Rear suspension linkage calculator

[erik]

Here's a spreadsheet I've put together to help understand changes to the rear suspension. It's for bikes with a 4 bar type linkage like my bandit 400 and sv650.
I thought I'd tidy it up and post it on here in case anyone else found it interesting.

I made it using OpenOffice, but I've saved it as an Excel spreadsheet also only it seems in the Excel version some of the formatting was odd - the linkage graph labels had changed and one of the lines went missing. There's also a pdf with the calcs to help understand it.

I got most of the measurements for my bandit and sv by taking a photos (zooming in and standing far away hopefully helped to reduce the distortion) and then importing them into a CAD program and taking measurements.

Here's the link:
http://cid-b37a983fa606d24a.skydrive.live.com/browse.aspx/Public

[iron chef]

I wouldn't normally dig up a thread this old, but it looks like the author is still around and this calculator is very very useful!

So Erik, can you explain the calcs a little further? My first question(s) is a simple one...

What does the three capital letter convention mean? Is FAD the angle between the two links FA and AD?

and also what does the capital 'X' stand for?

I would like to adapt this sheet to handle a linkage with only 2 links, so i can analyse the TZR250 2ma linkage that i race (similar to the pic attached). i need to understand it before i can change it.

Thank you

[erik]

Yes, FAD is the angle from line AF to line AD. For angles beginning with X, the angle is from a horizontal line running through the first point. Counterclockwise angles are positive, clockwise are negative (eg angle DAC between the swing arm dog bone attachment, swing arm pivot and rear axle is negative for the bandit but would be positive for your TZR).

I think you shouldn't have to modify any of the calcs for the TZR. From your photo it looks like the same bolt mounts the dog bones and shock to the lower linkage, so if you set lengths FH and HK the same and the angle FHK to 0, that should be correct.
You'll probably want to un-protect the sheet and change the x-axis minimum to -100 or so, so that point H is still on the chart.

I'm glad someone has found it interesting/useful. :)

[iron chef]

Thanks for your explanation Erik, that makes much more sense. Your spread sheet is exactly what I was after.

A bit of background.
I race a 1986 Yamaha TZR250 1KT in a series called the Yamaha Past Masters here in the UK. There are two types of linkages on these bikes (1KT & 2MA/2XT). They also suffer from ground clearance issues in standard form, so they are 'jacked up' in different ways depending on the linkage.

These little bikes handle great, but I reckon the rear could be improved. When pushing on, it can wallow a bit, and this has left me thinking if there is anything that can be done to alter the linkage to improve this. I've always been intrigued to find out if there is a difference between the two linkage types (I have the early style), or if the linkage is super progressive to allow for a pillion.

Here's the bike in action
https://www.youtube.com/watch?v=aO0keMiR9L0

Cheers

[ellipsis]

...cool bit of racing...:2thumbsup

[iron chef]

I drew up a quick and dirty model of the linkage at lunch today. The image attached shows the plot the your calculator, overlaid on the original image that I used to get dimensions. I'll measure up the linkage properly after I better understand the result.

I guess I'm aiming for some results to compare this data
http://www.promecha.com.au/leverage_linkages.htm

The first is the lever ratio, which I assumed is [force at shock/force at wheel]? Although a ratio of 4 seems high, and the leverage looks like it tails off...:blink:
But that could make sense, as the the spring is stiffer than the SV (10.5kg/mm).

It's early days, ill keep researching

[erik]

Nice start, it looked like a perfect day for a race.

The leverage ratio is [force at shock/force at wheel] or (change in suspension travel)/(change in length of shock), but neither of the graphs in my chart show that. I've added a new spreadsheet with a graph to show it: https://1drv.ms/f/s!AkrSBqY_mHqzkUv6BU2f2tnXB4zU

Most of my measurements for the bandit and sv were from photos, so I'm not sure how accurate they are. I posted this on svrider.com and someone replied saying the shock mount was 35mm out, which is a bit hard to believe but may be true. But don't read too much into it if you compare your results to those from the bandit and sv.

[Dirk777]

Hi Eric,
found your very nice worksheet through a websearch. Registered here although I come from the opposite side of the globe, hope this is no problem.
I try to optimize the rear suspension of my 2010 Triumph 675 and have several different link parts on hand. I want to save time mounting the different link plate and dogbone combinations and measure the travel(s) in hundreds of positions, so I tried to finde an appropriate excel sheet in the web.
Unfortunately math is not really my friend!

Due to differences in the construction of the rear linkage between Triumph and Suzuki I could not use your sheet. Because the lack of knowledge in math and geometry i am not able to modify the equations in your sheet to fit my demands. I kindly ask if you'd do this for me. Attached you find information about "my" suspension linkage, that hopefully will be sufficient.

