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Cantilever ( bellcrank )

#1
I have been toying aroung with this idea for a while. After reading the "searched" posts on cantilever and bellcranks, I found it was mostly theory and little useful numbers and angles. I still learned alot reading them, so don't think I'm tring to be a dick.

I attached a hand drawing that is 1/6 scale. So my numbers are not exact but close enough.
The black lines are the shock compressed (full bump) and extended (full droop)
The shock is a fox 2.5"x 14".
At full bump the shock is 90* to the bellcrank (drawn in red)
At full droop the shock rotates or pivots 11* (the bellcrank is blue)
The bellcranks pivot points; the shock side is 16", the axle side is 28", and the 3rd side is aprox. 24.75".
Inside angle of the bellcrank is 62* and it rotates 55* (full bump to full droop)
Total movement at axle end is 26" yeilding an "overall" 2:1 ratio. (I know it changes through the movement)

I was surprised that the shock only pivots 11* total. So a ride height the angle correction factor would only be about 5.5*.
This is the same as an A arm set up with the shock mounted at 84.5* to the lower arm pivots at ride height.
Also if the shock side of the bellcrank equal to the shock stroke the total was only 13* (not shown)

Now the questions. I am having trouble with the axle side and understanding how it REALLY WORKS!
Mainly with the bellcrank to axle "link". At first I reasoned that the force placed on it would be the same throught the travel regardless of the angles it operated at (obviously talking about operation in a narrow range that would not cause failure or binding) but now I am thinking that the force will change slightly because the leverage between the liks mounts will change as the link angle changes thoughout is travel.

Is this correct? Will the angle of the link change the force transfured though it? Or will it be the same?
or is it even worth thinking about or worring about?
Any help in understanding this would be great. Joel.
 

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#2
So I did some more thinking and searching. Ended up searching "torque" and found a bunch of useful info on Wikipedia.

"Torque, moment or moment of force (see the terminology below), is the tendency of a force to rotate an object about an axis,[1] fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist to an object. Mathematically, torque is defined as the product of force and the lever-arm distance, which tends to produce rotation.

The magnitude of torque depends on three quantities: the force applied, the length of the lever arm[2] connecting the axis to the point of force application, and the angle between the force vector and the lever arm. In symbols: where
τ is the torque vector and τ is the magnitude of the torque,
r is the displacement vector (a vector from the point from which torque is measured to the point where force is applied), and r is the length (or magnitude) of the lever arm vector,
F is the force vector, and F is the magnitude of the force,
× denotes the cross product,
θ is the angle between the force vector and the lever arm vector.

The length of the lever arm is particularly important; choosing this length appropriately lies behind the operation of levers, pulleys, gears, and most other simple machines involving a mechanical advantage."


Wish I would have found this before I posted! Oh well. So now im just gonna try and figure out how to do the math right, and build a few scale models for testing.
 
#3
That ratio change through travel is important. Have a look at photos of the various Ivan Stewart stadium trucks. Some of them even run the shocks backwards so they pull on the shock as the axle moves up.
 

Becerra

Well-Known Member
#4
looking at any intro to physics book will show you how to calculate forces and torsions depending on moment of inertias and theta changes( Angles between crank and link), with changes in angle, changes of displaced forces occur.
 

atomicjoe23

Well-Known Member
#5
Same info can be found in Machinery's Handbook as well as Statics & Dynamics textbooks. . .

. . .I started down cantilever lane about 2 years ago (maybe 3) and I pretty quickly figured out that I wasn't quite ready for that; I didn't have enough off-road driving experience or design/fabrication experience. . .so I shelved the idea until I was more adequately prepared. I'm hoping to hop back on the project in the next year provided I can get the projects I already have started finished.

Good luck!!!
 
#6
Same info can be found in Machinery's Handbook as well as Statics & Dynamics textbooks. . .

. . .I started down cantilever lane about 2 years ago (maybe 3) and I pretty quickly figured out that I wasn't quite ready for that; I didn't have enough off-road driving experience or design/fabrication experience. . .so I shelved the idea until I was more adequately prepared. I'm hoping to hop back on the project in the next year provided I can get the projects I already have started finished.

