Connect two lines in 3D

  1. 1. The problem statement, all variables and given/known data
    Given two lines, in 3D, connected end to end with lengths L0 and L1, a point P0 where the first line starts, and a point P1 where you want the end of the second line to be at. Find the configurations of the lines that put the end of the second line at P1. You can restrict the degree of freedom on the lines.


    2. Relevant equations



    3. The attempt at a solution

    I can easily connect 2 end-points together, but it seems like there's more to this question than that. The "find the configurations" part indicates there's many solutions? And not sure about the "restrict the degree of freedom".

    Pointers anyone?

    Much appreciated!

    EDIT: Removed doubled headings.
     
  2. jcsd
  3. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi m3x3! Welcome to PF! :wink:

    You have two rigid rods of fixed lengths and fixed endpoints …

    what are the possible configurations (positions)? :smile:

    (but I don't understand, in this case, what they mean by "restrict the degree of freedom" :confused:)
     
  4. Thanks! I've been an avid reader for quite some time and I thought it was about time to sign up! :)

    I might have been looking at this for too long, because I still don't see it. So if I have two lines, one which I need to connect by its "end-point" to the other - how can there be many configurations/positions of that? Or is this a annoying trick question? In either case it's doing my head in... :)
     
  5. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    Hi! :smile:

    I think you're not understanding the question …

    you have two metal rods, AB and BC, fixed at A and C, and jointed at B.

    (obviously, AB + BC must be greater than AC)

    Suppose A is vertically above C, and draw one position for B …

    now where are all the other positions B can go into? :smile:
     
  6. HallsofIvy

    HallsofIvy 40,306
    Staff Emeritus
    Science Advisor

    And remember that, as you title says, this is in three dimensions. Imagine holding one end of a rod in your left hand, the other in you right. The two rigid rods meet at some angle. Now swing them!
     
  7. Thanks for your pointers guys, but I'm starting to think that I'm retarded as I just cannot get around this. So is it:

    Code (Text):

           /
       L2 /
         /          * P1
         \
          \
       L1  \
           * P0
    So I need to find a way to connect the unattached end of L2 onto P1. And this I do by finding the degree of the angle of which I need to rotate L1 (around the connected joint) to attach it to P1?
     
  8. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    Hi m3x3! :smile:

    The join of L1 and L2 isn't given, so just ignore it …

    just start L1 at P0, and L2 at P1, and use ordinary trigonometry to find the angles so that L1 meets L2. :wink:
     
  9. Aaah! The pellet finally dropped, proving that indeed I am a retard, alternatively putting too much thought into it!

    Thanks so much for the pointers, much appreciated!
     
  10. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    is this the food pellet :tongue2: that they reward you with when you push the right button? :biggrin:
     
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