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Suspension Linkage Kinematics: The Basics of Anti-Squat and Pedal Kickback

October 14, 2014
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It is becoming more common of late to see the terms “kinematics” and “anti-squat” stuffed in to reviews and press releases of full suspension bikes. However, finding information on how exactly this applies to the performance of a bike is still very difficult. With trail, all mountain and enduro bikes all living within a travel range of about 40mm, and with downhill bikes becoming more and more sensitive to fine tuning, an understanding of the suspension kinematics of a bike is becoming a greater asset to getting the performance from a bike that a rider desires.

As cyclists, we like things we can quantify and relate to performance. We like numbers we can assign to performance factors because they make bikes and components easier to compare. A bike with a 66° head angle will likely descend better than a bike with a 68° head angle. A bike that weighs 27 lbs will likely climb better than a bike that weighs 30 lbs. A bike with 160mm of travel will handle drops better than a bike with 130mm of travel. So when it comes time to make decisions between bikes for a given application, we will inevitably have all the popular numbers nailed pretty close to one another. The travel of the bikes in being considered will all be within 5mm of one another, head angles within maybe a degree, top tubes within half an inch, and weights within a pound or two. However, even with all those numbers so close together, there is a still a plethora of numbers regarding the suspension kinematics that can be the difference between a bike being most at home eating up rocks on descents, or snapping itself up the climbs quickly.

First I think it’s important that we clear up exactly what “kinematics” means. Merriam-Webster defines it as: “a branch of dynamics that deals with aspects of motion apart from considerations of mass and force.” In other words, the kinematics of a suspension bike are figures that can be derived using only geometry, without concerning the forces that cause motion in the suspension. Factors like damping, friction and chassis flex are not components of kinematics, since they involve the input of mass and speed. There are a number of different elements that kinematics entails on a bike, but for now we will cover anti-squat because it is one of the factors that perhaps has the most noticeable effect on the suspension performance, and can have great discrepancy between two bikes that are otherwise quite similar in their numbers.

kinematics

 

When you accelerate hard in a car, you can feel your weight being thrown towards the back of the vehicle. Obviously this happens exactly the same on a bicycle, though to a lesser degree. This weight transfer happening over and over is what causes pedal bob. The sharp acceleration that comes with each pedal stroke shifts a rider’s weight around repeatedly and causes the suspension to bob up and down in the process. To remedy pedal bob, the bike’s linkage is designed so that the drive force being put through the chain will limit the amount that the suspension can move. The suspension being limited by the drive force of the chain to eliminate pedal bob is what we refer to as “anti-squat”.

Of course, different linkage designs will have different degrees of anti-squat. The benefits of having more anti-squat is a bike that will pedal more efficiently without bobbing, and will maintain a more forward riding position. This tends to be beneficial for climbing and sprinting. The downside of having more anti-squat is that the amount the suspension can absorb bumps will be limited while pedaling, and the suspension will create feedback through the cranks and pedals when absorbing bumps (this feedback is referred to as “pedal kickback” and will be discussed further down the article). On the other hand, a bike with less anti-squat won’t pedal as efficiently, but will absorb the terrain better while pedaling, and have less feedback in the pedals as the suspension moves through its travel. This tends to be and advantage while descending, where there is less pedaling, but bump sensitivity is more important.

Lucky for us number hungry mountain bikers, anti-squat can indeed be quantified. However, it is not quite as simple as some of the other numbers we use for comparison purposes. Due to the position of the pivots constantly changing in regards to one another as a bike goes through its travel, the anti-squat figure will change through the travel cycle. For this reason, anti-squat is displayed as a graph rather than a single figure. However, it is most beneficial to look at the single anti-squat figure at the point in the graph where the suspension sits sagged under the rider weight, since this will be the neutral point where pedaling almost always occurs.

Reign AS Sag Zone

A typical anti-squat graph. The highlighted area around the point of sag (25% in this case) is the focal point of the graph, because that is area where the suspension sits while pedaling.

 

Since it is the force through the chain that creates the anti-squat, the angle of the chain relative to the suspension linkage also plays a key role. This means that as you shift gears, the anti-squat properties of the bike will change. Being in a big rear cog and small front chain ring will create significantly different suspension properties than the opposite combination. This means that for every gear combination, there is a different anti-squat graph that can be plotted. In terms of suspension design, this is usually referred to as “chain line”. Though, in the application of suspension design, it applies differently to what is typically referred to as “chain line” on a bicycle. Typically bicycle chain line refers to the lateral path of the chain, commonly viewed from the rear or top of the bike. However, in regards to suspension design, “chain line” is referred to in a vertical sense, as viewed from the side of the bike (eg. its slope relative to the ground plane). The path of the chain in this manner is what influences the properties of suspension kinematics.

