Kinematics

TEAMROBOT
Posts
1374
Joined
9/2/2009
Location
Los Angeles, CA US
6/13/2025 11:46am
There currently aren't really rear shocks with position sensitive damping in the world of bikes, so shaft speed is the only factor in damping force shock...

There currently aren't really rear shocks with position sensitive damping in the world of bikes, so shaft speed is the only factor in damping force shock tune aside. There are a couple of things to look at to get a feel for rebound speed. One is the wheel force plot. That factors in spring force which is important because higher spring force deeper in travel promotes a faster rebound speed. The other thing, obviously, is leverage ratio. Leverage ratio is important alongside the wheel force plot because of how it impacts damping force as you feel it would be felt at the wheel, but it's a little more than just 1:1. The damping force at the wheel is inversely proportional to the leverage ratio squared. So while the shock might be pushing for faster rebound deeper in travel at a lower leverage ratio, the damping is able to do more to slow rebound than at top of travel. To me, the big takeaway from this is that if you compare a setup that gets a certain wheel force plot by using volume spacers or progressive springs and then compare it to a setup that gets the same wheel force plot but by adding progression with a linkage, you get a more consistent rebound speed across full travel with the linkage version.

"If you compare a setup that gets a certain wheel force plot by using volume spacers or progressive springs and then compare it to a setup that gets the same wheel force plot but by adding progression with a linkage, you get a more consistent rebound speed across full travel with the linkage version."

This is great info, and hard to come by in the MTB world. Also a great argument for buying a link to add bottom out resistance instead of plugging in more volume reducers.

3
6/13/2025 9:35pm Edited Date/Time 6/14/2025 6:45am
There currently aren't really rear shocks with position sensitive damping in the world of bikes, so shaft speed is the only factor in damping force shock...

There currently aren't really rear shocks with position sensitive damping in the world of bikes, so shaft speed is the only factor in damping force shock tune aside. There are a couple of things to look at to get a feel for rebound speed. One is the wheel force plot. That factors in spring force which is important because higher spring force deeper in travel promotes a faster rebound speed. The other thing, obviously, is leverage ratio. Leverage ratio is important alongside the wheel force plot because of how it impacts damping force as you feel it would be felt at the wheel, but it's a little more than just 1:1. The damping force at the wheel is inversely proportional to the leverage ratio squared. So while the shock might be pushing for faster rebound deeper in travel at a lower leverage ratio, the damping is able to do more to slow rebound than at top of travel. To me, the big takeaway from this is that if you compare a setup that gets a certain wheel force plot by using volume spacers or progressive springs and then compare it to a setup that gets the same wheel force plot but by adding progression with a linkage, you get a more consistent rebound speed across full travel with the linkage version.

TEAMROBOT wrote:
"If you compare a setup that gets a certain wheel force plot by using volume spacers or progressive springs and then compare it to a setup...

"If you compare a setup that gets a certain wheel force plot by using volume spacers or progressive springs and then compare it to a setup that gets the same wheel force plot but by adding progression with a linkage, you get a more consistent rebound speed across full travel with the linkage version."

This is great info, and hard to come by in the MTB world. Also a great argument for buying a link to add bottom out resistance instead of plugging in more volume reducers.

The argument of this is that, often the aftermarket links don’t only change the end stroke it will change the initial stroke as well.  Volume spacers will only change the end stroke.

Definitely cool info about the rebound speeds.

This was the idea behind the dual shock bikes, you can put the “spring” on the leverage curve that you want and the “damper” for comp and rebound on a more linear leverage curve for consistent damping. (Edited below, the spring and damper are opposite of this)

IMG 7016.jpeg?VersionId=j94LIMG 7015.jpeg?VersionId=4Tk6BpqTDglLMr2Uft3DxUmYMuqGqav
2
6/13/2025 10:35pm
The argument of this is that, often the aftermarket links don’t only change the end stroke it will change the initial stroke as well.  Volume spacers...

The argument of this is that, often the aftermarket links don’t only change the end stroke it will change the initial stroke as well.  Volume spacers will only change the end stroke.

Definitely cool info about the rebound speeds.

