#### Clockmaker 346

##### Registered User
For drawing everything clear.... But for calculation not.
I make example from book for 30 teeth esc wheel but I use 45 teth (will not work)
The book does not contain mathematical formulas just a few examples ... I do not know how to calculate the lead angle, angle of of rest, for 45 teeth.

Graham ESC mechanic with Lift on the teeth and the pallet.

#### Tinker Dwight

##### Registered User
I'm not sure what all the lines on the drawing you have mean.
It doesn't look like you have the concept of each pallet
being in use for 1/2 tooth span though.
Tinker Dwight

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