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The alignment tool article- a question

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  • old mart
    replied
    I see that it has to be 3 + 2, or 4 + 1 for full stability. I was in the middle of editing my last post, #25, when the HSM site went down and was unavailable last night.

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  • J Tiers
    replied
    Already "got it", see post #23.

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  • Paul Alciatore
    replied
    I may have been beat due to internet problems. But here is my answer:

    First lets state that principle about points of contact and constraint a bit more precisely.

    Any object in three dimensional space has six degrees of freedom: the three linear axis and the three rotational axis. Now the principle of constraining them is stated something like this:

    Each non-reduntant point of that object that is constrained to being/lying in a single plane, will constrain the object from movement in ONE of those six degrees of freedom. Thus, one point that is constrained to a plane will still allow all three rotational motions and two of the linear ones. Add a second such point and you remove ONE more degree of freedom, etc. The idea is that each such point is able to remove one more degree of freedom.

    I want to emphasize that it only states that the points are constrained to a single plane. There is absolutely nothing in it that talks about any forces being applied to them. This leaves out gravity or any other force that would be used. Now, some kind of force is necessary to effect this constraint, but the source of that force and it's direction is not talked about in the statement of the principle.

    Now, your drawing with four points of contact on a Vee way and a flat way seems to constrain the object resting on it in five degrees. We can all agree that the object is free to slide in one linear direction, along the ways. But you are ASSUMING that gravity is holding it DOWN on those ways. And that it will be at the lowest possible position that those four point allow. By having gravity holding it down in that lowest possible position, you have effectively added a fifth point. This fifth point would be on the top side of the object and it is not shown in your drawing. But remember that I said that the forces are not specified or even talked about in the statement of this principle of dynamics. So, if you are talking from a point of view of pure dynamics, then you can not use gravity to add this fifth point.

    I took the liberty of adding to your drawing to show the second, additional, rotational degree of freedom that these four points will allow.



    The circled point is to remain in contact and roughly in it's same position but it can move a bit on that plane as needed. The three arrows show how the other three points can move while staying in contact with their planes to allow the object to rotate about an axis. This is the second degree of freedom that your four point scheme does not constrain.

    So, in THEORY, your four points do not constrain it in five degrees of freedom, only four. Now, on a real lathe, they would actually work because the cutting forces along with gravity do add that fifth point. So, what you propose would work, but it does not use only four points to do so. There IS that fifth point due to those forces that you do not show.

    The author is correct in stating that five points are needed to constrain an object in five degrees of freedom. I have not read that article yet, but I suspect that he also forgot about that invisible point that gravity or some other force provides. So if you do include gravity or some other force, his stated five points do contain one point that is redundant and therefore not necessary. On the other hand I would not say that his design is over-constrained. Within reason his five points do work with gravity to determine where that sixth, gravity point is. If you look at it in another way, ANY of his five points can be moved in any direction on the object and the object will once again settle to a single, fixed position in five of the six degrees of freedom: the additional, gravity point will also move in the object to accommodate this. So in his design, that sixth point is not actually constrained to a plane in and of itself, but it is determined by the other five.

    We are left with the strange sounding conclusion that the author does have one point that can be removed, but it is NOT over-constrained.

    I love this example: it made me think. I hope that my analysis is perfectly clear.

    And this probably says a lot about why real world lathes use what is effectively a five or even a six point suspension for the carriage and tailstock.

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  • old mart
    replied
    I now see the tipping weakness with three on the vee and only one on the flat, but don't understand why four on the vee can rock with one on the flat. There was always going to be a minimum of one on the flat.
    Last edited by old mart; 03-10-2019, 06:51 PM.

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  • Mcgyver
    replied
    Originally posted by J Tiers View Post
    I thought there might be some added feature that you had which needed the 4, but which maybe was in the next section of the article. Evidently not.
    The added feature is not have it tip over. You need five constraints, four is not enough. Think of this way, put three on the V and it can rotate, put a fourth on the V and it will still rock back and forth. Add the fifth on the flat and it will only move in one direction, along of the ways. Perhaps this will help show why four won't work.

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  • J Tiers
    replied
    Originally posted by Peter. View Post
    If you configured it to sit on the edge of a flat/box way then 3 points will hinge where 4 points will not.
    Ah, there we have a good reason. I can see that. Thinking about it in context of V way was different.

    Very good, thanks you for the illustration. I was going to go and check a 3 point mockup, now I do not have to.

    The key point there is that the 3 points do define the plane, bit there exists more than one plane which they can be on. The extra point on the flat must move to allow that using with the V, but with the box way, the extra support does not NEED to move in order to allow the "hinging".

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  • Peter.
    replied
    If you configured it to sit on the edge of a flat/box way then 3 points will hinge where 4 points will not.

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  • J Tiers
    replied
    OK.

    I don't see that stability issue at all, but it is not a big deal. It can work either way with adjustment to make all 4 contact, or the automatic contact of three.

    I thought there might be some added feature that you had which needed the 4, but which maybe was in the next section of the article. Evidently not.

