rod that is pin jointed at both ends
rod that is pin jointed at both ends
(OP)
Hi
I am using a rod in compression and am fairly comfortable with using Eulers theorem.
However how could I resolve the situation where a compressive force is at an angle - see picture
I believe that this would actually force a torque on the rodding and perhaps should be more of a concern than Euler.
Would I resolve the force into the x and y components relative to the centre line of the rod and the force that is not resolved to the centreline is basically the torque that is acting on the rodding itself rather than transmitting force.
http: //files.en gineering. com/getfil e.aspx?fol der=d4bbce 14-a853-45 15-89fa-c2 fa4d7cb705 &file= cranks.jpg
I am trying to understand the forces in this rodding as presently it is bending.
regards
John
I am using a rod in compression and am fairly comfortable with using Eulers theorem.
However how could I resolve the situation where a compressive force is at an angle - see picture
I believe that this would actually force a torque on the rodding and perhaps should be more of a concern than Euler.
Would I resolve the force into the x and y components relative to the centre line of the rod and the force that is not resolved to the centreline is basically the torque that is acting on the rodding itself rather than transmitting force.
http:
I am trying to understand the forces in this rodding as presently it is bending.
regards
John





RE: rod that is pin jointed at both ends
If however, there is a moment (i.e. they really are not pinned joints at the column ends) then would treat it as a so called "beam-column".
Brian
www.espcomposites.com
RE: rod that is pin jointed at both ends
Or a schematic that clearly shows the nature of the pin joints?
RE: rod that is pin jointed at both ends
the angles would experience a load along the line of action of the rod.
then draw a fbd of the angles to deermine the pivot reactions.
RE: rod that is pin jointed at both ends
The black arrows are the only force you need to consider acting in a plane of the connecting rod and placing it under compression.
desertfox
RE: rod that is pin jointed at both ends
The force placed on the rod has two components, one will be along the plane as desertfox states and the other will will place a torque on the rod I presume?
The cranks are just normal 90 cranks with a centre stud.
regards
John
RE: rod that is pin jointed at both ends
no, the force on the rod has one axial component, only.
the rod axial force reacts the torque applied. the pivot point reacts the two forces applied to the cracnk, the rod force and the main drive force.
RE: rod that is pin jointed at both ends
similalry at the other crank, the load created in the output is the reaction to the torque applied to the second crank from the rod.
clear as mud ?
RE: rod that is pin jointed at both ends
Have a look at this example:-
http://
the resultant forces act along the axis of the two force member, just like the black arrow forces in your diagram.
desertfox
RE: rod that is pin jointed at both ends
I think I understand in that what you are saying is that pin joints do not transmit moments. But what I am thinking about is how the off centre forces are dealt with
In attached diagram I have exaggerated the problem, the cranks are set up for mechanical advantage.
F2 imparts a force, but what happens to its components? Is there an F4? or does it all travel as F7? Then at the other end what happens to F7's components or is it all transmitted through F5?
Have I drawn forces F4 and F3 correctly - what is this doing to the rod, can it be resolved to a moment acting on the bar itself - tending to want to bend it?
http:/
regards
John
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
Yes look at the example of the two force member they resolve component forces horizontal and vertical and then resolve the resultant force along the axis of the strut.
Yes pin joints don't carry moments.
desertfox
RE: rod that is pin jointed at both ends
Personally, unless the OP knows otherwise, I would ignore any torque here and just deal with the axial forces the rod sees.
Cheers.
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
the middle bit, loading hte rod looks messed !? There should be a single force in the rod (F2) offset L2 on one crank and L3 on the other ... F2*L2 does not have to equal F2*L3. At the end of the day, the sum of the input an output forces = the sum of the pivot reactions.
for a position of the cranks, you have a direction for the connecting rod, a line of action, and an offset from the pivots.
the crank pivot reacts the two loads applied to it. the crank arms will end up carrying axial load and bending (some transverse component).
do the cranks rotate, under load (changing the geometry) ?