This was the idea behind the dual shock bikes, you can put the “spring” on the leverage curve that you want and the “damper” for comp and rebound on a more linear leverage curve for consistent damping. (Edited below, the spring and damper are opposite of this)

IMG 7016.jpeg?VersionId=j94LIMG 7015.jpeg?VersionId=4Tk6BpqTDglLMr2Uft3DxUmYMuqGqav

I find the “consistent damping” thing interesting because I’ve never really seen a good argument for why you would want damping force to be the same for a given impact speed at any point in travel. I can see plenty of reasons you’d want damping to get stiffer deeper in travel. This is exactly why bypass shocks are a thing in motor sports. This is kind of what HBO does, so one could argue HBO is a bandaid if they wanted. Maybe for riding some chunk track where you’ll never conceivably bottom out anyway it would make sense. But the way I see it, there’s nothing less consistent than pinging off bottom out and having damping ramp through travel definitely helps with that.

4
TEAMROBOT
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Joined
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Location
Los Angeles, CA US
6/13/2025 10:45pm
I find the “consistent damping” thing interesting because I’ve never really seen a good argument for why you would want damping force to be the same...

I find the “consistent damping” thing interesting because I’ve never really seen a good argument for why you would want damping force to be the same for a given impact speed at any point in travel. I can see plenty of reasons you’d want damping to get stiffer deeper in travel. This is exactly why bypass shocks are a thing in motor sports. This is kind of what HBO does, so one could argue HBO is a bandaid if they wanted. Maybe for riding some chunk track where you’ll never conceivably bottom out anyway it would make sense. But the way I see it, there’s nothing less consistent than pinging off bottom out and having damping ramp through travel definitely helps with that.

"There’s nothing less consistent than pinging off bottom out"

True story. It's basically the worst feeling in the world during an "oh shit" moment.

6/14/2025 3:26am Edited Date/Time 6/14/2025 3:29am
The argument of this is that, often the aftermarket links don’t only change the end stroke it will change the initial stroke as well.  Volume spacers...

The argument of this is that, often the aftermarket links don’t only change the end stroke it will change the initial stroke as well.  Volume spacers will only change the end stroke.

Definitely cool info about the rebound speeds.

This was the idea behind the dual shock bikes, you can put the “spring” on the leverage curve that you want and the “damper” for comp and rebound on a more linear leverage curve for consistent damping. (Edited below, the spring and damper are opposite of this)

IMG 7016.jpeg?VersionId=j94LIMG 7015.jpeg?VersionId=4Tk6BpqTDglLMr2Uft3DxUmYMuqGqav
I find the “consistent damping” thing interesting because I’ve never really seen a good argument for why you would want damping force to be the same...

I find the “consistent damping” thing interesting because I’ve never really seen a good argument for why you would want damping force to be the same for a given impact speed at any point in travel. I can see plenty of reasons you’d want damping to get stiffer deeper in travel. This is exactly why bypass shocks are a thing in motor sports. This is kind of what HBO does, so one could argue HBO is a bandaid if they wanted. Maybe for riding some chunk track where you’ll never conceivably bottom out anyway it would make sense. But the way I see it, there’s nothing less consistent than pinging off bottom out and having damping ramp through travel definitely helps with that.

 This is just what I’ve gathered from talking with one of the designers, obviously don’t have first hand work with it, I could be inverse the damper on progressive link and spring on linear!

 

AgrAde
Posts
196
Joined
5/21/2015
Location
AL US
6/14/2025 3:42am Edited Date/Time 6/14/2025 3:44am

The bikes that have a linear damper and progressive spring on separate parts of the linkage just mimic the behavior of a rampy air spring on a linear bike. Which everyone decided was terrible years ago. I don't see the advantage of mimicking that behavior with a coil.

Linear bikes with a rampy air spring feel inconsistent as all hell with their damping IMO. I wish I could have a progressive linkage for my fork damper too.

3
1
6/14/2025 6:43am
AgrAde wrote:
The bikes that have a linear damper and progressive spring on separate parts of the linkage just mimic the behavior of a rampy air spring on...

The bikes that have a linear damper and progressive spring on separate parts of the linkage just mimic the behavior of a rampy air spring on a linear bike. Which everyone decided was terrible years ago. I don't see the advantage of mimicking that behavior with a coil.

Linear bikes with a rampy air spring feel inconsistent as all hell with their damping IMO. I wish I could have a progressive linkage for my fork damper too.

Now that I’m looking at the photo of the Cannondale the damper is on the bottom in the stock Jykle position which is progressive and spring is in a linear position.
Would the damper in progressive link give it a feel of a position sensitive damper? 


