# Calculating force exerted on plate by link

I am currently involved with a project using a mechanism similar to that seen in 'table tilters' and we are struggling to work out how to begin resolving the forces.

The image shows the state we are considering in equilibrium to resolve the forces. The plate (blue) is in a horizontal position and is 350mm in length

The linkages (red) are 270mm long and are at an angle of 20 degrees to the horizontal at this position.

The green component is restricted to motion in the vertical direction and is being pulled downwards with a force of 3000N.

We want to work out the downward force the linkages exert on the plate.

I started to try and break the system down into free body diagrams (below), but am struggling to make a start resolving the forces. Any advice would be greatly appreciated.

• What is this "resisting force" on the bottom of the plate? There's nothing in your 3d. – Wasabi Aug 8 '18 at 17:07

your sketches misses a bit of information. where is the resisting element?

Is it a post, or leg/legs under the table. Assuming the center of resisting forces falls right under the red bar on the point of contact. then the force on plate is same as 3 kN downward. If the resisting forces are not directly under the red bar then the downward force becomes bigger or smaller, depending on the location of resisting force.

Edit

After reviewing additional info, your table is receiving 3kN downward force. But you need to be mindful of horizontal forces at points green and yellow on the vertical; black bar. Those are $Fh = cos(20)/ Sin(20)\times 3kN = approx.\space 9 kN$

These two work as a couple trying to topple your table.

• Hi kamran, Thanks for your response. The resisting element can be assumed to be equal over the bottom surface of the plate. The linkage is connected in the center of the plate so this should mean the force is through the center of the resisting force as you mentioned? Am I wrong in thinking that some of the downward force on the green component would be resisted by a horizontal force at the purple pin connection? – Jacob Rodda Aug 8 '18 at 7:06
• I will add a new sketch with the resisting force to my original post. – Jacob Rodda Aug 8 '18 at 7:12
• Thanks kamran, so would this be approx. 9kN in total horizontal forces that will be distributed between those 3 points or approx. 9kN for each of the connections to balance? thanks again for your help. – Jacob Rodda Aug 10 '18 at 4:04
• @JacobRodda, there is going to be a horizontal component of the force at the green hinge on the black post pointing to left. And a horizontal force on the yellow hinge on the black post pointing to right. These two forces will create an overturning couple trying to topple the post counter clock-wise. – kamran Aug 10 '18 at 4:26
• Thanks kamran, this is making much more sense now. Am I correct in thinking that as long as all the post and the pin connections are heavy duty and strongly secured in place that the system will remain in equilibrium? – Jacob Rodda Aug 10 '18 at 6:25