I' be very glad for your help!

Thanks in advance.

Greetings to NZ
Dirk

351034351033351035

[erik]

Hi Dirk,
I'll have a go at modifying it tomorrow morning.

[erik]

Ok, I've updated the spreadsheet. I've also added a .dwg and .dxf (best to use the dwg and have the triumph675linkage.png in the same directory so it can show in the drawing file) that I used to get the appropriate measurements for the spreadsheet. Your drawing was missing a dimension for point D relative to the swingarm centerline. I've copied the distance from your drawing. Also, it might be good to measure the heights of the axle and swing arm pivot or some other point to check that the angle of everything relative to the ground is correct. I've also added a slider that lets you move the linkage display as you move it, but it only works in the .odf version in LibreOffice or probably also OpenOffice (I don't think it'll work in Excel). The calculations for the triumph linkage are done kind of backwards to the others. As such, you have to enter the vertical distance from the swing arm pivot to the axle rather than it all being controlled by the shock length.

https://1drv.ms/u/s!AkrSBqY_mHqzkUv6BU2f2tnXB4zU?e=176UFW

I hope it's helpful.

[F5 Dave]

Hi Dirk. Have you got the 675R? If so the real issue is the 12kg spring fitted and the rebound damping to match. If you are less than say 120kg then a 10kg spring and a revalve will make the bike really quite good.

[Dirk777]

Ok, I've updated the spreadsheet. I've also added a .dwg and .dxf (best to use the dwg and have the triumph675linkage.png in the same directory so it can show in the drawing file) that I used to get the appropriate measurements for the spreadsheet. Your drawing was missing a dimension for point D relative to the swingarm centerline. I've copied the distance from your drawing. Also, it might be good to measure the heights of the axle and swing arm pivot or some other point to check that the angle of everything relative to the ground is correct. I've also added a slider that lets you move the linkage display as you move it, but it only works in the .odf version in LibreOffice or probably also OpenOffice (I don't think it'll work in Excel). The calculations for the triumph linkage are done kind of backwards to the others. As such, you have to enter the vertical distance from the swing arm pivot to the axle rather than it all being controlled by the shock length.

https://1drv.ms/u/s!AkrSBqY_mHqzkUv6BU2f2tnXB4zU?e=176UFW

I hope it's helpful.

Hello Eric,
thank you so much! This is very helpful. Sorry for the late answer, but I'm short on time right now. It's mother's day....:wacko:
I'll check and measure everything and contact you soon.

Best regards
Dirk

[Dirk777]

Ok, I've updated the spreadsheet. I've also added a .dwg and .dxf (best to use the dwg and have the triumph675linkage.png in the same directory so it can show in the drawing file) that I used to get the appropriate measurements for the spreadsheet. Your drawing was missing a dimension for point D relative to the swingarm centerline. I've copied the distance from your drawing. Also, it might be good to measure the heights of the axle and swing arm pivot or some other point to check that the angle of everything relative to the ground is correct. I've also added a slider that lets you move the linkage display as you move it, but it only works in the .odf version in LibreOffice or probably also OpenOffice (I don't think it'll work in Excel). The calculations for the triumph linkage are done kind of backwards to the others. As such, you have to enter the vertical distance from the swing arm pivot to the axle rather than it all being controlled by the shock length.

https://1drv.ms/u/s!AkrSBqY_mHqzkUv6BU2f2tnXB4zU?e=176UFW

I hope it's helpful.

Hi Eric,

The wheel Axle is 315mm from the ground, The swingarm pivot 411mm. The distance from the axis through the wheel axle and swingarm pivot to D (where the linkplates are connected to the swingarm) is ~55mm. My equipment for this kind of measurment is not the best.

Thanks again!

[Dirk777]

Hi Dirk. Have you got the 675R? If so the real issue is the 12kg spring fitted and the rebound damping to match. If you are less than say 120kg then a 10kg spring and a revalve will make the bike really quite good.

Hi Dave,

it was standard originally, but I got hands on a Ohlins TTX from a later Daytona 675 which was equipped with a 10kg spring. Now I drive a 8.5 kg spring which works better. I'm 75 kg with gear.....on the light side.
But the rear is still unsensitive and I try to get better feedback and grip.

Best regards

[F5 Dave]

So. . . Have you serviced the linkage and checked Swingarm moves freely? Wouldn't be the first time.