 

1
6/14/2025 9:22am
Now that I’m looking at the photo of the Cannondale the damper is on the bottom in the stock Jykle position which is progressive and spring...

Now that I’m looking at the photo of the Cannondale the damper is on the bottom in the stock Jykle position which is progressive and spring is in a linear position.
Would the damper in progressive link give it a feel of a position sensitive damper? 


 

That would make a lot more sense to me. For a given wheel speed, damping force as felt at the wheel is proportional to 1/leverage^2 so any time the leverage curve is progressive you will effectively get position sensitive damping as felt at the wheel. The assumption here being that if you run over a root, for example, the wheel will generally initially be displaced at the same speed to clear it regardless of where you are in travel. 

1
6/14/2025 2:11pm Edited Date/Time 6/14/2025 2:12pm
Now that I’m looking at the photo of the Cannondale the damper is on the bottom in the stock Jykle position which is progressive and spring...

Now that I’m looking at the photo of the Cannondale the damper is on the bottom in the stock Jykle position which is progressive and spring is in a linear position.
Would the damper in progressive link give it a feel of a position sensitive damper? 


 

You could do it either way around depending on the track IIRC. It was so that the damper didn't "lose control." They said on progressive linkages, that the shaft speeds were too inconsistent for the damper, and the high speed circuit was handling things the low speed should be handling and vice versa depending on the position in the travel. 

It mimics the use of an air spring, as the damper is speed sensitive, but the spring on the progressive link is more position sensitive. The benefit is, it doesn't have the initial stiction of an air shock, and you can get a bit crazy with the progressivity of the shock without having to change the damper tune every time.

1
ebruner
Posts
345
Joined
3/29/2018
Location
Tustin, CA US
6/16/2025 8:18am

@CascadeComponents thanks for all of the help/feedback on setup changes and reality checks for me on my nomad.  I tossed the cascade link on, put the vorsprung tractiv tuned superdeluxe on and threw the smashpot in my fox 38 and the bike is unbelievable right now.  I definitely feel like the added bit of progression to the suspension made it easier for me to hit the feeling I wanted in the suspension across the board.  Spring rate/support, rebound speed, compression settings, etc.  Also, the additional chainstay length is so, so choice and really just tied the whole room together.  

9xknok
4
6/16/2025 9:54am
ebruner wrote:
@CascadeComponents thanks for all of the help/feedback on setup changes and reality checks for me on my nomad.  I tossed the cascade link on, put the...

@CascadeComponents thanks for all of the help/feedback on setup changes and reality checks for me on my nomad.  I tossed the cascade link on, put the vorsprung tractiv tuned superdeluxe on and threw the smashpot in my fox 38 and the bike is unbelievable right now.  I definitely feel like the added bit of progression to the suspension made it easier for me to hit the feeling I wanted in the suspension across the board.  Spring rate/support, rebound speed, compression settings, etc.  Also, the additional chainstay length is so, so choice and really just tied the whole room together.  

9xknok

Glad to hear you've got things running well! Also I really appreciate the meme.

On another note, and this is kind of unrelated to suspension but related to bike handling. I have a theory about the resurgence of steering dampers. Beside steering dampers, as of late people have been into short stems. I think one thing that gets glossed over with stem length is that the longer the stem is, the more the resultant force of an impact at your hands acts to center things. I wonder if shorter stems having less of that self centering affect has resulted in people looking to steering dampers to make up the difference.

4
Primoz
Posts
4542
Joined
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Location
SI
6/16/2025 11:25am Edited Date/Time 6/16/2025 11:27am

Off the top of my head I'd say a longer stem will have less of an off-centering effect when you don't distribute forces from the two hands on either side of the bars equally. As soon as you go off centre, there will be less torque applied to the steerer as the force equilibrium will align with the steerer at a lower angle - 0 mm stem will require a 90° rotation of the bars (regardless of the width) when pushing straight forward with only one hand while a 1 metre stem with 750 mm bars will only require 20°.

Does it make sense? Obviously the stem itself is just one component, at the end of the day the horizontal (longitudional) distance of your hands vs. the steerer is what matters, so stem length and handlebar setback (or reach as BikeYoke calls it).

Definitely something to check out as I somewhat regularly switch from a 35 to a 50 mm stem. I'll be on the lookout.