RE: rod that is pin jointed at both ends
If the green arrows are acting on the pinned joint, then only their axial component transfers to the rod through the pinned connection. Unless the cranks can rotate in the opposite direction to each other (producing torsion in the rod), then I would do as you both agreed...analyze for the axial force only using k=1.
RE: rod that is pin jointed at both ends
in a beam, transverse load is reacted by a moment at the far end, yes ?
in a pinned rod, there can be no end moment (as i said, you can have your friction moment, but i don't want it !) ... if there is no moment there can be no transverse force, 'cause there is no free body balance.
this is, IMHO, a really simple mechanism.
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
It is a simple mechanism, but as can be seen from the diagram is the off centre forces causing a bending moment?
http:/
thanks for your help so far on this.
John
RE: rod that is pin jointed at both ends
@rb: Just because you do not want a moment to exist in a theoretical problem, does not mean that it will not exist in the real world. Parts do wear out and grease does fail, plus countless other imperfections of design. I am not saying that it is there. I am saying it can exist.
And steel rods can take moment, as can any section of any material (just depends how much). Just try to bend one with your hands. Cheers.
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
it's a Long time since i've done mechanisms ! structures are easy 'cause they're in static equilibrium. it relatively easy to relate the movement of the input shaft to the movement of the output shaft. the two cranks are connected by a fixed link. The question is how much load is created in the rod ?
If it's in static equilibrium, then why does it rotate ? if it's less why does it stop rotating ? my "guess" is that the rod in the rod is the static equilirium load, and that the rotation is controlled by the movement of the input shaft.
RE: rod that is pin jointed at both ends
The OP stated initially that the rod is bending - fact.
The problem is that the diagram we are looking at is a two dimensional diagram, but the problem is three dimensional. I think what is happening is that the crank shaft axes and the rod axis are not in the same plane, inducing moments into the pinned joints at the ends of the rod. A moment has to exist or the rod would not be bending, unless it was bent prior to installation.
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
All the OP needs to do is draw a line parallel to the axis of the connecting rod at each crank end, then from that line draw two perpendicular lines one at each end which pass through the crank centre,knowing the torque on the crank and dividing this by the new lengths measured he can find the resultant force along the axis of the connecting rod.
desertfox
RE: rod that is pin jointed at both ends
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: rod that is pin jointed at both ends
However you can connect two cranks with a connecting rod without out of plane bending by machining each crank with a clevis and fitting the link in between with pins.
desertfox
RE: rod that is pin jointed at both ends
I have uploaded a file that might help, I think your resolving forces in the X and Y directions which is fine, however your resultant force on the connecting link with a simple pin joint at each end is down the central axis between the two pins, one way of getting this resultant is shown in the file.
desertfox
RE: rod that is pin jointed at both ends
The front crank is the drive end and only ever moves the bell cranks say half a turn either way from the mid point, most of the time it is static, holding the rear crank in position.
This is a simple rod connected by 2 bell cranks, bending is strictly in 2D due to the fixings as desertfox alludes to, it is a a fork type connection.
Because the rod is not square to the bell crank (in order to maximize the mechanical advantage it is futher out on the arm of the seccond crank) this means that the applied axial load is not all in the horizontal plane, relative to the rod, there is a small vertical component of applied force FB. Is this vertical component lost?
I suppose maximum efficieny occurs when the bell crank is at 90 degrees. Is this too small to be worried about?
Also - why do I have 2 equations for FD?
http:
regards
John
RE: rod that is pin jointed at both ends
Our posts crossed see my uploaded file.
Thanks for clarifying the mechanism.
Regards
desertfox
RE: rod that is pin jointed at both ends
Just looked at your calculations, firstly once you have Fb you need to divide it by Cos Alpha that gives you the force in the connecting rod that then transfers its force to Lc, then if you take the force in the connecting rod and draw its line of action perpendicular to the pivot point at Lc you can workout the torque acting on it.
