[TrueScotsman]

OK peeps- a question for ya;

When an idler/pulley is attached to the SWINGARM of a bike (like the Empire AP-1), is the important chain force line the one from the front chainring to the idler or from the idler to the rear sprocket?

It is my understanding that the chainforce line from the front chainring to the idler is the correct one (as per Tony Foale's 2002/2003 edition book) but the Linkage program uses the idler to the rear sprocket/cassette as the one for the Anti-Squat calculations.

Any further thoughts?

 

[Pslide]

IMO, you and Tony are right.

The Linkage program seems to use the DW patent definition of anti-squat, which has some limitations in its application.

 

[TrueScotsman]

Cheers, I also use the DW definition for anti-squat but believe that Linkage use the wrong chainforce line in their calculations.
Be cool if dw chipped in his thoughts.

 

[Slater]

Yes when attached to the swingarm, you are correct.
However in getting rid of the differential force lines based on which gear you are in, you make it dependent on your position in travel.

 

[TrueScotsman]

However in getting rid of the differential force lines based on which gear you are in, you make it dependent on your position in travel.

But Anti-Squat is always dependant on your position in travel

 

[Slater]

Yes of course, and body position.
I guess In thinking about it more, you lose the effect in changing gears altogether.

 

[Steve M]

I'm inclined to say the standard graphical method of calculation might not be applicable when a swingarm-mounted idler is used. The reasoning for this is basically as follows:

Chain force creates a PARALLEL force that acts through the centre of each sprocket, as well as a torque on the sprocket. This torque obviously isn't transmitted to the swingarm since each sprocket can rotate independently of the swingarm. The result is that you now have two force lines, one at the rear axle, one at the idler, which are PARALLEL and in opposite directions, but offset from the chainline itself at each end by the respective radius of each sprocket. This means that if the two sprockets are the same size (say 16t idler, 16t rear cog), the force lines will be coincident as well as opposing, and so they will cancel out. However if the sprockets are different sizes, the offset in the force lines (from the chainline) will be different, and so they will no longer be coincident. This means you get a couple moment acting on the swingarm (hence, for example, on a URT bike - chainline actually does matter), in ADDITION to the "standard" anti-squat forces that are being caused by the chainline between idler and chainring.

I think perhaps a better way of calculating anti-squat in this case would be to create a FBD of each part of the system and use an iterative calculation method (Excel should be fine, Matlab a bit easier though) to sum the forces acting to compress and extend the suspension, remembering that the chainline between idler and chainring also acts on the front triangle as well as the swingarm. Once you've got a defined chain force it's easy enough to calculate acceleration and load transfer. It's a pretty complicated interaction, there might be a graphical solution but if there is, I'm not aware of it and by the description you've given, I'm not 100% sold on Tony Foale's method since it appears to ignore the gearing at the rear wheel, and and resultant differences in reactions.

 

[Jumping J]

attached to the SWINGARM of a bike (like the Empire AP-1)

The idler is attached to the main frame.... not the swingarm.... have alook at there website

 

[tacubaya]

Very very interesting.... we need DW's opinion as well.

 

[davec113]

I can't think of any sane reason to attach an idler to a swingarm other than at the pivot of the swingarm if the pivot is back far enough, which means it's really attached to the frame.

Assuming a high single pivot with the idler between the pivot and rear axle, the chain forces between the front chainring and idler and rear gear cog and idler will sum to pull the swingarm down and affect the suspension depending on pedaling input. You'd have "pedal jack". I don't care to think about it too much more, it hurts my brain. Of course, I make no claims to be correct, either.

edit: also the chain force will be the same on either side of the idler, acting parallel to the chain, so you'd sum them at the idler to try to figure anti squat, I suppose the pedal induced forces could be used to cancel bob, but I still think it's strange and probably wouldn't work well.

 

[dilzy]

I can't think of any sane reason to attach an idler to a swingarm other than at the pivot of the swingarm if the pivot is back far enough, which means it's really attached to the frame.

Assuming a high single pivot with the idler between the pivot and rear axle, the chain forces between the front chainring and idler and rear gear cog and idler will sum to pull the swingarm down and affect the suspension depending on pedaling input. You'd have "pedal jack". I don't care to think about it too much more, it hurts my brain. Of course, I make no claims to be correct, either.

edit: also the chain force will be the same on either side of the idler, acting parallel to the chain, so you'd sum them at the idler to try to figure anti squat, I suppose the pedal induced forces could be used to cancel bob, but I still think it's strange and probably wouldn't work well.