1
sspomer
Posts
6056
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Location
Boise, ID US
6/16/2025 4:49pm

@TEAMROBOT grills Fabien Barel on Canyon's FrankenMule that was used to develop the new Sender.

1
6/29/2025 3:41pm

Hello hello hi, the flex stay discussion came and went while I didn't have access to linkage, and I won't reignite the discussion, but I have an interesting conundrum, and I was wondering if anyone familiar with linkage or kinematics could help? 

10000293521000029351

Here are two identical frames, with a linkage similar to the polygon collosus, except I have both set up as a split pivot/flex stay. One is classed as a VPP with a shock linkage, the other is classed as a 6-Bar. The travel is the same, the leverage rate is the same, but the anti-rise is different between the two. 1000029353Now I'm guessing it's because the rocker link isn't being counted on the VPP version, and on the 6-Bar version, it is being counted, but could anyone tell me which version of this would be playing out in real life? Thanks in advance!

1
6/29/2025 4:57pm
Hello hello hi, the flex stay discussion came and went while I didn't have access to linkage, and I won't reignite the discussion, but I have...

Hello hello hi, the flex stay discussion came and went while I didn't have access to linkage, and I won't reignite the discussion, but I have an interesting conundrum, and I was wondering if anyone familiar with linkage or kinematics could help? 

10000293521000029351

Here are two identical frames, with a linkage similar to the polygon collosus, except I have both set up as a split pivot/flex stay. One is classed as a VPP with a shock linkage, the other is classed as a 6-Bar. The travel is the same, the leverage rate is the same, but the anti-rise is different between the two. 1000029353Now I'm guessing it's because the rocker link isn't being counted on the VPP version, and on the 6-Bar version, it is being counted, but could anyone tell me which version of this would be playing out in real life? Thanks in advance!

I don’t have any familiarity with linkage, but anti-rise is a product of the instant center of the member the brake caliper is mounted to. With a split pivot you have two options. 

1
6/29/2025 5:02pm Edited Date/Time 6/29/2025 5:03pm
I don’t have any familiarity with linkage, but anti-rise is a product of the instant center of the member the brake caliper is mounted to. With...

I don’t have any familiarity with linkage, but anti-rise is a product of the instant center of the member the brake caliper is mounted to. With a split pivot you have two options. 

Ahhh okay! That makes sense! Would I be correct in saying, that if I mount the brake to the seat stay, the rocker is involved and if I mount it to the chainstay, it isn't?

1
6/29/2025 5:18pm
Ahhh okay! That makes sense! Would I be correct in saying, that if I mount the brake to the seat stay, the rocker is involved and...

Ahhh okay! That makes sense! Would I be correct in saying, that if I mount the brake to the seat stay, the rocker is involved and if I mount it to the chainstay, it isn't?

In the first image that would be correct in a sense. Hard for me to really tell what’s going on with the second one because there seems to be some transparency turned on. 

2
Primoz
Posts
4542
Joined
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Location
SI
6/29/2025 11:21pm

If I understand correctly the difference is just where the brake is mounted. So like mentioned, braking wise, it's a vpp 4-bar vs. A 6-bar and the same comparison would play out in real life too. 

Pedalling wise both variants are 4-bars. 

2
7/1/2025 5:49am
Hello hello hi, the flex stay discussion came and went while I didn't have access to linkage, and I won't reignite the discussion, but I have...

Hello hello hi, the flex stay discussion came and went while I didn't have access to linkage, and I won't reignite the discussion, but I have an interesting conundrum, and I was wondering if anyone familiar with linkage or kinematics could help? 

10000293521000029351

Here are two identical frames, with a linkage similar to the polygon collosus, except I have both set up as a split pivot/flex stay. One is classed as a VPP with a shock linkage, the other is classed as a 6-Bar. The travel is the same, the leverage rate is the same, but the anti-rise is different between the two. 1000029353Now I'm guessing it's because the rocker link isn't being counted on the VPP version, and on the 6-Bar version, it is being counted, but could anyone tell me which version of this would be playing out in real life? Thanks in advance!

I don’t have any familiarity with linkage, but anti-rise is a product of the instant center of the member the brake caliper is mounted to. With...

I don’t have any familiarity with linkage, but anti-rise is a product of the instant center of the member the brake caliper is mounted to. With a split pivot you have two options. 

I had assumed that Linkage was basically the standard that most people use for calculating kinematic performance. You obviously have quite a bit of experience, so what do you use instead, rigid body dynamics equations by hand, or is there an alternative software? 