Lastly the moment where Lc is you have:- Fd*(Lc+Ld) I think that is completly wrong.
desertfox
RE: rod that is pin jointed at both ends
thankyou for the sketch, yeah I think I am getting there with this, we are on the same lines
the fact is the small horizontal component has reduced the force from end to end, maximum efficieny is when the angle between F2 and FR (on your sketch) is zero. This horizontal component doesn't travel down the rod but is reacted againts the primary force (the vertical force)
Plugging in some numbers:
Force 2kN
L1 = 0.3m
L2 = 0.4m
angle of crank relative to the rod (angle between F2 and FR) = 10 degrees
LR = 0.4 x Cos 10 = 0.39
so FR = 2x103 x (0.3 + 0.39) = 1.38kN
a loss of (2x103 x (0.3 + 0.4)) - 1.38x103 = 20N (1%)
RE: rod that is pin jointed at both ends
It should be (2x103 x 0.3)/0.4 = 1.5kN
take away the horizontal component
The horizontal component (to the rod) is 1.5x103 x Cos 10 = 1.477kN
A reduction of 22.7N
RE: rod that is pin jointed at both ends
FC = FD x LD / LC and it acts directly on the pivot
so FB x LR x Sin 40 = 0, which I think it means its trying to say that there are no moments at all on C
regards
John
RE: rod that is pin jointed at both ends
Fr in my sketch should be greater than F2 because the right angled distance from the line of action of FR is smaller than the distance than L2, therefore to find Fr divide F2 by the Cos alpha angle which in your case is Cos of 10 degrees.
desertfox
RE: rod that is pin jointed at both ends
looking at your sketch i think there's a problem in your understanding of torque the torque of Fa is Fa*La Only if La is perpendicular to Fa (which it doesn't look to be in the sketch)
the torque arm at crank 2 of the rod force is less than Lc ('cause the rod is not normal to the arm of crank 2).
similarly Fd.
but none of this explains why the rod is bending (in real life).
RE: rod that is pin jointed at both ends
Fb creates no moment about C since it passed thru C.
it'd be Way more rational to take moments about the pivot of crank2.
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
I am with you also on the Force*Cos(angle)
working with your desertfox's sketch
LR = Sin (90-alpha) x L2 = Cos (alpha) x L2
So basically FR = (F1(v) x L1) / Cos (alpha) x L2
(v) denotes vertical component
[Interesting to note that as alpha decreases FR increases)
please tell me I'm right
cheers
John
I agree my attempts at taking moments are lame - thanks for
RE: rod that is pin jointed at both ends
Using your diagram earlier with the enlarged view of the crank and Fb, if Fb as drawn is perpendicular to the crank and the rod on the otherside is at an angle alpha, then the force in the rod is given by Fb/Cos Alpha, now imagine just altering the rod angle alpha (everything else staying the same) so that instead of being 10 degrees it is now 30 degrees, therefore as Alpha increases then the force in the rod FR increases, if Alpha decreases then the force FR decreases, I think your statement in brackets is the wrong way round.
Your statement in your original post:-
"I am trying to understand the forces in this rodding as presently it is bending".
Is it actually bending on the actual mechanism or are you thinking its bending because of your forces in your diagrams.
If its bending for real then what might be happening is that its buckling under the compression forces, we could determine that but would need the forces in the mechanism and the connecting rod sizes.
desertfox
RE: rod that is pin jointed at both ends
I just need to develop the free body diagram.
RE: rod that is pin jointed at both ends
Look at the example on the link I left you earlier and the sketch I uploaded recently.
