• Welcome to engineeringclicks.com
  • Best way to position components in all available degrees of freedom

    Discussion in 'The main mechanical design forum' started by matfix, Nov 29, 2012.

    1. matfix

      matfix New Member

      Joined:
      Jul 2012
      Posts:
      2
      Likes Received:
      0
      Hello everyone,

      I would be interested to hear how would you mount/fix 2 square blocks of let's say aluminium on a flat base plate so that they are positioned accurately (down to 1um, 0.5mrad or less) in all degrees of freedom. These blocks will be fixed to the base so I suspect there are 4 degrees of freedom which needs to be somehow defined. Please correct me if I'm wrong.
      You can do anything with all the parts, for example do the cut outs, drill holes, make them round, anything - there are no limits as long as the parts can be fixed (accurately in reference to each other) to the base.

      Advice very welcome.
      Looking forward to your thoughts.

      Mat
       
    2.  
    3. telecomguy

      telecomguy Member

      Joined:
      Aug 2011
      Posts:
      21
      Likes Received:
      0
      Do we get to assume the base is made of a material that has ZERO thermal expansion coefficient? lol
       
    4. Frugal-TPH

      Frugal-TPH Member

      Joined:
      Nov 2012
      Posts:
      5
      Likes Received:
      0
      I've never had to do this before, but I think I'd be looking to something called "Minimum Constraint Design". That is, the removal of all redundant constraints, to ensure that there is no ambiguity in which constraints are in play at any one time, each time the objects are removed and replaced. You could use this to define a set of features which will restrain the relevant degrees of freedom, and will require a seating force (may be weight).

      It will be difficult to meet your tolerances accurately in an absolute sense, but you should be able to repeatably achieve the same position to the tolerances you are targeting (assuming no material expansion or flexibility as touched on by telecomguy).

      There is a book by Lawrence J. Kamm called "Designing cost-efficient mechanisms", which I would recommend. I'm sure there will be plenty of ideas in there on how to achieve what you're after. A warning though, it is out of print and expensive to get hold of. My copy came from the US and cost me about £70. It's probably the best "design" book I've ever bought, and is full of sketches and ideas on how to solve all manner of mechanical design problem (just look at the contents pages to get an idea of what it touches on).
       
    5. bdzin1

      bdzin1 Member

      Joined:
      Sep 2012
      Posts:
      10
      Likes Received:
      0
      If you're using Geometric Tolerance's that should be your first direction to take.
       
    6. tonycro

      tonycro Well-Known Member

      Joined:
      Nov 2011
      Posts:
      78
      Likes Received:
      1
      Dowels. Drill, them ream locating dowel holes in the base and then set dowels into the blocks, you'd only need two per block to restrain them accurately.

      tony
       
    7. Frugal-TPH

      Frugal-TPH Member

      Joined:
      Nov 2012
      Posts:
      5
      Likes Received:
      0
      Two dowel's aren't minimum constraint design. They over-constrain and therefore impart stresses & deflections into the structure (albeit minimal ones, the more accurate you are). Better than two dowel holes would be one dowel in a hole and one dowel in a slot which was in line with the hole. But then you'd still have to ensure lots of very tight tolerances on things such as:

      * Flatness of the base part.
      * Flatness of each block sitting on the base part.
      * Position of the dowel hole.
      * Position of the slotted hole relative to the dowel hole.
      * Diameter of the dowels.
      * Straightness of the dowels.

      And I think that 1 micron is something which requires lapping (very expensive). 5 microns would be more reasonable for machining, I think, but still a push (or, expensive at least).

      There's also the question of whether we're talking absolute position, or repeatable position.

      In the former, you're target would be to achieve the requirement "position the blocks at stated / specific X, Y Z coordinates to +/- 0.5micron positional accuracy for each coordinate, and with orientation Rx, Ry, Rz to +/-0.25mrad rotational accuracy".

      In the latter, you'd be trying to achieve the requirement "fix the blocks to the base in a position and orientation that can be repeated to a +/-0.5micron positional accuracy and a +/-0.25mrad rotational accuracy".

      I think the latter one is the most achievable of the two, and could be achieved by machining three ball features onto each block and then corresponding locating features on the base, and then applying a seating force to each block...

      1. Mate one ball on the block into a cup on the base plate.

      2. Mate another ball on the block into a vee-groove on the base plate.

      3. Mate the final ball on the block onto a flat surface on the base plate.

      4. Apply a seating force to hold the body against the features (this could be its weight, or a spring, or some other force).

      Think of them like legs of a tripod. The 1st step restrains x,y,z, the 2nd step restrains two of the rotational DOF's, and then the 3rd step restrains the final DOF. The (inflexible) blocks then cannot physically be in any other position (it is an impossibility). You can remove the objects and replace them, and they will return to exactly the same position and orientation every time (ignoring flexibility, expansion, wear).

      I think you will likely achieve sub-micron position repeatability with this approach (measuring this might be a problem though), and for orientation, the further apart the three ball features sit, the better the rotational accuracy will be.

      You might also be able to be clever and share the vee-groove and flat surface features between the two blocks, to attempt to locate the two blocks relative to each other in an absolute sense too (but I'm not certain of this).
       
    8. matfix

      matfix New Member

      Joined:
      Jul 2012
      Posts:
      2
      Likes Received:
      0
      I indeed thought about dowels Frugal-TBH I think you suggestions are very interesting.

      Answering your question I would be interested more in a repeatable position.

      A question which come straight to my mind is if it is feasible to accurately machine the cup and the v-groove so that their positions match each other perfectly? Aren't we over-costraining the component again due to increased number of surfaces which will be used to locate the component?
       
    9. Frugal-TPH

      Frugal-TPH Member

      Joined:
      Nov 2012
      Posts:
      5
      Likes Received:
      0
      It should work, yes.

      Thinking about it now though, I made a mistake last night. Should use a conical hole instead of the spherical 'cup' feature I mentioned, or even better would be a three sided inverted pyramid (I think this is what the poster who mentioned 'diamonds' was talking about). Secondly, the vee-slot needs to be roughly in line with the the conical hole.

      There doesn't need to be tight tolerances on the features themselves. Their alignment can be very loose, but the resulting repeatable position ends up being very accurate, without possibility of looseness or binding.

      What happens is that three point contacts are made between the ball and conical hole (fixing X,Y,Z). Then when the 2nd ball touches down in the vee groove it makes two point contacts fixing two rotations. The final rotation is fixed when the final ball touches at one point on the flat surface. It doesn't matter that all the locating surfaces are only loosely toleranced; the balls touch down where ever they touched down the first time.

      If you were to bolt the thing down as the seating force, you would have to mind not to impart any further constraints with the screw itself (use a spherical washer and an oversized hole). Countersunk screws are notorious for this effect, because they try to pin things down where they don't want to be, deforming & stressing the work-piece.
       

    Share This Page