Basic Clock Design

The pallets could span nearly 180 degrees of the wheel on a Brocot because the actual pallets stick out from the frame so that is completely behind the wheel.

Longer arms give a flatter curve to the path of the pallet.

Arm length can be used to set the impulse angle - longer reduces it. Also the pallet diameter, smaller = less.

As long arms take up more space spanning near 180 degrees of the wheel would reduce the space needed.

It all depends on the impulse angle really. That's the point made in the old modern clock book. For precision type pendulum impulse angles the arms tend to get rather long. It seems that graham dead beats are usually designed for a 2 degree or less impulse angle. Maybe 1.5 by the brave.

So one calc can be done easily. A 2 degree impulse angle with a 2mm dia pallet needs a pallet arm length of 1mm/tan 2 degrees = 28.6mm. Even 1.5 degrees would only need to be 38mm long. So much for the comment in the book. It doesn't sound too bad to me but is more than a Graham.

The Grahams also has lock = clearance for the pallets to engage. The spread sheet spec's it as an angle and then gives the clearance. It's 1 degree rotation of the escapes wheel and comes out as 0.2mm for a 38mm dia wheel with 30 T. The Brocot info gives 10% of the pallet dia but the angle that represents depends on the diameter of the wheel.. It seems that the Graham is sometimes reduced to 1/2 degree. This how much the wheel "jumps" before a pallet actually locks the wheel. We are engineers not clockmakers and can make things to thou's.

I think recoil means that the pendulum will receive some force in the wrong direction after the impulse. I'd guess it's just a little less efficient but if say the impulse angle is 2 degrees and the pendulum swings 3 it's not going to be much. Wild describes Brocot as dead beat. I'm wondering if a rad can be cut on the active face of the tooth but all show it straight. It wouldn't be hard to make a form tool with a rad to match the pallet swing. Maybe the rad would have to undercut otherwise I suspect some one would already have done it.

Just a thought - hope it's correct. The crutch driving the pendulum is I think generally longer than the pallet arms so there is a leverage effect going back to the teeth on the escape wheel. That will reduce as the arms get longer so less load on the teeth which should also reduce friction effects. So less force needed there to impulse the pendulum.

 I hope I don't have some crackpot idea of making the pallet arms a foot long with absolutely massive pallets and a huge wheel. Sure I wont but to me the longer arm aspect isn't really a disadvantage.

John

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Edited By Ajohnw on 11/05/2016 11:54:20

The problem with that is that you need a concave curve for the leading pallet to act on and a convex one for the trailing pallet. So a straight edge is the best compromise unless you are going to use two escape wheels, one for each pallet.

Russell.

Yes Russell I was seeing it as a one sided action. If I make any other mistakes please do point them out.

John

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I have been trying to draw a Brocot escapement from the information posted here and on a couple of other sites. Does the attached look about right?

The escape wheel is 50mm diameter. The pallet arms are 37mm in length. The pallet OD is 2.2mm.

Regards,

James.

very hard to see the important bit around the pallets. - the bobbles on the ends of the teeth don't help.

I hope that this is a bit clearer. Annoyingly, I cannot remove the small circles at the end of the teeth: it seems to be the way the software shows the join of the two lines that form the tooth. The dark blue and the brown semi-circles are th eoperating faces of the pallets.

Edited By James Alford on 16/05/2016 23:42:51

Edited By James Alford on 16/05/2016 23:43:47

Duplicate post  - deleted

Edited By James Alford on 16/05/2016 23:42:34

No the right hand one should have just finished impulsing. The photo I posted always shows them as they should be with the left locking. That effectively means that the "pendulum" isn't vertical. It's at the impulse angle.

I haven't tried drawing it yet. Busy cleaning out a garage and outhouse but it will probably be best to show the drop / clearance on the left hand locking side. That will then put the edge of the right hand pallet at the flat directly on top of the point of the tooth = impulse just finished.

John

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You have drawn the pallet diameter far too small. The diameter should be the escape wheel pitch (distance between tooth tips) less the desired drop. Typically the drop would be about 5% of the pitch.

For the escape wheel profile you have drawn the pivot point for the pallet frame is too far away.  It should be at a point where the tangents to the pitch circle at the locking points meet so that the pallets swing in the direction of the leading edge of the escape wheel teeth.

Russell.

Edited By Russell Eberhardt on 17/05/2016 08:02:29

The easiest way to draw it is to put the pallets in the correct position and then construct the arms. You just need the actual position of the tips of the teeth to do that. In other word the very top of the active flank which is just a point. The arms come out slightly tilted at the impulse angle as the arms have equal length and the pallet centres are on a rad struck from the arms pivot. Then draw a tangent to the to get the active flank of the teeth. That way the arms can be any length. How the tangent is actually drawn has to account for no single angle being ideal for left and right impulses / locking. They are drawn tangential to a circle with a diameter of 1/2 pitch on the pallet centres. For an odd tooth count spanned on the locking side as drawn the tangent is clockwise from the pallet centre. For even tooth count anticlock. Drawn from the wheel centre touching the 1/2 pitch diameter circles.

