Torque around a point from lever linkage

In summary, the conversation discusses a problem involving a system with a force acting at point A, a lever AB, and multiple links BC and CD. The goal is to resolve the force into a torque around point D. The conversation includes equations and diagrams to help solve the problem, and suggests using a modern cad system for visual calculations. Ultimately, the solution involves determining the value of F_b and the torque around D.
  • #1
BatsDude
14
0
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.
SWs7w.png


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.
 
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  • #2
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
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
 
  • #4
Anyone able to help?
 
  • #5
BatsDude said:
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 Fb).
What equilibrium equations can you write for the point B?
What equilibrium equations can you write for the point C?
 
  • #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) ]
 
  • #7
BatsDude said:
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.
 
  • Like
Likes BatsDude
  • #8
Thank you for your help!
 

FAQ: Torque around a point from lever linkage

What is torque?

Torque is a measure of the force that causes an object to rotate around a fixed point. It is typically measured in units of newton-meters (N*m) or foot-pounds (ft-lb).

How is torque related to lever linkage?

Lever linkage is a type of mechanical system that uses a lever to amplify the force applied to an object. The longer the lever arm, the more torque can be generated. In other words, the longer the lever arm, the greater the distance the force is applied from the fulcrum, resulting in a greater torque.

What factors affect the amount of torque generated in a lever linkage system?

The amount of torque generated in a lever linkage system depends on the length of the lever arm, the force applied, and the distance of the force from the fulcrum. Additionally, the angle at which the force is applied and the weight of the object being moved can also affect the torque.

How can I increase the amount of torque in a lever linkage system?

To increase the amount of torque in a lever linkage system, you can either increase the length of the lever arm or increase the force being applied to the lever. Alternatively, you can decrease the distance of the force from the fulcrum or increase the angle at which the force is applied.

What are some real-world applications of torque in lever linkage systems?

Lever linkage systems are commonly used in everyday objects such as scissors, pliers, and seesaws. They are also used in more complex systems such as car engines and construction equipment to generate and control rotational motion.

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