From what you are saying I believe the links just buckling, have you considered using a circular connecting link ie uniform 'I' value in all directions.
desertfox
RE: rod that is pin jointed at both ends
have your calcs shown that the original rod buckled ?
alpha is defined two ways in your sketch, as the angle between the rod and the normal to the crank1 arm, and as the angle between the rod and the crank2 arm ?? are the cranks parallel ?
if alpha (=a) is the angle between the rod and the crank1 arm, note this is not your definition, for you have alpha as the angle between the rod and the normal of the arm; i think you need three other angles defined ...
the angle (=b) betwwen the input for and crank1 arm,
the angle (=c) between the rod and the crank2 arm, and
the angle (=d) between the output force and crank2 arm.
then using the arm lengths A for crank1 at input force,
B crank1 at rod attmt,
C at crank2 at rod attmt, and
D at crank2 at output force.
then Prod*B*sin(a) = Pinput*A*sin(b)
and Prod*C*sin(c) = Poutput*D*sin(d)
RE: rod that is pin jointed at both ends
hi rb1957
The Euler equation bears what we are seeing. I have attached a free body diagram which hopefully explains it better, this is a difficult to get across with text!
I can use the same principle for the rear crank, there's really no reliable dimensionable relationship between the position of the front and rear crank except the force travelling down the rod. So I almost have to treat them as seperate entities.
At least now I have a formula for the force in the rod/link thanks to you guys.
http:
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
Sum Mb = 0 ...Pav*0.305 = Pbh*x (why is x a variable ?)
the reactions at the pivot are wrong ... there are contributions from both forces (Fa and Frod) in both directions.
RE: rod that is pin jointed at both ends
x is variable to suit the installation (a sleeve on a crank arm)
I have the reactions for FA as FA Vertical and FA Horizontal similarly for FC (the rod) FCV and FCH - all relative to the crank. The moments (FCH and FCV) don't act on the centre pin.
I have drawn the pin reaction arrows the wrong way around.
RE: rod that is pin jointed at both ends
Fa has h- and v-components, both these are reacted at the pivot.
can you draw a free body diagram ? sum forces in both directions ??
i'd've thought x was known (since you've already got this thing built, no?)
RE: rod that is pin jointed at both ends
http:
RE: rod that is pin jointed at both ends
ΣFx = 0 = FAx-RBH-FCy
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
sumFx = 0 ... Fbh = Fax-Fcy
your diagram is not incorrect, but it is very sloppy ... you're using "datums of convenience" ... it's "better" to have a consistent +ve direction and to measure angles to the same datum. 'cause then the math works out better. with your approach, you need to be looking at thepicture to understnad why you're combining x- and y- components, +ve and -ve signs.
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
I have swapped the labels around for FCy and FCx - schoolboy error!
Okay Terio and rb1957 I'll take it as read that FCy and FAy should be included so therefore amended diagram is attached.
rb1957 - I'm probably overegging this anyway by taking account of 'theta A' angle since is it is only a few degrees at most, for this purpose I'll keep it simple since I am seem to be struggling with this as it is
http:
RE: rod that is pin jointed at both ends
Yes,if you "see" the rod bending in that 2 dimensional structure it is due to the dynamics of the problem , i.e. acceleration in the mechanism and friction.
If the mechanism is dead slow or almost stopped, then the static case is in play and there can be virtually NO moment carried in the rod, even with friction present
RE: rod that is pin jointed at both ends
It appears to me that your summation of moments in your last post is incorrect Fcy doesn't have a moment it is a vertical force going through the pivot at B and the force you have actually found in equation 1 is not Fcy but Fcx.
I will try to help you some more on probably Friday.
desertfox
RE: rod that is pin jointed at both ends
"datums" of convenience" ... your +ve direction for each force suits the direction you think the force will be acting ... Fax is +ve in one direction, Fcx the other. "Normally" you'd start by defining a +ve co-ordinates system x +ve to the right, and Fc will be a -ve number. The advantage of this system is you can say Fax+Fbx+Fcx = 0 (instead of Fax-Fbx-Fcx = 0); i suspect Fbx is negative.
not sure how this helps answer your original problem ... why is the rod bending ? If the calc'd load exceeds the euler buckling load, you then have to ask yourself, what's controlling the displacement of A ? ('cause if the rod buckles, it's stiffness goes to zero and the crank'll rotate, unless A has soe displacement control).
