Statics question about FBD of a backhoe (w/ pin reactions)

[mhrob24]

Homework Statement

Draw the FBD of the Backhoe as shown in the figures

Relevant Equations

M=0
Fx=0
Fy=0

So, for the link "AB"...they didn't directly list the pin reactions from pin "A" here, but I want to be sure that I understand what those reactions are. So, from what I see in this image, the member is pushing at the pin "A" (red arrow) because otherwise, the bucket would want to rotate counterclockwise (blue arrow). That means that the pin "A" reaction on the member "AB" is also pushing back against member "AB" (green arrow), so it's a two-force member with compression forces at each end. I THINK the book is showing the same thing, because if you look at what they have for the FBD of pin "B", they have the member "AB" at "B" pushing against pin "B", so the reaction from pin "B" will push back against it; just like pin "A" does.

Is this correct? I have another question about how this book drew the forces, but I’ll ask after I clarify this…

 

[Lnewqban]

Your description is correct.
The weight of the bucket has to be supported by the ground; the mechanism is just a chain that connects bucket and ground.
As the links AB, AE and BC are articulated, each can only support compression or traction loads; none will be subject to external moments.

If you can imagine that each link has some degree of elasticity, you could visualize links AB and AE getting shorter and link BC stretching, as it prevents pin B from moving too much to the right.

 

[mhrob24]

Your description is correct.
The weight of the bucket has to be supported by the ground; the mechanism is just a chain that connects bucket and ground.
As the links AB, AE and BC are articulated, each can only support compression or traction loads; none will be subject to external moments.

If you can imagine that each link has some degree of elasticity, you could visualize links AB and AE getting shorter and link BC stretching, as it prevents pin B from moving too much to the right.

Thank you for your response.

There is a moment about point “D” though, right? Because like, if you were to remove the link AB, that bucket would rotate around “D” in the CCW direction. So the force from the member “AB” is preventing the moment about “D”, but member “AB” still does not experience an external moment. Am I saying this correctly?

Lastly….about the pin “A” reaction forces on the BUCKET. To satisfy Newton’s third law, the reaction forces on the BUCKET are in the OPPOSITE direction of the reaction forces on member “AB”, correct?

 

[Baluncore]

Rhetorical question: What is a backhoe?
Is it simply a bucket that faces towards the operator, like a hoe?
Or is it the bucket and the chain of linkages that positions the bucket?

 

[Lnewqban]

Let's call input the internal moment induced by bucket weight at G times horizontal distance to pin D.
The output is not a moment but a pair of forces applied at D and A.
As pin D is unable of transferring any moment up into the chain of links connecting to ground, we don't have to consider that internal moment, only to determine the magnitude of forces at D and A, considering distance AD.

There is actually a shear load on pin A.
Two cross sections of the pin are resisting the efforts of the two pin housings of the bucket and the pin house of link A to shear them off.
When the bucket is full of sand or dirt, that shear load increases much more.

 

[Baluncore]

When the bucket is full of sand or dirt, that shear load increases much more.

The weight of the bucket and contents is minor compared to the enormous hydraulic forces that are applied to the linkages through the pin joints while the bucket is being used for digging.

Maybe you should close the circular linkage chain through the stabiliser legs, by considering the ground forces acting on the teeth of the bucket while it is digging.

 

[mhrob24]

Let's call input the internal moment induced by bucket weight at G times horizontal distance to pin D.
The output is not a moment but a pair of forces applied at D and A.
As pin D is unable of transferring any moment up into the chain of links connecting to ground, we don't have to consider that internal moment, only to determine the magnitude of forces at D and A, considering distance AD.

There is actually a shear load on pin A.
Two cross sections of the pin are resisting the efforts of the two pin housings of the bucket and the pin house of link A to shear them off.
When the bucket is full of sand or dirt, that shear load increases much more.

View attachment 292777

Right, I see that: the bucket and the link AB are trying to shear the pin by pushing on it in opposite directions at the ends. But because the pin obviously doesn’t shear, there has to be a pin reaction force on both link AB and the bucket, right? And these two reaction forces are opposite to each other due to Newton’s third law, right?

And I understand the internal moment explanation you gave as well; that was a good explanation. Thank you.

 

[mhrob24]

Rhetorical question: What is a backhoe?
Is it simply a bucket that faces towards the operator, like a hoe?
Or is it the bucket and the chain of linkages that positions the bucket?

The second option.

I think you’re asking this to try and get me to realize it’s not just a simple transfer of the weight from the contents in the bucket; it’s being transferred through multiple members/links….. ultimately being supported by the actual machine itself. Like, the weight of the machine that’s on the ground. I do realize this.