"Pedal Jack", as you call it, is exactly what is used to create anti-squat. It's that simple.

 

[davec113]

"Pedal Jack", as you call it, is exactly what is used to create anti-squat. It's that simple.

Isn't tire force also a factor?

 

[Steve M]

"Pedal Jack", as you call it, is exactly what is used to create anti-squat. It's that simple.

Yerp - unless you have a REALLY high pivot (roughly , you're going to need some degree of chain extension in order to generate a reasonable amount of anti-squat.

 

[fluider]

Hi all. So I'll try to add my understanding of this. I've drawn simple diagrams similar to those used in Linkage "knowledge" texts. Swingarm mounted coaxially with input sprocket. Green arrow depicts chain pull force. The blue arrow depicts component of chain force vector that creates moment at rear sprocket. Idlers are mounted to the swingarm.
I do admit that chain force can have affect on swingarm rotation even on the idler. So, both chainlines (rear sprocket and idler) should be taken into account. But I don't understand why idler should be considered differently if mounted on swingarm or mainframe. I'd like to believe (although I hate to say "belive") there is only one general principle behind this.

Aloha

 

[TrueScotsman]

Hmmm, this is getting very interesting and confusing!
Here is a copy of the relevant page in the Tony Foale book (2003 edition).
Sorry for the poor quality- my scanner is broken so I had to take a photo of the page!

 

[fluider]

I think I'm starting to see it and now I'm 70% for Tony Foale's approach. Thus my FBDs might be wrong. I looked at it as jackshaft mounted on the swingarm. The rear-sprocket-to-jackshaft-sprocket chainline has no ability to create moment at rear sprocket around swingarm pivot. But the jackshaft-to-input sprocket does create moment at jackshaft around swingarm.
In case of idler attached to the mainframe the rear sprocket-to-idler chainline should be considered, IMO.
I'm slow today, at least I can use yesterday beer session as excuse . God save the beer.

Edit: now I noticed one small detail in A-Trak configuration drawn in the book. Upper idler seems to be at position that makes chainline of rear-sprocket to idler parallel with swingarm. But parallel chainline doesn't create moment at rear axle, does it? In every case, Tony explicitly stated a different approach to chainlines according to idler attachment.

 

[Steve M]

I think I'm starting to see it and now I'm 70% for Tony Foale's approach. Thus my FBDs might be wrong. I looked at it as jackshaft mounted on the swingarm. The rear-sprocket-to-jackshaft-sprocket chainline has no ability to create moment at rear sprocket around swingarm pivot. But the jackshaft-to-input sprocket does create moment at jackshaft around swingarm.

I disagree with this part, as I said above - there is a moment created (as you even illustrated yourself?) by any sprockets that are not the same size that are both mounted on the swingarm. I think there may be a flaw with your diagrams too, in that you're only taking chain force as acting in one direction - as a tensile force, it acts in both directions, in other words, there should be another green arrow going backwards (or upwards in the diagram) from the idler, and as a result another additional component of the blue arrow added to what you've already drawn.

Another explanation is found here - http://www.rdrop.com/~/twest/mtb/pathAnalysis/index.html#ChainLineDoesNotMatterInAURT

 

[LMC]

The idler is attached to the main frame.... not the swingarm.... have alook at there website

True, it just looks like its fixed to the bottom of the swingarm. There was a bike on the dirt website a while back from a small scale framebuilder that employed the idler on swingarm technique. and the Corsair of course.

 

[dw]

OK peeps- a question for ya;

When an idler/pulley is attached to the SWINGARM of a bike (like the Empire AP-1), is the important chain force line the one from the front chainring to the idler or from the idler to the rear sprocket?

It is my understanding that the chainforce line from the front chainring to the idler is the correct one (as per Tony Foale's 2002/2003 edition book) but the Linkage program uses the idler to the rear sprocket/cassette as the one for the Anti-Squat calculations.

Any further thoughts?

Idler attached to swingarm, the chain force line to use is the chainring to the idler. The linkage program is great at making pretty pictures but it's not too useful when it comes to anti-squat.

 

[Kamanchi]

We are using an adjustable idler on our swingarms to create and modulate the amount of antisquat. Works very well.