RE: rod that is pin jointed at both ends
"Yes,if you "see" the rod bending in that 2 dimensional structure it is due to the dynamics of the problem , i.e. acceleration in the mechanism and friction.
If the mechanism is dead slow or almost stopped, then the static case is in play and there can be virtually NO moment carried in the rod, even with friction present"
------------------------------------------------------------------------
Firthwer comment:
While the dynamic situation would cause some bending in the rod I do not believe it to be of the magnitude to cause the "observed " bending.
So, I basically agree with the conclusion of others that since there is NO moment acting at either end of the rod there cannot be any bending within the rod. As a consequence, if the OP observes bending then it's cause is Euler buckling due to a single compressive force in the rod, period.
I think the OP should post the forces and rod dimensions so we can put this to bed. If the numbers suggest Euler buckling then case closed. If not, then we have to look for something in the pin connections that could "clamp" one or both ends and thus cause the "observed" bending.
RE: rod that is pin jointed at both ends
rb1957 - I understand what you mean about negative and positive forces, and yes FBx will be negative to how I have drawn it, since FCx >> FAx I can virtually eliminate FAx.
I have now at least arrived at a Free Body Diagram which provides the compression force in the rod, thanks to all who pointed me in the right direction and having patience!! Especially rb1957, desertfox, Terio and zekeman. The rear crank will follow the same pattern.
Once I understand more I can search for relevant information and found some great resources:
How to add moments in a 4 part series: http://youtu.be/MUMcn-VJsOc, use the simpler method!!
How to solve FBDs: http://youtu.be/vNwOcEUU7Jg
I have now answered my original question of what is the force in the rod, which is really determined by the load, the actuating force just increases to meet the demand. It is my opinion that the off-axis load tends to accelerate the situation once the critical Euler load has been exceeded.
thanks all
http:
RE: rod that is pin jointed at both ends
Sorry I thought the thread had ended which is why I didn't post anymore, anyway if your happy with your anwsers now goodluck and your welcome.
desertfox
RE: rod that is pin jointed at both ends
it's really simple to solve the problem correctly ...
determine Fc from sum of moments about B.
determine the pivot reaction from Fa and Fc.
neglecting terms as early as you have will get you into trouble. And these no reason to.
sorry, but IHMO your final sentence shows you haven't learnt anything. there is No off-axis load in the rod.
and you penultimate sentence implies that maybe the applied loading is a displacement (rather than a defined load) and a seized crank2 could explain the behaviour of the rod.
desertfox,
three times "your" should be "you're"
RE: rod that is pin jointed at both ends
RE: rod that is pin jointed at both ends
Removing FAx is to help me investigate the suitability of the crank pin.
Again, I agree, you can't have an off axis load through a pin - I do learn rb1957! Have faith
RE: rod that is pin jointed at both ends
still wonder if this column buckling ... if the rod was buckling then the rod would lose axial stiffness and crank1 would rotate freely.
but maybe this is a displacement load ? does a move x" controlled by the linkage attached to it ??
RE: rod that is pin jointed at both ends
I know that angle thetaA is probably 5 to 10 degrees at the most so FAy is relatively small, similarly with thetaB.
RE: rod that is pin jointed at both ends
are the fasteners at the ends of the rod clamped up tight ?
really dumb question ... is the rod too long ?
RE: rod that is pin jointed at both ends
Thanks for correcting my mistakes - didn't know this was an English class, thought we were in an Engineering forum (grin). By the way "and you penultimate sentence" should be "and your...."?
Regards,
desertfox
RE: rod that is pin jointed at both ends