Solving 5 Unknowns with 6 Equations 1

[newreynolds]

Probably a stupid question but I am doing a static force analysis using a Method of Joints. There are 3 joints of interest, so 6 equations but I only need to solve for 5 unknowns.

The last unknown is in the last 2 equations so I solve one and then do a check with the final equation but it's never zero. My question is then, should that last equation be satisfied since I only really needed 5 equations?

I believe it should but after looking over my algebra and not finding an error, I'm questioning things.

 

[electricpete]

Let me try pasting the link into the message:

http://files.engineering.com/getfil...f-f9e5-4493-b6a4-62aef0116bf8&file=FILE1c.pdf

=====================================
(2B)+(2B)' ?

 

[FeX32]

Perfect pete.
4 eqns 4 unknows, then the mid joint utilized to solve for Fs. Exactly how we (me, you, zeke, rb (some more directly than others)) mentioned many posts above.

About the direction of the force, could we not just assume the spring pivot (bottom side) could change to suit the direction ? So it would move way left to a position calculable from the force direction. This also proves that the author of the problem didn't really think about the problem at all. The problem is totally flawed from the beginning.
Seems we have completely destroyed it. haha.

Quote of the discussion goes to pete

Everyone has their own slant, and that's what makes it interesting.

Cheers to that.


Fe

 

[FeX32]

The site is a bit wacky this evening (glitchy). (admin: feel free to kill this post later if you like )


Fe

 

[GregLocock]

There's major glitches right across the site today.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[Cockroach]

I still shake my head. This problem is an engineering STATICS issue, what's with the dynamic model?

Four ropes hold a four bar linkage in equilibrium. A spring is to maintain orientation of linkage 4 & 1 at a particular angle to the right hand horizontal datum. Given the rope tensile load and orientation, we are asked to compute that spring force.

So what is with "dynamics"? The system is in equilibrium, there is not motion, not velocity, no acceleration.

This problem has been a nightmare since improperly posted 104 entries ago!

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[zekeman]

Cockroach,

I couldn't agree with you more.

The first post to the thread should have read

'Mr Newreynolds

6 equations in 5 unknowns could be entirely correct.
But at least one of them is a linear combination of the 5 others. If you formulated it correctly, you should have found at least a few sets of 5 equations and obtained the same answers. You did not, so the problem is either you did not formulate it properly OR the problem you received was not in static equilibrium.
Please post the original problem and you can get help here. If you choose not to post the problem then we cannot help you.'

That's hindsight!

 

[FeX32]

I thought we agreed that as stated the problem is not in static equilibrium... the external forces simply create a moment about that fixed pivot that cannot be reacted upon by the mechanism. Thus, if those loads were applied the system would move...hence dynamic.

I do agree with zekeman's response, as that would have been perfectly appropriate.


Fe

 

[Cockroach]

I don't agree, not a dynamic problem at all since motion is impending. We know nothing of the linkage mass, inertia, etc, how are you going to pull dynamic information?

Attached is a scaled layout of the problem. The 4 Bar Linkage can be seen as labelled in black, length and angles preserved to the datum (magenta, horizontal right). Same with the ropes (yellow), 200 N each, four in total, orientated as shown. I have arbitarily set the intersection of links 1 & 4 as the origin, (0,0).

The red circles are the position of links 2 & 3. There are two intersection points, the spring stretches from the lower to upper point. That spring is drawn in at the lower position in green.

So the problem then is to compute the spring force required to maintain equilibrium, i.e. motion impending.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[Cockroach]

The attachment, as per above.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[FeX32]

There is no attachment.

We know nothing of the linkage mass, inertia, etc, how are you going to pull dynamic information

This is regardless of the linkage moving or not. It will move whether we know the inertias ect. or not. So, if it were a real problem, and the linkage started to move but you didn't know the inertias you would consider it a static problem still? I hope not.

I don't want to be controversial. It's just that many of us think that with the given applied loads by the OP, the linkage would rotate about that pin joint. Of course we know it is given as a static problem.
We can still solve it as electricpete did above. But it shows that the spring must exhibit a force and moment for it to be in equilibrium.


Fe

 

[FeX32]

IMO, even though this thread has blown up it is still interesting


Fe

 

[newreynolds]

The original problem was a statics problem. Thus it was clearly a bad problem. I think we should move on with our lives, no?

 

[FeX32]

Haha. Yea, why not .
It's typical of engineers to go nuts on details. Some of us combine that with stubbornness and you know what happens next..


Fe

 

[electricpete]

As was mentioned, there are two solutions for the pair of angles (psi1,psi2).

The previous attachment covered the solution: (phi1 = 3.70, phi2 = 2.494 radians)

Attached is revised attachment which covers the other solution: (phi1 = -1.95, phi2 = 2.04 radians)

The conclusion is the same.

I have no further comments ;-)

http://files.engineering.com/getfil...8be77affdcbe&file=FILE1c_OtherOrientaiton.pdf

=====================================
(2B)+(2B)' ?

 

[FeX32]

Fe

 

[Cockroach]

Spring load is 276.2 N at 71 degrees. I have used Method of Joints to get the solution, the geometrical interpretation of the 4 Bar Linkage is fully described in my computation.

Having trouble posting attachments. It may be my system, but I am trying.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[Cockroach]

Seems to be uploading today, maybe operator error. My apologies for the lack of response yesterday.

I forgot to mention, compressive 276.2 N @ 71 degrees. The spring is in a state of compression. All other members are in tensile loading.

This solution is for Pts A, the spring being 5.42692 m long. The second solution is for Pts B were the spring is 8.52523 m long.

There you have it. No dynamic motion, forget dynamic model. If I were use an extremely heavy spring, stiff as a structural steel member, would you still argue dynamic model? There is no motion.

But agreed, a very interesting problem.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[FeX32]

Cockroach,

Thanks for the input. It has now become more interesting. You have approached the problem totally different that I would have. It is also a much different approach to what electricpete posted. I do agree with electricpete's calculations. Yours I also find no fault from 5 minutes of following it through. However, you state in your calculations that; "since no dynamic information is given, the solution is static with motion impending." Impending? I agree here. This solution is the instantaneous static solution right before it moves . You agree?
If you don't agree, then how come you don't have a moment balance, which would still show an unbalanced moment about that pin joint. Regardless, good discussion.




Fe

 

[FeX32]

Also, in a real life situation, I believe the dynamic forces in the members would superseded those of the instantaneous static ones. So, from a design perspective (assuming motion is wanted) the dynamic solution still needs to be conducted. No? Treating it as a textbook problem, it's a nonsensical conclusion, and all of us are correct to a certain point.


Fe

 

[FeX32]

hmm. Instantaneous vs. equilibrium solutions.
All we need is perspective. Personally, I would have gown with equilibrium.


Fe