lock physics/engineering question

[westbj2]

Perhaps some of the engineering types out there can comment on this question.
On a lock using tumbler arm/link/mainspring design, one can feel the "let-off" while moving the cock or hammer rearward.  A number of variables are at play here but, my question is only about one of them.
Assume there are 3 identical locks. Also assume lock X has a dimension of say .400" from the center of the tumbler axle to the center of the swivel/link connection.  Lock Y has a distance of .450" and lock Z has a distance of .500".   If one were to measure the pressure needed to move the hammer or cock of these 3 locks with only this change and then plot the results,  would the resulting plot line be straight or curved? If curved, in which direction?
Thanks.
Jim Westberg

[flintriflesmith]

Jim,
I'm not an engineer but I have spent some time thinking about this issue and am very interested to see the responses. thanks for posting the question for discussion!
Gary

[Tom Currie]

With a practical understand of mechanics I would state that the difference in pressure required to move the cock on locks Y and Z , would be greater than the difference in locks x and Y. My reasoning being that changing the connecting point  distance away from tumbler axis would  exponential require more pressure to compress the spring not a linear increase. It's the same idea changing the sear to pivot point on a trigger.

I believe we see this as we cock any lock , being that the point of contact distance between the mainspring and tumbler axis is decreasing as we pull back therefore making it easier the further back we pull the cock.

I know it's early and the caffiene hasn't had it's full affect yet but I think thats a pretty good educated guess

 

[omark]

the one with .400 distance should be the easiest to cock, but would have to travel the farthest at the hammer, as there would be the most leverage on the hammer.and i believe the plotted course would be slightly curved.  jfbo,  (just a farm boys opinion)  mark

[Acer Saccharum]

You got me there, Jim, but I'd have to say that the the graph would be a curve, since rarely is anything in nature linear.

As the distance from center of tumbler to pivot increases, with all other things being the same, the force required to move the cock back will increase.

'Where' in the stroke the pull to full cock gets easier is a matter of geometry and leverage, no matter how long the distance is.

That distance directly affects power and speed of stroke, and I think, sitting on my butt, that they are inversely proportional, to use big words. The more power you develop, you are reducing the speed of the downstroke. To increase the speed, shorten the center distance from pivot to tumbler, but you lose power.

There must be a happy medium somewhere in that range.

[Dale Campbell]

Yes, interesting question.  I don't have my physics text with me (silly me), and its been a few dec... years, however, as a first pass:

Assume the downward force of the spring is constant (it isn't, as the tumbler to spring distance is increases, the spring will be deflected differently), the tumbler and cock weight are constant, and since the distance the tumbler moves is constant (full cock to hammer stop) in all three cases, then:

The only variable is the change in radius.  Since the radius increases linearly, the work will increase linearly.  This work is the physical product torque, which equals the radius times the force.

Extra, real world stuff might push the behavior into non-linear.  For instance, the extra force needed to overcome the longer radius of the tumbler will slow the initial movement of the flint.

In the interest of full disclosure, I checked this stuff on Wikipedia under Work (physics) and torque.

However, for real world application, we need a metallurgist like Jim Kibler, since the difference in spring deflection will have an effect.

[Bob Roller]

NONE of the fine mid 19th century British locks have a short tumbler arm OR a stiff mainspring and anyone,even the inexperienced can feel the difference. The .400 distance between the center of the tumbler and the end of the tumbler arm is an absurdity unless we are thinking of a miniature lock.
I have just finished the 10th Twigg lock and it has a long,limber and preloaded mainspring with a .625 center distance between the center of the tumbler and the tumbler arm and this is a very smooth and very fast big lock.I have also finished a Ketland using the superbly cast external parts from  Jim Chambers shop. It has a shorter center distance of about .562 and the mainspring is about 1/4"shorter than the Twigg. The shorter center distance and the shorter but equally preloaded spring makes it a bit harder to start the hammer back to half cock but from half cocked to dead stopped full cock,little effort is required. Another advantage the Twigg has is a tall hammer.
I have been trying to make the Ketland malfunction with rebounding frizzen but even after a flint change,I can't make it misbehave.
The flint strikes the frizzen 7/16 of an inch below the top and continues its rake or scrape for 3/4 of an inch and there is then a 1/4 inch unscraped area but the fire slams directly into the pan. I think the position of the flint has all to do with the performance of this lock.
Extreme mainsprings would create problems of their own such as overloading the full cock notch and the tip of the sear.About 40 years ago,the late Tom Dawson made some powerful forged mainsprings for the large Siler lock and and they did exactly that,wipe out the full cock notch and the sear. With a linked tumble,the link or the tumbler arm could fail with destruction of the lock mortise guaranteed. I think this was mentioned here recently.