Similar to what was stated above about focal points of all these numbers, it is usually best to just find a few key gear ratios and look at the figures around the point of sag. Looking at an anti-squat graph for a 28t chainring and 11t rear cog doesn’t make much sense, because it’s not a gear combination people tend to ride in.

Now that we’ve looked at the two key factors that effect anti-squat numbers (geometry of the linkage design and the chain line) we should look at what those numbers mean.

Anti-squat is measured as a percentage. An anti-squat percentage of 0 means that the drive of the chain does nothing to prevent pedal bob in the suspension at all. At 0% anti-squat, the drive train does not effect the suspension in any manner. Not surprisingly, the other significant number is 100%. An anti-squat percentage of 100 means that the drive force completely eliminates any bobbing created by the accelerating mass of the rider. While you can probably imagine the anti-squat characteristics between 0% and 100% will be something of a middle-ground between what I just described, it is important to acknowledge that suspension designs often operate with figure above 100%, or below 0%. An anti-squat percentage above 100 will actually make the suspension extend under pedaling load. It is fairly common for suspension designs to have figures above 100% because it creates a very firm pedaling platform and forward riding position for good climbing performance. Likewise, a percentage below 0 will cause the suspension to compress under pedaling load, though this is seen less frequently.

As was previously noted, using high anti-squat numbers, especially above 100%, will come at the expense of bump sensitivity. If the suspension is being limited by the drive force through the chain in order to prevent pedal bob, it means the drive force will also hinder the suspension’s ability to absorb bumps. As you can imagine, the drivetrain of a bike having an effect on the suspension means that the suspension will also have an effect on the drivetrain. This concept is referred to as “pedal kickback”. Pedal kickback is primarily the result of the chainstay growth in a suspension design tugging the cranks backwards as the suspension moves through its travel.

Similar to anti-squat, pedal kickback is expressed as a graph spanning the length of a bike’s travel, and is specific to each gearing combination. However, while anti-squat is measured as a percentage, pedal kickback is measured in degrees to indicate how much the pedals rotate backwards at a given point in the travel. Pedal kickback grows proportionally as anti-squat increases, so suspension linkage design is always a trade off between an efficient pedaling platform and how much independence the suspension has from the drivetrain. I mentioned above that some designs will occasionally have anti-squat percentages below zero. This is most commonly seen on downhill and other big-hit bikes at points deeper into their travel. This is done in order to completely free up the suspension from the drivetrain in the event of big hits where the bike nears the end of its travel.

aspkchart

This chart plots the anti-squat to pedal kickback ratio of various bikes at the point of sag. Notice the linear relationship that the two have. Thanks to Antonio Osuna of the blog Linkage Design for the image.

 

It is important to note the significance of the fact that changing gear combinations produce different suspension characteristics. This is one of the key factors that makes mountain bike suspension unique over other vehicles. Very rarely do you see other wheeled, suspended vehicles with changing paths of drive force. While this ostensibly can complicate designing the suspension, it also creates a wealth of potential for optimizing suspension performance for different riding situations.

We have established that pedal kickback and anti-squat are performance considerations which are at odds with one another. But because of the changing gear combinations, a suspension design can be made to perform with high anti-squat values in gear combinations where one will be doing more high power climbing and pedaling, while at the same time having lower anti-squat values in higher gear ratios where speeds are high, pedaling is minimal, and suspension performance is paramount.   Many suspension designs have anti-squat numbers above 100% in some lower gear combinations (which creates high pedal kickback) while having anti-squat numbers below 0% in other combinations (creating no pedal kickback).

Reign 38-11 ASPK

An anti-squat graph and its corresponding pedal kickback graph for the highest gear on the bike. The pedal kickback graph has two curves on it representing different amounts of front wheel travel in relation to the rear wheel, but the blue curve is the one most applicable to real world riding situations. Note that at roughly the point in the travel in which the anti-squat curve drops below 0% is about the same point at which the amount pedal kickback begins to drop off sharply.

Reign 24-36 ASPK

The anti-squat and pedal kickback graphs for the lowest gear on the bike. The amount of anti-squat is much higher than the 38/11 gear combination, which creates a very good pedaling platform comparatively. However, the pedal kickback is also much higher in this gear combination, so bump sensitivity will be greatly reduced.

 

The difference in squat and kickback profiles creates a strong case for the relevance of a double or triple chainring transmission. Because the main pivot of bicycle’s suspension is typically close to the crankset, shifting between the large and small chainring can give the bike radically divergent pedal kickback and anti-squat numbers. Even while using overlapping gear ratios, suspension performance can differ greatly between the small and large chainring. For example, at a 1.8:1 gear ratio, a 2015 Giant Reign with a double chainring transmission will have an anti-squat figure of about 87% in the big chainring. If you shift to the small chainring to achieve the same gear ratio, the anti-squat will be around 169%. This creates better pedaling performance in the smaller chainring where speeds are usually low with lots of pedaling, while maximizing the activity of the suspension and bump compliance in the large ring.