[Dirk777]

Ok, I've updated the spreadsheet. I've also added a .dwg and .dxf (best to use the dwg and have the triumph675linkage.png in the same directory so it can show in the drawing file) that I used to get the appropriate measurements for the spreadsheet. Your drawing was missing a dimension for point D relative to the swingarm centerline. I've copied the distance from your drawing. Also, it might be good to measure the heights of the axle and swing arm pivot or some other point to check that the angle of everything relative to the ground is correct. I've also added a slider that lets you move the linkage display as you move it, but it only works in the .odf version in LibreOffice or probably also OpenOffice (I don't think it'll work in Excel). The calculations for the triumph linkage are done kind of backwards to the others. As such, you have to enter the vertical distance from the swing arm pivot to the axle rather than it all being controlled by the shock length.

https://1drv.ms/u/s!AkrSBqY_mHqzkUv6BU2f2tnXB4zU?e=176UFW

I hope it's helpful.

Hi Eric,
with the vertical distance between wheel axle and swingarm pivot (96mm) the swingarm angle should be 9.3°. The horizontal distance is 585mm measured and calculated. I controlled everything as good as possible on a smooth and horizontal concrete ground and found out the following:
vertical distances to the ground:

A:411 mm
G:569 mm
H:156 mm
C:315 mm

Horizontal distance from the swingarm pivot (A):
G:~60 mm
A: 585 mm
H:~14 mm

The shock length is 284mm (static sag 6mm), the free length of the shock is 290 mm.

Why does the calculator state a vertical distance of 153 mm between axle and swingarm pivot? This would need very long legs...:lol:

Have a nice day!

[Dirk777]

So. . . Have you serviced the linkage and checked Swingarm moves freely? Wouldn't be the first time.

Hi Dave,
everything clean and smooth moving freely.
Without play in the bearings. Don't get me wrong, everything fine so far. I have no mechanical issue, but I want to improve the function. Working with different angles in the link plate and lenghts of the dogbone do change the leverage ratio. But trial an error is a very expensive and long lasting thing here. With eric's calculator the behaviour could be predictable.
Best regards

[F5 Dave]

Worth asking. Local guy here has done revalve work a few times before hes asked customer to bring bike in. Customer much happier with moving linkage.

[erik]

Why does the calculator state a vertical distance of 153 mm between axle and swingarm pivot? This would need very long legs...:lol:


Because I treated the edge of your drawing as level. That's why I asked you to measure from the ground to the axle and swing arm pivot, to check if it was.

So I've rotated the drawing (I'm using Nanocad free version) and made another pdf. The measurements are slightly different to what your new measurements are measuring from the ground, I don't know which are more accurate.
I also changed the free shock length to 290 but assuming those height measurements were under free sag conditions, it says the shock should be 282.5 at static sag. Anyway it's not too far off. I also changed the spring rate to 8.5kg/mm. I have no idea what the preload, or top out spring should be. I've just left them the same as my old zx6r shock (I can't remember how accurate they were for that either...).

I've updated the spreadsheet and the zip file at the same link: https://1drv.ms/u/s!AkrSBqY_mHqzkUv6...XB4zU?e=176UFW

With the corrected measurements, you can see the angle between FH and DF is bigger which makes the suspension even more progressive. It stands out in the effective spring rate graph.
I think the easiest way to reduce the progressiveness would be to change the triangle linkage plates. I tried changing the dimensions DF to 100mm, FK to 79mm and DFK to 45° and it's greatly reduced the progressiveness (probably too much?). I adjusted them so that the shock was close to 282.5mm in the first line of the results, but I think it'd be better to do it based on laden sag. Anyway, those numbers are just an example that the progressiveness can be changed, not a suggestion of what dimensions to use. It seems other people have had the same thoughts, there's this thread here (I haven't read it): https://www.triumph675.net/threads/r...ed-them.26006/

[Dirk777]

Hi Eric,
thanks a lot again! I know the thread you referred to very good, and built the link plates according to these designs. But you won't find the geometrical theorie which lead to the differnt approaches.
There are problems concerning the rideheight and RSU length in many cases and I wanted to improve the design but avoid trial and error.

The linkplates you put into the calculator are "Flux II" plates, that should be an improvent to former "Flux I". But these "Flux II" give a more progressive feeling even than the OEM Triumph plates.
Therefore I want to find out the progression of the different designs and compare it with the feeling on the road/track. I'll be back with the results! I'll take your comments into account.

Best regards
Dirk

[Dirk777]

Oh,
I made a mistake...... 284 mm shock length is free-sag (bike weight only) , 290 mm free length . Sag with driver not measured.

[erik]

I look forward to seeing your results. Are you familiar enough with spreadsheets to copy the triumph worksheet and change the graphs so you can compare several different linkages?

[Dirk777]

Hi Eric!
Yes I think so. I alter the dimensions of the different triangles and dogbones in the input section and look for the resulting GK and lever Ratio. Then I check which combination fits my shock length and take the most linear combination.... That's the plan.

Best regards!