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Torque around a point from lever linkage

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  1. May 7, 2017 #1
    Hi all. Brushing up on some of my force and torque stuff so I can do some modelling in software.
    1. The problem statement, all variables and given/known data
    I have a system as shown in the picture. A force F acts at point A, which is the end point of the lever AB. Connected to the lever is a link BC, and connected to BC at point C is another link CD, which is anchored to the ground.
    I'm trying to resolve this into a torque around the point D. I know the lengths, and all the angles involved, I'm just confused about how the force travels through the linkage.
    SWs7w.png

    2. Relevant equations
    T = F*r*sin(theta) is the equation for torque from a force acting at an angle

    3. The attempt at a solution
    My attempt was to try and equate the forces through the lever first.
    Let F_b be the output force of the lever at point B, resulting from F acting at point A.
    F*(alpha/2)*sin(theta) = F_b*(alpha/2) *sin(phi). Solve for F_b.
    From here, I would assume that this force F_b is acting on member CD at an angle of omega and at a lever length of lambda. From this I can calculate the torque around D.

    However, I'm not at all sure if this is correct.
     
  2. jcsd
  3. May 7, 2017 #2

    Nidum

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    Draw the vectors representing the forces directly on the diagram . You should be able to see a way of solving this and similar problems very easily .

    Just for interest - since you mention software modelling - you can use a modern cad system as a visual calculator for linkage problems .
     
  4. May 7, 2017 #3
    Hi Nidum,
    Thanks for your reply. I've drawn the force vectors that I think are happening, as seen below. Is that correct? The main issue I'm having is actually determining the value of F_b and whether or not it interacts along BC or if it acts at an angle on BC. fjgS2Px.png
     
  5. May 7, 2017 #4
    Anyone able to help?
     
  6. May 7, 2017 #5

    haruspex

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    Let the tension in BC be T (your Fb).
    What equilibrium equations can you write for the point B?
    What equilibrium equations can you write for the point C?
     
  7. May 7, 2017 #6
    So would the torque around D just boil down to = F_b*lambda*sin(omega)?

    Where F_b is = [ F*(alpha/2)*sin(theta) ] / [ (alpha/2)*sin(phi) ]
     
  8. May 7, 2017 #7

    haruspex

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    Yes.
     
  9. May 7, 2017 #8
    Thank you for your help!
     
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