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Prove mathematically that the lengths of the crank...

  1. Dec 2, 2016 #1
    1. The problem statement, all variables and given/known data
    Design an offset slider-crank mechanism which has the following specifications:
    1. Stroke length of slider block C = 150 mm
    2. Advance-to-return time ratio = 1.2
    3. Offset height h = 50 mm

    Prove mathematically that the lengths of the crank and of the connecting rod are AB
    = 71 mm and BC = 178 mm respectively to the nearest millimetre.

    upload_2016-12-2_2-6-21.png

    I would appreciate any help to find the process and ecuations necessary to solve this problem.
    I have tried to use differet ways to solve it but it gets very complicate and it suppose to be something easier..

    I found a possible solution using the next representation and equations:

    upload_2016-12-2_2-11-10.png

    2. Relevant equations


    We take into account that:


    upload_2016-12-2_2-15-18.png

    upload_2016-12-2_2-16-12.png
    When I got this quadratic equations I realise that its getting too complicate, plus even solving this equations at the end there is not solution and I need to use a graphic way to find the length of the crank, and I have to use only mathematically process to solve it, I cant solve it graphically.



    Another possible solution that I found was using the next steps:

    upload_2016-12-2_2-40-2.png

    3. The attempt at a solution
    Another way that suppose to drive to calculate the lengths is using complex numbers but I started and it is quite complicate also.

    Does anybody know where could I find a non very complicate way to solve this, my teacher told me that it suppose to be a mathematical method that is not very complicate?
    I dont need anybody to make it for me, only a little help to where could I find formulas and the right approach to solve it.

    Thank You.
    Have a good day
     
  2. jcsd
  3. Dec 2, 2016 #2

    Nidum

    User Avatar
    Science Advisor
    Gold Member

    Back solve from the given answers .
     
  4. Dec 3, 2016 #3
    Hello.
    Iam still stuck, I am using the ratio formula to get the angles, I tried using the cosine and sin rules, but still not going anywhere, with these formulas that I put in the last part of my post I cant get anywhere because I dont have enough data, I need to use the length to go somewhere and that exactly what I need to calculate, so I cant use this data.
    Any possible advice of how to proceed?
    I guess I am missing something that I can´t realise
     
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