Bicycle Mechanics - Front Suspension Design

I am designing a new bike from scratch. The front suspension will be a multi-link design allowing for a 'J' shaped axel path, similar to the Whyte PRST.

The problem I have is my lack of mathematical know-how. To figure out this problem on my own from a starting point of almost zero knowledge, will more than likely take me a rather long time.

I am sure that this is in all actuality a completely simple mathematical problem. Those who design suspension all say so, but unfortunately I do not have access to these experts and I am pessimistic over their agreeing to provide me with a little 'friendly' help. I do not have the budget to commission a consultant engineer.

I expect my problem is just a bit of a mental block. Nevertheless, I would appreciate it immensely if anyone here could either provide a link to a site which can teach me the basics, or a link to an on-line CAD prog which could work it out for me. Or if anyone here indeed knows how to work out the math's of 'J' shaped axel path front suspension set-ups and is willing to help me directly (if I was to email my design details), then please let yourself be known. I would very much be in your debt.


Muchas Gracias.

You dont need mathematics, just a large piece of paper, pencil, measuring scale and large compass. Draw a setup to scale and use the compass to trace the movement of the front pivots of the links. The distance between the front pivots will always be the same, so for each point in the movement of the bottom link you can mark the position of the pivot in the top link. From these sets of front pivot points you can plot the axle positions. Then you can repeat the process with longer and shorter top link, and longer and shorter distance between front pivots. This will show how changes in these dimesions affect the movement of the axle. This wont be quick, but it will be an interesting project for the long dark evenings in the winter. Note that the point of contact of the wheel on the ground is the important thing, to keep the trail within limits.

You might want to poke around on the K2/ProFlex Riders Group website (http://idriders.com/proflex/). Many of us K2 riders have the crosslink parallelogram fork and spent some time analysing the J-path and suspension dynamics. Look in the "files" (http://idriders.com/proflex/files/) link for some models. And feel free to ask on the forums. Good luck. When I was in college, I designed a 4-bar FSR-like suspension frame for a class project. I was fortunate enough to have access to computer modelling software though but you can actually model some of the dynamics using Excel or some other spreadsheet program. I also made a 2-D model by cutting up bits of cardboard and pinning them together using pop-rivets.

Khuon, if you send a few sketches over, I can make it on computer for you along with animating the kinematic movements.

Khuon, if you send a few sketches over, I can make it on computer for you along with animating the kinematic movements.

I might just do that. I'll need to dig through old moldy boxes and rummage around inside the contents of some 5-1/4" floppies :eek: to find stuff. BTW, what are you using? I modelled using SDRC's I-DEAS and ANSYS primarily.

I might just do that. I'll need to dig through old moldy boxes and rummage around inside the contents of some 5-1/4" floppies :eek: to find stuff. BTW, what are you using? I modelled using SDRC's I-DEAS and ANSYS primarily.

I have a copy of I-DEAS with full FEA along with autodesk mechanical desktop which also has FEA and kinematics but I haven't use either of those in over a year.
I'm using autodesk inventor now, it's kind of like ideas but a lot simpler and faster to design with, the kinematics and constraints used in solid modeling are amazingly quick to implement. I use inventor at work but I have all 3 programs at home that I like to mess around with when I'm bored.

I'm using autodesk inventor now, it's kind of like ideas but a lot simpler and faster to design with, the kinematics and constraints used in solid modeling are amazingly quick to implement.

You know, I haven't used a decent modelling program in over ten years... primarily because my job field doesn't require it. I do remember how much of a pain it was with ANSYS. I always forgot something critical and my models would blow up. My first eye-opener to paying careful attention to my boundary constraints was when I forgot to constrain along one whole axis on an FEA model and it took off for +infinity while exceeding lightspeed. Needless to say, I was not happy. This was also on a system where we were charged by CPU cycles by the seat. Ahh... the days of suckass licensing.

lol, the licenses I have are.. shall we say, unrestricted.
I believe ideas and ansys merged, or something like that. Or autodesk bought em out.

lol, the licenses I have are.. shall we say, unrestricted.
I believe ideas and ansys merged, or something like that. Or autodesk bought em out.

Interesting. I didn't know that. I should ask my step-father for a copy since he uses them on a daily basis so he should have updated versions. I've never actually used I-DEAS or ANSYS on anything but SGIs, HP-Apollo workstations and DEC VMS clusters so I don't know how "wintel" licensing is done.

It uses flex-lm and you need to set up a server to run the license. The version of ideas that I have creates a virtual server off your computer and as long as your computer is hooked up to either an ethernet hub or you have a loopback plug in your card, it fakes the connection.

It uses flex-lm and you need to set up a server to run the license. The version of ideas that I have creates a virtual server off your computer and as long as your computer is hooked up to either an ethernet hub or you have a loopback plug in your card, it fakes the connection.

