Linkage Analysis and force study

[jai_helsing]

Hi All,

I am working on this linkage mechanism. Please see the attachment for images. There are 3 pivot points. Two of which are connected to the ground. The" Inside Leg 1" is telescopic to "Leg 2" and has a 120 LB compression gas spring connected at mount points as shown in the image. The leg 3 is geometrically placed to have the correct opening angle(of Leg 2 which is 40 Degrees). At the open position as shown in the image the gas spring is fully extended and the system stands stable. I was looking to do a force analysis of this linkage system and study the amount of force needed to pull the leg 2 down( i.e closed position for the mechanism). Please see the attached the document for details.
Thank you.

 

[BvU]

the gas spring is fully extended and the system stands stable. I was looking to do a force analysis of this linkage system and study the amount of force needed to pull the leg 2 down

Well, that depends on how much it takes to break things ! The 51 inch one is the side that wants to extend further if leg 2 is to go down ...

 

[jai_helsing]

Hi BvU. Thank you for the reply. The total length of that link(leg) is 83in (51+32). There is a smaller telescopic tube (23 inches long,sorry for not providing that length before) inside the 83 inch long leg which pivots at point 1. The fixed end of the gas spring is connected to the smaller telescopic tube at the opposite end to the pivot point1. The moving end of the gas spring is connected to the longer leg(83in), which slides in a slot build in the telescopic tube(23in). I am trying to determine the vertical force needed to applied at the end of the longer tube to start moving the link down. Hope this makes my question more clear. Please let me know if any information is missing. Please see the attached photo.

 

[BvU]

Still can 't make sense of the thing. Can you make a diagram like the one at the bottom of Force Calc Linkage.docx with only the essentials -- i.e all things freely sliding inside others removed and clearly shown what the spring mount points are attached to. Avoid using different names for the same thing (front mount point = fixed end -- Rear mount point = sliding end ? or is it the other way around ? Why not use A and B instead of causing confusion).

I gathered Pivot 3 is not sliding. But I have a hard time understanding what the spring is doing against what.
Something like

?

Only external forces are at A, B and D, so they must add up to zero. And A and B horizontal components cancel.
Can't think of a useful force and torque balance yet.

 

[Tom.G]

If the image by @BvU matches you problem, here is my take on it.

1. Seems to come down to how the length of AC changes as the angle A changes
2. multiply AC change in length by the spring constant
3. then account for mechanical advantage you have at AD versus AC

Cheers,
Tom

 

[jai_helsing]

Hello @BvU and @Tom.G . Thank you for your inputs and support to help me solve my problem. Please see attached the document with detailed information on the system and its working. Can you please take a look and let me know. Thank you again.

 

[Tom.G]

Here is a more readable image from the above post by @jai_helsing :

 

[jai_helsing]

Hi @Tom.G and @BvU . Based on the Above details can you please formulate the equations and diagrams to help me solve the problem. Thank you.

 

[jrmichler]

study the amount of force needed to pull the leg 2 down

Are you familiar with free body diagrams (FBD)? If not, spend some time studying them. The force at D needed to pull the linkage down will be different between the open and closed positions, so you need to solve those two cases separately. There will be two separate FBD's.

Based on the Above details can you please formulate the equations and diagrams to help me solve the problem. Thank you.

We will help you, but you need to do some work yourself. As a master's student, this should be well within your capabilities. I'll give you some suggestions to get started.

Start by showing the force at pivot A. Keep in mind that forces are represented as vectors, that vectors can be decomposed into components, and those components can be in any direction. With that in mind, the total force at A has a component parallel to the link ACD. That component is the force to compress the gas spring. Show that component on the FBD.

Show the unknown force at point D as F. You do not yet know the magnitude of F, but you do need to specify the direction on both FBD's. Is it vertical, horizontal, perpendicular to link ACD, or some other direction? Since you know the direction of force F, you can calculate the components parallel and perpendicular to link ACD, or you can calculate the vertical and horizontal components. You may need to do either or both.

Now start calculating other forces or force components. If you do not know what to calculate next, try calculating the sum of moments about points A, B, C, and D. At least one of them will allow you to move forward.