Kinematic study of connected rods

[magicfrog]

Homework Statement

ToDo

Relevant Equations

Torque equation

Good morning everyone, I am currently working on a kinematic problem that I am having difficulty solving.

I have been asked to calculate the torque at node F based on the geometry and the force (W) applied at node G in the AG direction.

In particular, node G and node A can translate along the vertical axis and also rotate. Node F cannot translate. There are three rigid bodies, HG, AHB and FB.

I have calculated, correctly I hope, the torque at node A, considering it as a crank-connecting rod case:

T_A = W*AH*sin(alpha+phi)/cos (alpha)

From this, since AHB is a single rigid body, I can say that the rotation of point A is equal to the rotation of point H and, consequently, to the rotation of point B. But how do I link the torque at point A with the torque at point F?

I think I'm missing something, but I don't understand what.
I am attaching the kinematic diagram and my considerations.
Thank you all!

 

[magicfrog]

I would like to add that the kinematics are placed on a horizontal plane, so the applied force (W) is orthogonal to gravity.

I would like to take this opportunity to add another consideration/question. For the purposes of calculating the torque in F (dependent on angles, levers and force), would a simplification as shown in the attached diagram be acceptable (I consider the force applied in G as applied in B for balance considerations)? In this way, I should be able to write the expression of the delta angle as a function of the alpha and phi angles.

I apologise if I have written nonsense!
Thank you!

 

[Lnewqban]

Have you been given any dimensions for the links and geometry?

 

[magicfrog]

Have you been given any dimensions for the links and geometry?

Yes, I have all the necessary data. I would like to be able to write the torque in node F as a function of the parameters in the attached diagram, i.e. force, dimensions and angles.

 

[Lnewqban]

You are on the right path.
I would use the concepts of moment (F x perpendicular distance) and work conservation (F x distance = constant for all nodes).
Consider the exact direction in which each node is free to move at the instant shown in the diagram (those constantly change with time as the mechanism moves).