2
Primoz
Posts
4542
Joined
8/1/2009
Location
SI
7/1/2025 5:54am

Does Linkage even support calculating suspension behaviour without having a shock in the frame? As far as I played around you had to have a shock in there which limits the ability to play around as it requires you to have the layout much more defied than just trying out the main pivot locations and seeing what it does to antisquat and antirise... 

synBike
Posts
46
Joined
3/15/2021
Location
North Vancouver, BC CA
7/1/2025 9:38am Edited Date/Time 7/1/2025 9:40am

To my knowledge I’m the only public alternative (https://syn.bike). Not to speak for Cascade but I believe he developed his own equation solver. 

You can’t model AR/AS without the shock as shock position still has an impact. Neither software effectively models flex-pivots because it requires applying a measured angular spring rate to the effective pivot. That being said, the value is quite high so you can get a good approximation by modelling it as a conventional 4 bar with the brake and wheel attached to the chainstay (sometimes called faux-bar). Kona uses this layout for reference. You can see the impacts of the approximation as the position of the seatstay to chainstay pivot has very minimal impact on the antirise. This makes sense as the critical change is how the brake torque is translated to the frame  


 The reason Horst link bikes have very different (and usually considered better) antirise characteristics is because all of the brake torque tries to the rotate the seatstay member and does not get translated directly to the main pivot like it does when the wheel/brake is attached to the chainstay. 

2
7/1/2025 10:21am
I had assumed that Linkage was basically the standard that most people use for calculating kinematic performance. You obviously have quite a bit of experience, so...

I had assumed that Linkage was basically the standard that most people use for calculating kinematic performance. You obviously have quite a bit of experience, so what do you use instead, rigid body dynamics equations by hand, or is there an alternative software? 

A combination of mathematica and 2D sketches in CAD. I write out all the equations using whichever variables I want to change and then use mathematica to solve them and generate plots. Conceptually all the equations are simple. I like doing it this way because it makes you really understand everything that's going on, it's quick to iterate dimensional changes, and I can come up with pretty much any metric I want if something out of the ordinary makes a comparison better. For example, those plots I posted about ramp in leverage curve vs ramp in damping force as you'd feel it at the wheel came from this: Screenshot 2025-07-01 102007

5
7/1/2025 10:32am
I had assumed that Linkage was basically the standard that most people use for calculating kinematic performance. You obviously have quite a bit of experience, so...

I had assumed that Linkage was basically the standard that most people use for calculating kinematic performance. You obviously have quite a bit of experience, so what do you use instead, rigid body dynamics equations by hand, or is there an alternative software? 

A combination of mathematica and 2D sketches in CAD. I write out all the equations using whichever variables I want to change and then use mathematica...

A combination of mathematica and 2D sketches in CAD. I write out all the equations using whichever variables I want to change and then use mathematica to solve them and generate plots. Conceptually all the equations are simple. I like doing it this way because it makes you really understand everything that's going on, it's quick to iterate dimensional changes, and I can come up with pretty much any metric I want if something out of the ordinary makes a comparison better. For example, those plots I posted about ramp in leverage curve vs ramp in damping force as you'd feel it at the wheel came from this: Screenshot 2025-07-01 102007

That's pretty cool. I've thought of maybe doing something similar in MATLAB and making a GUI in the built in app designer, but always thought that the $25 to get Linkage would just be easier, also considering my Matlab license is about to run out. Is there a good website with all the AR/AS equations available for VPP/Horst/single-pivot available? Even if derive the equations from scratch, I'd prefer to have a way to validate it. 

1
7/1/2025 10:35am
synBike wrote:
To my knowledge I’m the only public alternative (https://syn.bike). Not to speak for Cascade but I believe he developed his own equation solver. You can’t...

To my knowledge I’m the only public alternative (https://syn.bike). Not to speak for Cascade but I believe he developed his own equation solver. 

You can’t model AR/AS without the shock as shock position still has an impact. Neither software effectively models flex-pivots because it requires applying a measured angular spring rate to the effective pivot. That being said, the value is quite high so you can get a good approximation by modelling it as a conventional 4 bar with the brake and wheel attached to the chainstay (sometimes called faux-bar). Kona uses this layout for reference. You can see the impacts of the approximation as the position of the seatstay to chainstay pivot has very minimal impact on the antirise. This makes sense as the critical change is how the brake torque is translated to the frame  


 The reason Horst link bikes have very different (and usually considered better) antirise characteristics is because all of the brake torque tries to the rotate the seatstay member and does not get translated directly to the main pivot like it does when the wheel/brake is attached to the chainstay. 