Ahhh... I'm quite familair with FlexLM and I already have one of my Solaris boxes acting as a FlexLM license server for other things.

You dont need mathematics, just a large piece of paper, pencil, measuring scale and large compass. Draw a setup to scale and use the compass to trace the movement of the front pivots of the links. The distance between the front pivots will always be the same, so for each point in the movement of the bottom link you can mark the position of the pivot in the top link. From these sets of front pivot points you can plot the axle positions. Then you can repeat the process with longer and shorter top link, and longer and shorter distance between front pivots. This will show how changes in these dimesions affect the movement of the axle. This wont be quick, but it will be an interesting project for the long dark evenings in the winter. Note that the point of contact of the wheel on the ground is the important thing, to keep the trail within limits.


Thanks for the reply.

Of course I have drawn many diagrams already but forsooth, torpor, my lack of precision due to boredom, and my inability to maintain a decent attention level for prolonged periods, gets in the way. This I feel prevents me from 're-discovering' the true math's behind this problem through process of hit and miss investigative drudgery, which would be required for success.

I have a lack of confidence in determining the crucial factors and really understanding the fundamental dynamics of the type of suspension in question this way. I know that many are in receipt of such knowledge, I guess I will just have to keep searching, maybe contact a local college or even commission a math's tutor for a few hours in order to get this one solved.

You might want to poke around on the K2/ProFlex Riders Group website (http://idriders.com/proflex/). Many of us K2 riders have the crosslink parallelogram fork and spent some time analysing the J-path and suspension dynamics. Look in the "files" (http://idriders.com/proflex/files/) link for some models. And feel free to ask on the forums. Good luck. When I was in college, I designed a 4-bar FSR-like suspension frame for a class project. I was fortunate enough to have access to computer modelling software though but you can actually model some of the dynamics using Excel or some other spreadsheet program. I also made a 2-D model by cutting up bits of cardboard and pinning them together using pop-rivets.


Thanks very much for the links, I have now registered with idriders.

I took a look at the files section and saw a text file on 'J' shaped axel path myths explained. I downloaded it, but unfortunately it would not open. I do intend to post on that forum though, and I will make a request to have that text file pasted on it, or e-mailed to me. Looks like a very good forum.

I tried using Turbocad (free version) but found that it repositioned some of the lines I made for no obvious reason, I certainly did not want it to. It moved them only by a very small amount but still enough to give me a headache, raise my blood pressure, and prompt me into vowing never to use Turbocad again. I am quite inept with computers, to be honest.

Regarding the 'J' shaped axel path itself I looked at various designs, read the marketing hype, and sought out magazine editorial on the subject. I found very little, but after thinking long and hard over it I reached a conclusion. I determined that to maintain constant trail throughout front end compression the front wheel should move backwards slightly as the yoke / front of the bike descends. This produces a straight lined upwards sloping axel path (ideally). Constant trail is maintained because it is assumed that during this backwards sloping axel path movement, the rear suspension remains unaffected. Ie. the front compresses when ridden over a bump and then extends back to normal by the time the rear wheel reaches the same bump. So in effect, the initial stage of front wheel compression is dependent on the entire bike pivoting forwards from the rear wheel axel with no rear suspension compression, in order to maintain constant trail whilst smoothing out the ride and preventing 'dive'.

The second and final stage of front end suspension compression is designed to work in perfect synchronicity with rear wheel suspension on very hard hits, such as landing from a jump. So the second and final stage of front wheel axel travel follows the steering angle, just as regular common suspension forks do.

That is what I think anyway. I may be wrong, I hope anyone reading this will let me know either way. It seems logical to me, but I am no expert.

Did you do the lines in 2D or 3D?
This moron at work draws perfectly 2D views plus isometrics in autocad. But then when I went to rotate the view, the whole thing went to hell. He had lines where the end points connected in 2D space but like spiked out in 3D.
So you might have a box where each corner in X-Y looks fine, but look at it in 3D and you realize that the coordinates are like (0,0,0) (1,0,0) (1,1,343) (0,1,0).

Did you do the lines in 2D or 3D?


2D. I was just trying to make a basic point to point straight line drawing (+ circles for wheels), to help finalize the bikes geometric basics.

For example, on, say the x axis I plotted a point at 6.00mm. A little later on after plotting another point, the mark made at 6.00mm would then inexplicably be positioned at 6.45mm. I have no idea why it moved 0.45mm. It seemed odd to me. But never mind, I think I will remain in allegiance with Mike Burrows regarding the use of computers for bike design work!

2D. I was just trying to make a basic point to point straight line drawing (+ circles for wheels), to help finalize the bikes geometric basics.

For example, on, say the x axis I plotted a point at 6.00mm. A little later on after plotting another point, the mark made at 6.00mm would then inexplicably be positioned at 6.45mm. I have no idea why it moved 0.45mm. It seemed odd to me.

Some CAD programs attempt to join lines. Check your snap settings.