Good luck!!!
Thank you for the reply. I have read your cantilever tread(s) a few times over, and was bummed it got shelved, but glad it may be back on soon.
The formula that was on wiki did not "copy and paste" on post #2.

1st formula; t=rxF or 2nd formula: t=rFsin0 (the sin0 had a diagonal line through the "0")
I was wondering if this is what you mentioned about the info found in Machinery's Handbook, and Statics & Dynamics textbooks? Does it match?

I think I need to use the second formula because the link will not always be 90* to the pivot arm, therefore needing the angle correction factor. The first formula seem to be used when the link (or force) is at a constant 90* angle to the lever arm.

Also I made a scale model and plotted out the wheel travel vs shock travel. I was vary surpised to find that, for my little set up, the line was very linear. It had a slight raising rate from full droop to ride height, and from ride height to full bump it was basically linear. The last two inches were technially falling rate, but not by much.
I will try to post up the graph later.
 

atomicjoe23

Well-Known Member
#7
I would have to go back and look that stuff over again. . .the one thing I do remember for sure is that you want to avoid a falling rate. . .
 

Becerra

Well-Known Member
#8
Your first formula is to calculate torque due to a tangential force ( t=rF ). A tangential force F applied at a fistance r from the axis of rotation produces a torque. Your other formula is to calculate torque for a general force ( t= rFsin*theta ). A force exerted at an angle theta with respect to the radial direction and applied at a distance r from the axis of rotation. The only thing that i think would be difficult in trying to calculate your torque or forces would be to figure out your true inital force that then can be inputed into your equation.
 

socalmoto

Well-Known Member
#9
DEFINITELY pay attention to the angles and travel numbers and use something like Excel to graph them. Its very simple and im sure you can google some instructions if you havent used it. If you can draw the bellcrank as it cycles and get axle travel numbers every inch or half inch (shock travel and wheel travel), you can graph your motion ratio and see if your motion ratio is increasing all the way up to bump or if you have digressive valving. Changing the angle of the link mount on the axle and the angle of the link itself from the axle to the crank will change the MR quite a bit.

If this crank is being used with an axle with leaf springs you may have to fiddle with it quite a bit as the motion ratio graph is going to somewhat screwed up since the leaf pack doesnt just swing in an arc. The leaves straighten out and push the axle backwards. Leaves also rotate the axle quite a bit. So depending on the angle of your link and link mount on the axle, it can will screw with the MR curve. Leaves generally will rotate the axle backwards (pinion points up) on bump so if the crank is behind the axle the last few inches of travel will probably start going digressive. If this is for an axle with links, try and get it in front of the axle as the motion ratio curve is very smooth and easier to make progressive (you can tailor the MR curve very easily).

If you are looking at the moment equations to find out how strong the crank needs to be, you will also need to look at the side loads on the axle side. When the axle articulates it will move the link in board creating an angle out of plane and will add another moment to your crank. If your crank is not wide/strong enough it could bend.
 

atomicjoe23

Well-Known Member
#10
DEFINITELY pay attention to the angles and travel numbers and use something like Excel to graph them. Its very simple and im sure you can google some instructions if you havent used it. If you can draw the bellcrank as it cycles and get axle travel numbers every inch or half inch (shock travel and wheel travel), you can graph your motion ratio and see if your motion ratio is increasing all the way up to bump or if you have digressive valving. Changing the angle of the link mount on the axle and the angle of the link itself from the axle to the crank will change the MR quite a bit.

If this crank is being used with an axle with leaf springs you may have to fiddle with it quite a bit as the motion ratio graph is going to somewhat screwed up since the leaf pack doesnt just swing in an arc. The leaves straighten out and push the axle backwards. Leaves also rotate the axle quite a bit. So depending on the angle of your link and link mount on the axle, it can will screw with the MR curve. Leaves generally will rotate the axle backwards (pinion points up) on bump so if the crank is behind the axle the last few inches of travel will probably start going digressive. If this is for an axle with links, try and get it in front of the axle as the motion ratio curve is very smooth and easier to make progressive (you can tailor the MR curve very easily).