Bob Roller

 

[heinz]

I am not sure of the question here.  I think you started referring to a lock with a stirrup link from the tumbler to the mainspring.  This mechanism is akin to the roller setup in the compound bow.  It acts like a cam because the leverage angles and consequent distances are changing.
The length of the link and the length of the tumbler from the center axis are both important in the camming behavior.  Think of the direction of the force at the link to tumbler joint and the the direction of the force at the link to spring joint.  If you start out just making the "length of the tumbler" longer you will go from an angle that lifts the spring when you start the hammer back and eventually get an angle that pushes the against the spring trying to move it forward instead of lifting it.
In general the longer you make any lever arm the easier it is to move the end, because you move it further to go through the same angle of displacement.  When you have a double lever, the relative lengths, and the angles the forces are exerted at, become important.
So, a short answer to the question I think you asked is increasing the length of the tumbler would reduce the force until you interfered with the link angle at the spring.  I think 0.010 would get you in trouble

[westbj2]

Bob,
"The .400 distance between the center of the tumbler and the end of the tumbler arm is an absurdity unless we are thinking of a miniature lock."
Bob, I picked those numbers just to try phrasing the question.  There are several Brazier percussion locks in the shop but I did not measure them.
Dale,
I was afraid that, at least in part, the answer would be difficult for me to understand having had no background in physics or engineering.  I will study your post more. Thanks.
Jim

[westbj2]

Heinz posted the thoughtful information above just before I hit the post button.
I see where the length of the link has a bearing on the question of tumbler arm length and its effect.  Perhaps the question as to the "plot line" one may determine if measuring the hammer pressue should be re-phrased. " What happens as the length of the tumbler arm increases while the link/swivel length also increase proportionately?"
i.e.  Would the plot line be straight (static) or curved (dynamic).  If the latter, is the direction up or down?
Jim

[Dave Faletti]

The force to cock the hammer would go up in proportion to the change in radius with a couple of  assumptions.  The angle that the link makes with the mainspring, and spring deflection would have to be the same. Realisticly that will change so you will have to consider how the interaction with the spring will change and that will be lock dependant.   

[AeroE]

The force to cock the hammer would go up in proportion to the change in radius with a couple of  assumptions.  The angle that the link makes with the mainspring, and spring deflection would have to be the same. Realisticly that will change so you will have to consider how the interaction with the spring will change and that will be lock dependant.   

It's even more complicated than that, the spring for each lock would have to be unique in order to produce exactly the same spring rate at the point when the hammer is cocked.  The shape of a force vs. deflection curve for each spring would also be different due to the geometric nonlinear behavior of a flat spring.

Using the same spring with each lock won't work due to the difference in deflection required by each tumbler geometry.  The longer tumber arm moves through a longer arc causing the spring to deflect farther and hence produce more force.  So, there is a doubling up of causes for increasing force with the longer arm in this situation, one due to the greater spring deflection and the other due to the decreased mechanical advantage.

[Dave Faletti]

Lee quite true.  Thats part of what I was trying to say without going into a lengthy explaination.  Spring and link length/position/dimensions, tumbler rotation amount will all play into it.  The answer to the question as written is lock dependant and there is insufficient information to actually answer it.  I made an assumption as to the question and directed my answer to that.

[AeroE]

My intent was to add to your post.

This is a difficult medium for discussing complicated topics in sufficient detail that they are understandable to everyone that is interested.  Either lots of words or pictures plus words are required to truly be effective.

[EC121]

As the hammer moves back, the length of the arm effectively shortens as the link swings under the arm.  This gives the hammer more leverage causing the reduction in force felt as it reaches full cock.  The reverse is that as the hammer drops, the spring gains leverage as the effective distance increases.  The curve can't be linear, because of the changing geometry and leverage of the arc of the arm.  Maybe a really well made spring could load the arm equally through its arc.

[Dphariss]

As the hammer moves back, the length of the arm effectively shortens as the link swings under the arm.  This gives the hammer more leverage causing the reduction in force felt as it reaches full cock.  The reverse is that as the hammer drops, the spring gains leverage as the effective distance increases.  The curve can't be linear, because of the changing geometry and leverage of the arc of the arm.  Maybe a really well made spring could load the arm equally through its arc.

I wrote this earlier this AM but decided not to post then.

Forsythe talks of the "heavy first lifting" of the hammer, this was 1850s, being one indication of a good lock.
A good link mainspring lock, flint or percussion, will have very similar if not identical tumblers. As the cock is drawn back the mechanical advantage of the mainspring changes so that pressure on the sear surfaces is reduced.
This accomplished by a long arm to connect to a properly designed link and a arched and so preloaded mainspring of the proper length to allow the "hooks" of the main spring to move closer the the tumbler center as the tumbler rotates.
This performs several important functions.
In percussion guns the high pressure this generates at the down position holds the hammer on the nipple when firing pressure is present. In flint guns this significant  increase in pressure helps maintain cock speed as the flint  scrapes the frizzen.
The other important thing accomplished by this is that at full cock pressure on the sear is reduced significantly at full cock. This reduces the PSI on the sear nose which as Mr Roller pointed out can be anywhere from "high" to "extreme". This reduction in pressure also makes it easier to get a nice trigger pull.