The photo I posted shows how it's constructed, the middle 2 diagrams on the left. Drop / clearance is neglected at that point and the tooth pitch is used instead of the pallet diameter. Well that is the instructions. The ticks in the diagram are at 1/2 the tooth pitch

This is all done by hand at a scale of 10:1 or by CAD but to me the following calculations could be used to get at the actual dimensions from a simple sketch but it suggests doing this after drawing it out.

The instructions are rather weak on setting actual pallet diameter and position. That is what the lower left diagram is for - to actually calculate them. The clue there is that angle Y wont be twice angle Z as Z includes the impulse angle from the pallet. There is a need to think about what has happened as they are usually drawn. The pallet on the right has just allowed the pendulum to be impulsed and the wheel has turned clockwise. As soon as this impulse pallet clears the wheel will "jump" clockwise to take up the clearance on the other pallet. That will add to the impulse angle. To be honest I suspect books and other sources on designing things like this are sometimes just repeating what they have been told or have read somewhere and the same thing gets repeated over and over again with various modifications which may or may not be a good idea. What seems to be going on in this case is that the graphical method is aimed at getting dimensions on paper at 10x size that can then be transferred to scribers and a centre punch etc on metal. There is a suggestion that if higher precision is needed use the calculations. Done that way the drawing is just needed to get a grip on the maths needed. In this case the drop needs to be enough to account for the precision that the parts can be made to - not some arbitrary fraction of the tooth pitch that will account for the accuracy of a purely graphical method. Pallet diameter and position can be achieved to a few thou. The other error will be the accuracy of the divisions when the wheel is cut. So draw it out as it should be some how and do some sums. As shown the right hand pallet will be where it usually is but the left hand one will be a little clear of the flank of the tooth which just means that the that arm will be at a slightly different angle. The pivots of the 2 parts will always be on a straight line. Angling that may help when using cad. It's probably easier than trying to rotate the wheel.

I have looked at using a cad package for this but there seems to be some difficulty getting things where needed. Paper and pencil may be easier.

All easier done than said but I hope that all makes sense.

John

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Maybe this will help with the flank tangents

I can sort of see how this fits in with a 10x graphical construction as the tangents are tooth pitch based not dia of the pins but for best accuracy I suspect that the pin diameter needs accounting for as well. Not sure. One other way of getting at the angle is to look at each pallet at lock. The tangent angles will differ so take the mean, The construction method might do this automatically or the 1/2 pitch dia circles might just be a rule of thumb.

John

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Well, I am trying again to draw the escapement and have concluded that I am being dense.

The sketch below shows my progress so far. The dimensions are:

OD of wheel 25.4mm

OD of pallet 4.8mm

I think that the pallets are in the right position, and I have drawn the tangents from the centre to the edge of a circle which is 2.4mm OD.

However, I am not sure what to do now with these tangents. Could someone please clarify before I move onto the arms?

Regards,

James.

Edited By James Alford on 18/05/2016 22:56:13

Edited By James Alford on 18/05/2016 23:23:34

Perhaps this will help:

Russell.

I have assumed that these tangents are parallel to the flank angle of the teeth. Otherwise why bother drawing them. They must have some purpose.

Maybe Russell will tell us if that is correct, or what they are parallel to.

I can see the need to average the perfect angle for the left and right pallets when they are in lock as no single angle will be correct for both.

Just add - it looks like solvespace may be capable of drawing it and rotating the wheel as needed. I have a mental block concerning sketching things roughly and adding dimensions later though.

John

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Edited By Ajohnw on 19/05/2016 10:36:30

Thank you, Russell and John.

Using the tangent of this circle to set the angle of the teeth makes sense. I confess that I seem to recall reading somewhere or other that the "working" face of the teeth was parallel to a diameter line of the escape wheel, but I cannot find this information again, so assume that I was wrong.

Regards,

JAmes.

I'm still hoping Russell or some one can confirm this.

I suspect that if I manage to draw it in a cad package I will draw 2 view to see the optimum angle for either pallet when at lock. As Russell pointed out earlier it is possible to use 2 wheel with one pallet working on one and the other on the other wheel. Not that I would do this but ...............

John

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I can imagine a setup that uses one pallet moving between two adjacent wheels. I wonder if it would work?

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I think it would almost certainly 'run away', Neil

MichaelG.

O.K. In the common case that the working faces of the escape wheel are truly radial (unlike James' drawing) the tangents to the circle at the locking point meet at the pivot point of the pallet frame. Thus, for small movements of the pallets they slide along the tooth face with no movement of the tooth (dead beat). They are perpendicular to the working face of the tooth.

Sometimes it is convenient to move the pivot point closer to the wheel and the tooth can be undercut to maintain that perpendicular. In that case the lines drawn are, of course, no longer tangents.

John, Whatever the angle of the tooth it will be parallel to a diameter of the wheel. Was there a particular diameter line you were thinking of?

Russell.