A2Q1 force equations

[kohmax]

For the force equations provided for the n=2 case, I am a bit confused about the following equations:

• joint 3, vert: f3 = -w1
• joint 5, vert: af5 + f7 + af9 = -w2
• joint 7, vert: f11 = -w3

From the horizontal equations, it seems like the f_i’s are just magnitudes and the direction of the force is accounted with signs (+ is used force in right direction, - is used force in left direction).

However, based on the equations above (for vertical directions), it seems like f_i’s and w_i’s are not just magnitudes (or else f3 = -w1 is the same as f3 + w1 = 0 but f3 and w1’s force should point in opposite directions yet they have the same sign +).

I am wondering if there is something I am not understanding properly for this problem. If so, could someone point me in the right direction? Thanks in advance!

[ccc]

I think I see your point. Let me try to explain.
The way the equations are written assume that the f_i’s include some sign, so they are not just magnitudes.
In fact, some will turn positive and some negative.
But the w_i’s are defined as positive in the code, so each is accompagnied by a minus sign in the equations to give it a direction.
In this setting, directions towards left and towards top are considered positive.
I could have defined negative w_i’s and taken off the minus from the equations.
Does this capture what you asked?

[kohmax]

Yes. Thank you!