 

[fluider]

Then, there seems to be a mistake in estimation of antisquat in Linkage.
Who knows, if Linkage was a typical commercial CAD where each functional request from customer must be paid for by customer, then I'm sure it would be more useful but less used.

Idler attached to swingarm, the chain force line to use is the chainring to the idler. The linkage program is great at making pretty pictures but it's not too useful when it comes to anti-squat.

 

[hmcleay]

this is a bit of a grave dig, but here goes:

I have spent quite a bit of time coming to this conclusion, but I finally think it makes sense.

In short, both chainlines need to be considered.
If the idler is exactly on the pivot, then the extension (or compression) of the swingarm that occurs due to chain tension, is dependant on the relative sizes of the sprockets.
Considering the two chain segments separately (and picturing the bike from the right hand side):
If the idler is smaller than the rear cog, this would induce some anti-clockwise movement of the swingarm relative to the front triangle (anti-squat).
And, if the idler is smaller than the front cog, this would induce some anti-clockwise movement of the front triangle relative to the swingarm (pro-squat).
I guess the overall system would sum these effects.

In order to consider an idler that is at a location other than exactly on the pivot, it is important to understand the 'nature varies smoothly' concept in the 'path analysis' text.
Basically, now that we understand what happens with the idler on the pivot location, we should know that the 'answer' to this problem would be pretty much the same if we were to consider the idler at a new position, say 1mm (small distance) away from the pivot. regardless of whether the idler is on the swingarm or the main triangle.

I have a suspicion though, that as soon as the idler is moved away from the pivot point, the extension/compression effects due to cog size, pale into insignifance when compared to the extension/compression effects that occur due to relative movement between the idler and the front chainring (in the case of the idler attached to the swingarm). Thus, it would be a reasonable approximation to consider only the chainline between the idler and the front chainring for a graphical analysis (as DW has suggested).

Interestingly, in Tony Foale's explanation of the A-Trak system, he uses the words "for ESTIMATION of anti-squat performance" (not exactimation), and, he has drawn the chainline from the rear cog to the idler as being parallel to the swingarm, therefore not having an effect on the system.
I guess he has described it like this so that the same 'graphical anaylsis' can still be used. In fact, he is using this example to compare the anti-squat curve of this system to that of a traditional system. so he needs to perform the graphical analysis in the same way, so that he is comparing 'apples to apples'.

To perform a 'graphical analysis' that does consider both sections of the chain line, perhaps one could calculate the anti-squat value for each of the two chain sections separately, and then add the two together?

I'm not 100% convinced by my argument, but for now it is making some sense.
I'm interested to hear everbody's thoughts.

Cheers,
Hugh.

 

[fluider]

My take on this may sound little bit rustic but I'd say the chainline segment connecting those two sprockets where one is on a swingarm and 2nd one is on mainframe, that this segment is the one to take into account. This place is where the swingarm/mainframe interaction comes from.

Case A: idler mounted on the swingarm; sprocket-idler chainline has no effect on swingarm, but idler-chainring (red line) does have because these two are located on different parts. A2 is slightly different layout but with the same effect.

Case B: idler mounted on the mainframe; sprocket-idler (red line) is that chainline having effect on swingarm because it connects chainrings from different and adjacent parts of the system.

 

[hmcleay]

My take on this may sound little bit rustic but I'd say the chainline segment connecting those two sprockets where one is on a swingarm and 2nd one is on mainframe, that this segment is the one to take into account. This place is where the swingarm/mainframe interaction comes from.

Case A: idler mounted on the swingarm; sprocket-idler chainline has no effect on swingarm, but idler-chainring (red line) does have because these two are located on different parts. A2 is slightly different layout but with the same effect.

Case B: idler mounted on the mainframe; sprocket-idler (red line) is that chainline having effect on swingarm because it connects chainrings from different and adjacent parts of the system.

But then what happens in "Case C", when the idler is ON the pivot location?
By your reasoning above, neither chainline would have an effect on the swingarm.
However, we know (apparently - I still don't fully understand why) that in a non-idler system where the swingarm pivots at the bottom bracket, the chainline still plays an important role, even though there is no relative movement (distancing) between the BB and the rear cog.

Can anybody explain the above scenario a bit better?
I think that holds the key to understanding the situation where the idler is at the pivot point, which in turn can help us understand what happens if we gradually move the idler away from the pivot point.