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  • Mcgyver
    replied
    Originally posted by reggie_obe View Post
    In general, why is the flat top of the V way not used as a stable horizontal reference point?
    It can be used to give very good hints at figuring out what you've got, but its not ground in the same up as the two V surfaces (as I've seen it being done) so there are not guarantees on it, and you don't scrape it (whereas those surfaces you do scrape can be relied upon). A key benefit of this tool is when you got a V scraped are working on say the flat paired with the V, the only surface I want to reference are the ones already scraped or those being scraped. You can and do use those for some things but I don't know how it would help for say when you've go the two sides of a V done and want to make the flat parallel to it

    Mr Wade's device is adjustable, and my question to him was why he felt (as he stated in the article) that he "had to have" 4 points. That has been answered, basically that he, like myself, followed the original design which has 4 points set up the same as mine below.

    it seems as if 3 would be entirely sufficient, and might be more reliable, especially as things wear. I did not think too hard about it when I made mine, nor apparently did Mr Wade. I think that if I make another it will have three.
    you misunderstand, I do think you need the constraints I gave which is why they are there, I believe geometrically, but certainly stability wise. I just didn't want to spend my Sunday in a dancing on the head of a pin discussion about it. Build a model based on point contact, or balls in tangential contact (which is what you end up with), without the 5 it will not stay in the same position.
    Last edited by Mcgyver; 03-10-2019, 05:34 PM.

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  • reggie_obe
    replied
    Originally posted by Peter. View Post
    It might have been dressed to remove marks near the chuck, or is at least likely to have burrs from dropped parts. If you could PROVE it against other non-working faces such as the flats between two ways then you could be reasonably sure of it, otherwise you're making a risky assumption.

    I just had my South Bend ground and the grinder deliberately cleaned up the vee way tops just so they could be used as such for levelling.
    I was thinking about the flat top of the V way as an unworn reference. Hadn't thought about the dings and dents from parts and tools.

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  • J Tiers
    replied
    Originally posted by MattiJ View Post
    I was thinking of only the V-way part as others seemed to talk about it also. If considering only the V-way the 3-point support would still allow rotation AND "axial" misalignment.
    Fourth support point like in your drawing should fix both of the problems but maybe it is more prone to "settle crooked" or something.

    But as far as I can think of the 5-point system(4 on V-way and one on flat) is not over-constrained either.
    "Overconstraint" simply means that you have more points constraining movement than are required. it also means that one of them may be out of alignment, which in the case of 4 points, then means that there are two stable positions, each with three points in contact.

    The points contact the V in a plane through the V. Three points can only be in one plane, and can have only one position on their support plane, but with 4, one can be out of the contact plane, just like the 4th leg of the chair. So it is extra.

    As someone said above, similar to Mr King's discussion of 3 points of support.

    In any case, the question was not to somehow complain that Mr Ward had done anything wrong.... but to ask if there was a particular reason for having the 4 points. And, his statement is that there is no such particular reason or feature. I could not complain anyway, my version of the device also has 4 point contact!

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  • MattiJ
    replied
    Originally posted by J Tiers View Post
    ??????????????????????????????????????

    No different that it would with four. You are referring to the support(s) on one side sliding up the V-way, and the support(s) on the other side of it sliding down, producing a rotation. But, so-what?

    The anti-rotation comes from the support over on the flat way, it is the exact same with either 3 or 4 contact points on the V.

    That's the point. The behavior is the same with 3 points or with 4 (if they all do contact), so one of them is not required.

    Just to clear up some confusion, the three points on the V-way would be similar to this (yes I already had the lathe bed model for a different project):

    https://imgur.com/8BrLmfa][img]http://i.imgur.com/8BrLmfa.jpg
    I was thinking of only the V-way part as others seemed to talk about it also. If considering only the V-way the 3-point support would still allow rotation AND "axial" misalignment.
    Fourth support point like in your drawing should fix both of the problems but maybe it is more prone to "settle crooked" or something.

    But as far as I can think of the 5-point system(4 on V-way and one on flat) is not over-constrained either.

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  • old mart
    replied
    I see, the setup is for measuring the wear of the vee in the bed. If you had a three point front half, turning it round would prove the concept, by giving differing, or identical test results.

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  • Peter.
    replied
    Originally posted by reggie_obe View Post
    In general, why is the flat top of the V way not used as a stable horizontal reference point?

    It might have been dressed to remove marks near the chuck, or is at least likely to have burrs from dropped parts. If you could PROVE it against other non-working faces such as the flats between two ways then you could be reasonably sure of it, otherwise you're making a risky assumption.

    I just had my South Bend ground and the grinder deliberately cleaned up the vee way tops just so they could be used as such for levelling.

    Leave a comment:


  • J Tiers
    replied
    Four points do not have to all be in a plane. Three points DEFINE a plane, so four can be like an uneven 4 legged chair.

    Mr Wade's device is adjustable, and my question to him was why he felt (as he stated in the article) that he "had to have" 4 points. That has been answered, basically that he, like myself, followed the original design which has 4 points set up the same as mine below.

    it seems as if 3 would be entirely sufficient, and might be more reliable, especially as things wear. I did not think too hard about it when I made mine, nor apparently did Mr Wade. I think that if I make another it will have three.

    Originally posted by old mart View Post
    JT, your picture in #10 helps greatly in my understanding the contact points, and I believe that having only three on the vee may have a problem. If wear occurs unevenly, particularly to the left front contact point, the saddle will tend to rotate slightly on a horizontal axis, loosing the precision when facing cuts are made. I think the problem of wear would be lessened by having two contacts on the inboard side of the vee opposite the outboard ones.
    It's not a "saddle".... it is a measurement device..... Similar to this one that I made, only Mr Wade made a larger unit with provisions to mount full size levels on it. In mine, there are 4 contact points where there is a section cut out of the round portion in foreground, you can maybe see the fatter parts of the cylinder at each end. Mine is made just like the original "Kingway" tool. Mr Wade used the same principle, but went at the contacts a bit differently, making them adjustable independently.

    In mine, I think that even if it were uneven, the cylindrical part could be turned until the 4 points touch, although the rod might not be vertical. In the article, the 4 being adjustable means they can be made to touch. In either case, the points do not "automatically" all touch, which 3 would have to.

    Last edited by J Tiers; 03-10-2019, 04:47 PM.

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