Torque around a point from lever linkage

[BatsDude]

Hi all. Brushing up on some of my force and torque stuff so I can do some modelling in software.

Homework Statement

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.

Homework Equations

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

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.

 

[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 .

 

[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.

 

[BatsDude]

Anyone able to help?

 

[haruspex]

determining the value of F_b and whether or not it interacts along BC or if it acts at an angle on BC.

Let the tension in BC be T (your F_b).
What equilibrium equations can you write for the point B?
What equilibrium equations can you write for the point C?

 

[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) ]

 

[haruspex]

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) ]

Yes.

 

[BatsDude]

Thank you for your help!