# Homework Help: Torque around a point from lever linkage

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1. May 7, 2017

### BatsDude

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.

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. May 7, 2017

### Nidum

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 .

3. May 7, 2017

### BatsDude

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.

4. May 7, 2017

### BatsDude

Anyone able to help?

5. May 7, 2017

### haruspex

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?

6. May 7, 2017

### BatsDude

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) ]

7. May 7, 2017

Yes.

8. May 7, 2017