Do you have any plan to have a discounted hobbyist/ home use single time purchase license available? I have no plans to make anything commercial, and obviously $150/ month is a bit steep for tinkering around on my free time. 

1
joshmtb
Posts
55
Joined
4/17/2025
Location
Haslemere GB
7/1/2025 10:44am

For those looking for free ways to solve the maths.... I've used python + sympy for solving symbolic equations then using jupyter notebook as a handy way to visualise.

4
synBike
Posts
46
Joined
3/15/2021
Location
North Vancouver, BC CA
7/1/2025 11:59am
synBike wrote:
To my knowledge I’m the only public alternative (https://syn.bike). Not to speak for Cascade but I believe he developed his own equation solver. You can’t...

To my knowledge I’m the only public alternative (https://syn.bike). Not to speak for Cascade but I believe he developed his own equation solver. 

You can’t model AR/AS without the shock as shock position still has an impact. Neither software effectively models flex-pivots because it requires applying a measured angular spring rate to the effective pivot. That being said, the value is quite high so you can get a good approximation by modelling it as a conventional 4 bar with the brake and wheel attached to the chainstay (sometimes called faux-bar). Kona uses this layout for reference. You can see the impacts of the approximation as the position of the seatstay to chainstay pivot has very minimal impact on the antirise. This makes sense as the critical change is how the brake torque is translated to the frame  


 The reason Horst link bikes have very different (and usually considered better) antirise characteristics is because all of the brake torque tries to the rotate the seatstay member and does not get translated directly to the main pivot like it does when the wheel/brake is attached to the chainstay. 

Do you have any plan to have a discounted hobbyist/ home use single time purchase license available? I have no plans to make anything commercial, and...

Do you have any plan to have a discounted hobbyist/ home use single time purchase license available? I have no plans to make anything commercial, and obviously $150/ month is a bit steep for tinkering around on my free time. 

It's free to use for non-commercial usage. Small businesses can get in touch for alternative pricing. Basically it's the honor system that get's audited occasionally for non-compliant usage. 

If you want to write your own solver I highly recommend avoiding all of the graphical approximations used and just solve the force matrix. Once you have that the antis are trivial to calculate as they are just proportions of the vertical force to the shock force for a given input. The basic process to solve for all points in the travel is:
1. solve the loop closure equations to determine the position of each link at a given shock displacement (I found ~1mm increments is great. You don't get much out of higher resolutions

2. for each instance of a position configuration solve the force matrix to get the forces at each link for a given input force (for static leverage this is just a nominal 1 unit force vertically at the wheel). 

- Leverage is the proportion of vertical force to shock force

- Anti-rise is the proportion of horizontal tire force + brake torque to shock force

- Anti-squat is the proportion of horizontal tire force + chain forces to the shock force

Validation is time consuming; partially because it's tough to understand the exact input conditions another solver might use. Linkage for example used to offer both a static and a dynamic anti value. Now they treat the frame as fixed with respect to the GCS and just move the wheel. 

There are a lot of edge cases around linkage inversions, loop closure directions, and small angle trig with floating point math that make a univeral solver tricky but for basic 4 bars iterative solving isn't too complicated. 

1
7/1/2025 12:02pm
synBike wrote:
To my knowledge I’m the only public alternative (https://syn.bike). Not to speak for Cascade but I believe he developed his own equation solver. You can’t...

To my knowledge I’m the only public alternative (https://syn.bike). Not to speak for Cascade but I believe he developed his own equation solver. 

You can’t model AR/AS without the shock as shock position still has an impact. Neither software effectively models flex-pivots because it requires applying a measured angular spring rate to the effective pivot. That being said, the value is quite high so you can get a good approximation by modelling it as a conventional 4 bar with the brake and wheel attached to the chainstay (sometimes called faux-bar). Kona uses this layout for reference. You can see the impacts of the approximation as the position of the seatstay to chainstay pivot has very minimal impact on the antirise. This makes sense as the critical change is how the brake torque is translated to the frame  


 The reason Horst link bikes have very different (and usually considered better) antirise characteristics is because all of the brake torque tries to the rotate the seatstay member and does not get translated directly to the main pivot like it does when the wheel/brake is attached to the chainstay. 