If you are looking at the moment equations to find out how strong the crank needs to be, you will also need to look at the side loads on the axle side. When the axle articulates it will move the link in board creating an angle out of plane and will add another moment to your crank. If your crank is not wide/strong enough it could bend.

All good info there. . .and you can see how quickly this begins to effect that, and how you can get confused fairly quickly with all the numbers and calculations which is why I decided to shelf my cantilever project until I get some more experience under my belt.
 
#11
Thanks for the replies and help. As for the formulas I was just going to guess on the initial force, and then do the calculations for min and max angles and a few in throughout the suspension cycle. I figured this would help me to see a pattern, if any, in relation to the angle beween the arm and the link. But now I am starting to think I should just focus on the motion ratio. I don't really care about the forces applied as from an engineering stand point, but rather I was thinking that it would help me to be able to understand the relationship between the rotation and angle change vs motion ratio.

Anyway, here is a basic graph of the wheel travel vs shock travel. This one is set up for 24" of wheel travel and has an inside bellcrank angle of 90*. Also the bellcrank is mounted behind the axle in this graph. I have one of it in front of the axle but have not measured or graphed it yet, and honestly may not be able to make it fit between the axle and the truck cab. Still need to do a rough measurement of space avaliable. So like all suspensions, compromises must be made.

What do you think?

I was surprised at how linear the line is, but then again this is my first run at it. And if I did go ahead and build it I would be using the dual rate coils, shock bump zone, and hydraulic bumps as the progression in my suspension.
 

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socalmoto

Well-Known Member
#15
Can i ask how you actually got that graph? Did you actually model it with a moving axle (with either links or leaves)? Or did you just model straight up movement on the cantilever link and see what the shock did? Those are two VERY different things.

Your graph is shock travel VS wheel travel. A motion ratio graph would be (shock travel divided by wheel travel) VS wheel travel (at least i like it vs wheel travel). Your graph shows that your motion ratio goes from around 0.58 to 0.46 motion ratio which is pretty much just constant. With links this MIGHT be possible.....

Reason i ask about your graph is this photo below was a graph of a cantilever setup on the back of a leaf spring truck (behind the axle). Not mine, but i was able to ACTUALLY measure the shock vs wheel travel (at every one inch of wheel travel with main leaves on). We were going to see if it was worth the time and hassle to redesign it, but with the leaf springs doing funky things and his graph for the most part moving towards a 1/1 motion ratio at bump we decided to leave it. The last 2 inches of travel drop off on the motion ratio due to the axle rotating at full bump. We decided that there wasnt much chance to eliminate the drop off on motion ratio without reducing bump travel, remounting the springs, shackles, and redoing the whole rear so just tossing in a hydaulic bumpstop would add more benefit then remaking everything. To be clear, 1/1 means the shocks and wheel travel are the same, so a .5 motion ratio in the graph would mean .5 inch of shock for 1 inch of wheel travel. The uneven graph is due to changing angles between the link and cantilever, shock angle, axle movement, and axle rotation.

 
#20
Can i ask how you actually got that graph? Did you actually model it with a moving axle (with either links or leaves)? Or did you just model straight up movement on the cantilever link and see what the shock did? Those are two VERY different things.

Your graph is shock travel VS wheel travel. A motion ratio graph would be (shock travel divided by wheel travel) VS wheel travel (at least i like it vs wheel travel). Your graph shows that your motion ratio goes from around 0.58 to 0.46 motion ratio which is pretty much just constant. With links this MIGHT be possible.....
I got the info for my graph the old fashioned way. I made a funtional scale model of the rear suspension (shock, bellcrank, bellcrank to axle link, axle, and 4 link) out of paper and thumb tacks! And so far it is just cycling in side view only. Ended up looking like some sort of suspension "pop up book", but I loved it.

Next I was going to make a full scale model in side veiw and double check the numbers. I have all my stuff just need to find the time to do it.

This is for a linked rear suspension, and I want to redo the graph so that it is in the correct format.

And thanks for all the tips and the cool pictures!
 
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