 

[Steve M]

this is a bit of a grave dig, but here goes:

I have spent quite a bit of time coming to this conclusion, but I finally think it makes sense.

In short, both chainlines need to be considered.
If the idler is exactly on the pivot, then the extension (or compression) of the swingarm that occurs due to chain tension, is dependant on the relative sizes of the sprockets.
Considering the two chain segments separately (and picturing the bike from the right hand side):
If the idler is smaller than the rear cog, this would induce some anti-clockwise movement of the swingarm relative to the front triangle (anti-squat).
And, if the idler is smaller than the front cog, this would induce some anti-clockwise movement of the front triangle relative to the swingarm (pro-squat).
I guess the overall system would sum these effects.

In order to consider an idler that is at a location other than exactly on the pivot, it is important to understand the 'nature varies smoothly' concept in the 'path analysis' text.
Basically, now that we understand what happens with the idler on the pivot location, we should know that the 'answer' to this problem would be pretty much the same if we were to consider the idler at a new position, say 1mm (small distance) away from the pivot. regardless of whether the idler is on the swingarm or the main triangle.

I have a suspicion though, that as soon as the idler is moved away from the pivot point, the extension/compression effects due to cog size, pale into insignifance when compared to the extension/compression effects that occur due to relative movement between the idler and the front chainring (in the case of the idler attached to the swingarm). Thus, it would be a reasonable approximation to consider only the chainline between the idler and the front chainring for a graphical analysis (as DW has suggested).

Interestingly, in Tony Foale's explanation of the A-Trak system, he uses the words "for ESTIMATION of anti-squat performance" (not exactimation), and, he has drawn the chainline from the rear cog to the idler as being parallel to the swingarm, therefore not having an effect on the system.
I guess he has described it like this so that the same 'graphical anaylsis' can still be used. In fact, he is using this example to compare the anti-squat curve of this system to that of a traditional system. so he needs to perform the graphical analysis in the same way, so that he is comparing 'apples to apples'.

To perform a 'graphical analysis' that does consider both sections of the chain line, perhaps one could calculate the anti-squat value for each of the two chain sections separately, and then add the two together?

I'm not 100% convinced by my argument, but for now it is making some sense.
I'm interested to hear everbody's thoughts.

Cheers,
Hugh.

To me, what you say sounds bang on except for the part about adding the graphical analyses together. Part of the reason the graphical analysis works is that it accounts for the chain force component pulling the frame back towards the axle as well as the axle towards the frame - this is why you can't just calculate the net force vector on the rear axle alone and compare that to the axle path to calculate anti-squat. Graphical analysis using the same method does not work for the component of the chainline between the swingarm-mounted idler and the rear axle, because that does not have the same effect on the front triangle.

 

[klunky]

People are missing the point here. TrueScotsman, you seem to be asking questions like this fairly often and I want to know what you are making!

 

[Steve M]

But then what happens in "Case C", when the idler is ON the pivot location?
By your reasoning above, neither chainline would have an effect on the swingarm.
However, we know (apparently - I still don't fully understand why) that in a non-idler system where the swingarm pivots at the bottom bracket, the chainline still plays an important role, even though there is no relative movement (distancing) between the BB and the rear cog.

Can anybody explain the above scenario a bit better?
I think that holds the key to understanding the situation where the idler is at the pivot point, which in turn can help us understand what happens if we gradually move the idler away from the pivot point.

No, his explanation still holds. When a cog is concentric to the pivot (including BB-centric bikes with no idler), the chain transmits a force through the pivot that is parallel to the chain force. Obviously it can't transmit a moment because the cog will simply rotate. This occurs on both cogs, front and rear. When the cogs are not the same PCD (say front 32t, rear 16t), the two force vectors (one acting forwards and slightly upwards from say the rear axle, the other equal in magnitude but acting rearwards and slightly downwards from the BB/cog centre) are not coaxial, because the centre of each cog is offset from the chainline a different amount. As you're aware, any two forces that are equal in magnitude and opposite in direction BUT that are offset so as not to be coaxial will generate a couple moment, which is why the cog size matters even for the same chainline.

 

[TrueScotsman]

Klunky- are you going to Ft Bill WC this weekend?
We could meet up and I would tell you exactly ;-)

 

[Vrock]

Ok, i've been playing a little with idlers and here is my opinion...