Do you have any plan to have a discounted hobbyist/ home use single time purchase license available? I have no plans to make anything commercial, and...

Do you have any plan to have a discounted hobbyist/ home use single time purchase license available? I have no plans to make anything commercial, and obviously $150/ month is a bit steep for tinkering around on my free time. 

synBike wrote:
It's free to use for non-commercial usage. Small businesses can get in touch for alternative pricing. Basically it's the honor system that get's audited occasionally for...

It's free to use for non-commercial usage. Small businesses can get in touch for alternative pricing. Basically it's the honor system that get's audited occasionally for non-compliant usage. 

If you want to write your own solver I highly recommend avoiding all of the graphical approximations used and just solve the force matrix. Once you have that the antis are trivial to calculate as they are just proportions of the vertical force to the shock force for a given input. The basic process to solve for all points in the travel is:
1. solve the loop closure equations to determine the position of each link at a given shock displacement (I found ~1mm increments is great. You don't get much out of higher resolutions

2. for each instance of a position configuration solve the force matrix to get the forces at each link for a given input force (for static leverage this is just a nominal 1 unit force vertically at the wheel). 

- Leverage is the proportion of vertical force to shock force

- Anti-rise is the proportion of horizontal tire force + brake torque to shock force

- Anti-squat is the proportion of horizontal tire force + chain forces to the shock force

Validation is time consuming; partially because it's tough to understand the exact input conditions another solver might use. Linkage for example used to offer both a static and a dynamic anti value. Now they treat the frame as fixed with respect to the GCS and just move the wheel. 

There are a lot of edge cases around linkage inversions, loop closure directions, and small angle trig with floating point math that make a univeral solver tricky but for basic 4 bars iterative solving isn't too complicated. 

Thank you, that's great info! I'll have to try your software out. 

1
7/1/2025 12:15pm Edited Date/Time 7/1/2025 12:15pm

Fun fact, leverage ratio is the derivative of Y wheel position with respect to shock position. You can save a lot of time spent doing equations for wheel force knowing that. 

5
7/1/2025 12:55pm
Primoz wrote:
Does Linkage even support calculating suspension behaviour without having a shock in the frame? As far as I played around you had to have a shock...

Does Linkage even support calculating suspension behaviour without having a shock in the frame? As far as I played around you had to have a shock in there which limits the ability to play around as it requires you to have the layout much more defied than just trying out the main pivot locations and seeing what it does to antisquat and antirise... 

You can just click and drag points around to see what changes it makes - or define the x,y coordinates of each point if you want to make finer changes. You can also constrain certain dimensions, eg if you want a link or the shock to stay at a fixed length or position while the points around it are moved. Is that the kind of thing you meant? Some features are limited to the Pro version so I'm not sure if thats available in the free/basic versions

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Primoz
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7/4/2025 11:44pm
Primoz wrote:
Does Linkage even support calculating suspension behaviour without having a shock in the frame? As far as I played around you had to have a shock...

Does Linkage even support calculating suspension behaviour without having a shock in the frame? As far as I played around you had to have a shock in there which limits the ability to play around as it requires you to have the layout much more defied than just trying out the main pivot locations and seeing what it does to antisquat and antirise... 

You can just click and drag points around to see what changes it makes - or define the x,y coordinates of each point if you want...

You can just click and drag points around to see what changes it makes - or define the x,y coordinates of each point if you want to make finer changes. You can also constrain certain dimensions, eg if you want a link or the shock to stay at a fixed length or position while the points around it are moved. Is that the kind of thing you meant? Some features are limited to the Pro version so I'm not sure if thats available in the free/basic versions

What I thought at the time would be cool was being able to define the suspension pivot points (so the single one for a single pivot or the 4 pivots for a four bar), see what the axle path, antisquat, antirise and pedal kickback is like (by limiting the travel to an arbitrary number) and THEN do the shock driving and derive the leverage ratios and the like. 

This way you could have a decoupled, two step process focusing on certain things first and then off a base focusing on the final details. If I'm not mistaken you have to define everything from the start which means everything becomes a lot more complex as, oi have to fine tune the pivot points and shock placement in such a way to get the desired travel from the shock stroke. This way Linkage looks more like a fine tuning tool than a clean sheet design tool. 

1

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