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Old Mar 15th 2017, 02:02 PM   #1
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Static Force Analysis

Hi!

I'm trying to complete a static force analysis on the bar linkage shown below. The goal is to find the payload mass in terms of the cylinder forces and everything else in a static environment.


To simplify things I've made the assumption that the mass of the payload in the bucket acts at the centre of mass of the bucket. Also, the bucket cylinder is attached to the boom, and the boom is attached to an anchor point.

From what I understand, to do the static force analysis, you freeze everything in place, and then calculate the force and torque that each link must exert on each other for it to hold that position.

My attempt at the problem has been to break the linkage apart and try to work my way through each component and write down the forces and moments acting on them. For example, the bucket has a force from the boom, a force from the bucket link, and a force downwards from payload mass.

Then, I've tried to do the next component like the bucket link, and repeat the process. My attempt for the bucket and bucket link are below in the photo.



However, I'm terrible at this, so would anyone be able to help me? To reiterate, my end goal is to get an expression for the payload mass in the bucket, in terms of cylinder forces and everything else. I'm thinking the best way would be to take a sum of the torques around the boom pivot point, but I'm not really sure how to get there.

Many thanks in advance.
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Old Mar 16th 2017, 08:15 AM   #2
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To get you started I suggest consider the torque about the pin joint connecting the boom to the bucket, which I labeled point A in the attached figure. Because this is a pin joint, the sum of torques acting on the bucket about point A must be zero. I have attached a free body diagram for the bucket - the torques that need to be considered are due to (1) the weight of the bucket - 'W', (2) the horizontal force of the bucket link, and (3) the vertical force of the bucket link. Note that because of the pin connection between the bucket link and the bucket at point B there is no torque present at that joint either. So, sum of torques about point A yields:

$\displaystyle \Sigma T = (W \times D1) - (F_{BL_X} \times D2) - (F_{BL_Y} \times D3) = 0$

You also know that the ratio of F_BLY to F_BLX must equal the tangent of angle theta (again, because the pin joints at either end of the bucket link cannot transmit any torque):

$\displaystyle F_{BL_Y} = F_{BL_X} \tan \theta$

Now you have two equations in two unknowns (F_BLX and F_BLY), so you can solve for these.

I suggest you do this calculation, then see if you can next work out the horizontal and vertical forces at point A. Please post back with what you find.
Attached Thumbnails
Static Force Analysis-loader.jpg  

Last edited by ChipB; Mar 16th 2017 at 08:18 AM.
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Old Mar 16th 2017, 12:22 PM   #3
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Hi, The "bucket-link and both hydraulic cylinders" are 2-Force
members. Those forces act along the line from pin center
to pin center.

I didn't see it... but? Do you have dimensions for link lengths,
weights of members?

Good Luck, JP
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