This design does not need a thick heavy mainspring. In fact thick heavy mainsprings are a detriment. A lighter mainspring, properly tempered with a significant preload is needed.

The link must be exactly the right length too short or too long and the desirable features can disappear and it might be impossible to even cock the lock due to parts binding.
The easiest way for the reader here to see the design is to buy the original Purdey rifle plans that are available from TOW and others. The lock internals appear to be identical to the late Manton flint guns of similar plate size.

The best grade English locks, from perhaps 1760 onward were really works of art in their function.
Understanding this requires finding and cocking a good English percussion or flint gun, or a good copy, a few times.

Dan

[LH]

Good post Dan.   Do you happen to know if the lock Pedersoli uses in their Mortimer flint rifle is a direct copy of the original? 

[Dale Campbell]

Now see what you've done, Jim?  I think I answered your original question regarding the difference in the distance of the mainspring contact on the tumbler from the center of the tumbler.  Longer distance, linear response all other things being equal. But they aren't.  There have been some really excellent posts on reality from really knowledgeable people. Between them they have a grasp of the engineering, history and practical application of lock geometry and behavior.

[westbj2]

Dale,
Yes, you did answer the question in a way that even I can understand. Thank you.
There indeed have been some thoughtful posts which as you say reflect the knowledge out there.  Having made a few locks (but always to the proportions of the originals) I have been curious about messing with the tumbler arm length but unsure of what I may get into.  Current conclusion:  Don't try to re-invent the wheel.
Dan,
As you went through the lock function description in your post, It was as if I had one in my hand....good job.
For those following this discussion, here is a thing of beauty.
Jim

[Bob Roller]

Yes ideed.a work of art and a thing of beauty combining simplicity and elegance. I think I have made about 25 of these since 1987 and I have a set of fixtures for a scaled down version taken from a 30 caliber Whitworth. I think I have made 7 of these little ones. Now I have one more to do,the same mechanism but on a Rigby plate. I have made only one of this pattern and that was in 2008. These are labor intensive locks to make but the end result is most satisfying. Thanks for posting this picture.

Bob Roller

[Larry Pletcher]

In 1992, Jim Chambers and I collaborated on an experiment with one of his locks and an assortment of parts.  Jim sent me the lock, two cocks, and three tumblers. I timed the lock with all six combinations. (I reported the results in the Dec 92 issue of MuzzleBlasts.  If you keep your issues, its the one with Monte Mandarino's wonderful fowler on the cover.)  The article is also at this link:

http://www.blackpowdermag.com/featured-articles/lock-timing-part-iii.php

Of the six tests the one with the lengthend cock and the modified Siler tumbler was unique.  The tumbler required the main spring to be placed closer to the tumbler. This combination resulted in a pronounced camming effect. It broke just as you moved past half cock. The effect was strong enough that when cocking the lock in your hands, one had to take care to stop at half cock - many times I ended up at full cock when I meant to to stop at half cock.  Dan's borrowed phrase from Forsythe, "first heavy lifting" really was in evidence.  The longer neck on the cock helped I'm sure.  But as the tumbler rotated, the spring "climbed" closer to the tumbler's center of rotation as well.  This would have given the tumbler greater mechanical advantage.  The combination very effective.  I was impressed enough to ask Jim set up a lock like it for me.

Regards,
Pletch

[Bob Roller]

The Pedersoli muzzle loaders seem to have the external appearences right. The mechanisms are apparently engineered to be produced by CNC equipment but are functional. The late Joe Hepsworth asked me to design a replacement mechanism for the Pedersoli/Gibbs long range muzzle loader to give it more of a "feel"like an old English lock and to eleminate a complaint which was the "fly".The lock had to be pulled back beyond normal full cock to get the fly to release and then the hammer had to be lowered to full cock which is not right. I made and sold quite a few kits to replace all the internal parts of that lock except the sear spring which was in place and worked alright.
There is now no need for the kit because Pedersoli has revamped the lock and the ones I have examined function flawlessly with no needed over travel to make the lock work.

Bob Roller

[Jim Kibler]

Pletch,

What's most interesting about these tests to me is that imcreasing the "camming" effect didn't have any negative impact on lock speed.  A substantial let-off when cocking the lock is great in terms of decreasing the required trigger pull. 

Thanks,
Jim

[Bernard]

Simply put.
Assume a force of 50 lbs from the spring applied to the .400 radius tumbler = 20.0 inch/lbs
                           50 lbs from the spring applied to the .450 radius tumbler = 22.5 inch/lbs
                  and   50 lbs from the spring applied to the .500 radius tumbler = 25.0 inch/lbs
The relationship is linear.

[westbj2]

Bernard,
Thank you!!!    Your assessment  is was what I was curious about but had difficulty putting into a question.
Jim