I'm using the Appalache Real for the experiment. 38T-15T, Idler diameter=rear cog diameter. Idler on the axle (concentric) so I use the Idler-Cog line. I get 52% of anti-squat, I hope everyone agrees on this part. Now I move the Idler 0.00001mm inside the swingarm and I use the Idler to front cog Line ¿Right?. I get 152% of Anti-squat and I'm sure that this is not correct because the Torque of the Idler in the Swingarm is almost nothing, it should be 53% or something like that, but never 152%.

If I move the Idler an Inch or two to the rear The torque of the Idler axle on the swingarm becomes an important force so I would try to calculate it and add it to the Anti-squat that I get with the standar method. It would be something like 52%+XX%.

 

[Slater]

Based on that Diagram your 52% number is calculated incorrectly. It looks as if the 152% number is calculated correctly. Thus the real number when it is concentric should be higher.

 

[Vrock]

I think the 52% is right. Cog and Idler are the same Diameter. Chainline and swingarm are parallel, they cross at infinitum, so I draw a parallel line from the tire contact point and I get 52% with the COG at 1m, it's the stardar method used for a normal bike.

 

[TrueScotsman]

Hmmm, interesting!
I get what Vrock is saying.
I am currently building a frame to test these theories in real life- see the seperate thread on this.

 

[Steve M]

Based on that Diagram your 52% number is calculated incorrectly. It looks as if the 152% number is calculated correctly. Thus the real number when it is concentric should be higher.

Nah, his diagram is correct. As I said before, I don't think the graphical method actually works properly for swingarm mounted idlers.

 

[Vrock]

Ok, another Experiment....

Same bike, Appalache Real. 38T-15T. Now we remove the Idler and check the Anti-Squat. It's a high monopivot so I get 364%. It doesn't matter if the model is perfect or not, It's going to be a very high number.

Now I mount an Idler 0.00001mm inside the swingarm close to the rear axle, parallel to the swingarm... And you know what it's going to happen... If I use the Idler to to rear cog chainline I get 52% again (It's the wrong number this time). If I use the idler to front cog I get 364%. It makes sense.

So the only thing we know for sure is that with the idler on the main pivot we have 52%, and without Idler we have 364%. My theory is that if the Idler is on the middle the Antiscuat is in the middle too. Maybe it's not a linear relation, but something close.

 

[Slater]

Oh whoops I missed the part where you said the cogs are the same size front and rear.

 

[TrueScotsman]

Okay, I thought I would also post and bump this thread as what I have learned is relevant.
The reason I started this thread is because my own bike project featured a swingarm-mounted idler and I had queries regarding the specifics of some published information.
I can now conclude that if an idler is attached to a swingarm and that swingarm is concentric to the front cog, the idler makes no perceptible difference. The following diagram is what I initially thought (based on published literature, I have to say!) was the case, but is NOT;

Suffice to say I am pretty gutted! I made this conclusion based on a test rig that i quickly mocked up. I just wish that I had done this long ago. Well done to those people who figured this out mathematically. I guess I am a pretty graphical kinda guy, and as Socket pointed out I don't think the graphical method transfers to this situation. Oh well!

Here's a pic of the test rig;

Notice the rear cog is fixed to the vertical bar (representing the wheel) and can only move vertically (hence the lower tie-bar). The front cog is connected to a crank-bar and both are free to rotate around the swingarm pivot. The idler is attached but free to rotate ON the swingarm.

 

[fluider]

I started to worry there's gonna be no technical discussion this summer .
What did you Ian observed when you pulled the free end of chain ?

 

[no skid marks]

I can't remember the thread, nor have I reread it, but was the inital question in regards to a concentric pivot? and are the results the same for an above BB pivot? Also does wheel dynamics(motion, moments etc) play any part? that's your cue Socket.

 

[TrueScotsman]

fluider-when I rotated the crank on the front chainring the swingarm moved upwards (indicating a pro-squat response). When I tried it without routing the chain over the idler there was no perceptible difference. Hardly scientific, I know, but still....

 

[TrueScotsman]

I can't remember the thread, nor have I reread it, but was the inital question in regards to a concentric pivot? and are the results the same for an above BB pivot? Also does wheel dynamics(motion, moments etc) play any part? that's your cue Socket.

No the initial question didn't specifically mention a concentric pivot. But, as V-Rock says, a pivot 0.0001mm from being concentric can't give hugely different results. Surely it must be a sliding scale.


BTW- can someone wake up Socket and hand him a cold beer, we need his input!