I'm trying to calculate the force and toque in a linkage system and was wondering if someone could do a quick check and see if I did anything wrong. You can find the diagram at the link below
Points 1, 2, 3, and 4 are pivot points. Point 1 is fixed in space. Points 2 and 4 are free to move in the plane. Point 3 can only move up and down (closer or further from point 1). The links connecting points 1 & 2, 2 & 3, 3 & 4 and 4 & 1 are all the same length (L). A force (F) is applied at point 3.
What I want to know is the torque about point 1 applied by each link as the angle (a) varies from 5 to 85 degrees.
Step 1 find the force in the links from 2 to 3 and 3 to 4 which should be the same.
Fl = .5 * F/cos(a)
The .5 is because each of the two links (2 to 3 and 3 to 4) will have half of the force F.
Step 2 find the perpendicular distance (Torque Arm: TA):from point 1 to the line through points 2 and 3.
TA = L * cos(x)
x is 90 - (2 * a)
Step 3 multiply Force and arm length
Torque = FL * TA
So the full formula would be
Torque = .5 x F/cos(a) * L * cos(90 - (2 * a))
Thanks for the help.