The suspension performance benefits of having multiple chain rings is very rarely acknowledged, but there is a lot of potential here. While shifting gears in the rear does make a change in the anti-squat as well, the proximity of the crankset to the main pivot on most bikes means the difference in anti-squat and pedal kickback between different chain rings is quite large. You can even think of shifting between front chain rings and changing your linkage performance from “climbing mode” to “downhill mode”.

 

 

1) F: 38t – R: 11t

Anti-Squat: 63%

⁃    This is the highest gear available on the bike, which as such is conducive to the highest speed downhill sections you will encounter. Notice that the feedback in the pedals here is very minimal. The cranks move very little through the suspension travel. This gear combination results in an anti-squat percentage of 63% and a total pedal kickback of about 1.2°. These properties make this gear choice ideal for downhill applications. Thought the anti-squat figure is somewhat on the low side, this is not a gear where pedaling is a priority. However, the very slight amount of pedal feedback means the suspension stays very active and will have great performance on the bumps.

2) F: 24t – R: 36t

Anti-Squat: 126%

⁃    This is the complete opposite end of the spectrum from the above gear combination. This is a gear that is only used for extra steep or long sit-and-spin climbs. The video shows that the amount of pedal feedback here is very high compared to the above gear ratio, with a total pedal kickback of about 26.0°. However, this is not a gear where bump compliance and pedal kickback is generally a performance issue. The more important figure in this gear is the anti-squat percentage of 170%. This creates an excellent, firm pedaling platform, which in turn gives the bike a very forward geometry to create a good rider position for hard pedaling.

 3) F: 38t – R: 21t (1.8 gear ratio)

Anti-Squat: 81%

⁃    In this clip, and in clip 4, I show how gear selection can have an effect on the pedaling performance, even if the two different sprocket combinations result in the same gear ratio. In this clip I illustrate the 1.8 gear ratio using the big chainring, and a 21t rear cog. This gear combination results in slightly low anti-squat of 81%, but a low pedal kickback figure that peaks at 3.6°, which will result in fairly active suspension and decent bump compliance. The next clip shows the same gear combination, but with much different results.

 4) F: 24t – R: 13t (1.8 gear ratio)

Anti-Squat: 170%

⁃    As mentioned, this repeats the 1.8 gear ratio from clip 3. However, this uses the small chainring with a 13t rear cog. This combination results in a very high anti-squat of 170%, and a correspondingly high pedal kickback figure of almost 13°. Note the difference in overall rearward crank rotation between clips 3 and 4. This is a good indication of how a small chainring can be seen as “climbing mode” to maximize anti-squat and pedaling efficiency, while the bigger chainring can be seen as “downhill mode” in order to reduce pedal kickback and increase bump sensitivity.

Now that we have learned a fair bit about how anti-squat and pedal kickback effect suspension properties, the question begs to be asked: How do we go about getting this information for a bike?

In the long run, the most effective way is to download a program called “Linkage” from www.bikechecker.com. This program can be had for $25 (though you’ll have to shell out $300 if you want the professional version), and allows you to analyze the suspension properties of any bike with just a high resolution side photo of the bike. The program will work you through a step-by-step process of picking key points on the bike and entering a few key geometry numbers in order to create a 2D profile of the bike from which the suspension properties can be extrapolated. The downside to this is that it costs $25. A meager price, but still not free. Also, finding decent high resolution side shots of some bikes can sometimes be difficult, and going through the setup process takes some time.

A simpler, though more limited approach, is to head to the blog Linkage Design. This is a blog that publishes suspension graphs for various bikes, with a bit of commentary on each of them, and a handful of interesting and informative tutorials on top of that. While it obviously does not have every suspension bike posted, the library of bikes is over 800 long, so it has a covered a great deal of ground. The website is in Spanish, so you will have to use a web translator if you want to read the commentary (unless of course you can read Spanish).

Finally, I encourage you to investigate the two resources above for a few reasons. Of course it helps when deciding between bikes you plan on purchasing. But knowing the anti-squat profiles of a bike can also be a great help to figuring out how to set up some of the suspension on a bike you already have. If your bike runs a lower anti-squat percentage, especially if you have a 1x drivetrain, you will have much more use for a platform/lockout setting on your rear shock (Propedal, Climb Switch, etc). On a bike with high anti-squat numbers, you can potentially run higher amounts of sag if you desire, without sacrificing much to pedal bob. Also, it is interesting to look at how different suspension designs may seem similar to one another in appearance or concept, but can have very different properties once in motion. Many people liken the performance of DW-Link with VPP designs, because their linkages look somewhat similar. But it is easy to tell the difference when looking at their actual numbers. Even looking at Specialized’s application of the FSR platform versus Norco’s shows how much difference can be granted even when using the same kind of suspension design.

Matt Faulkner was born in North Bay, Ontario, where he started mountain biking and racing downhill at the age of fourteen. He completed a diploma in Mechanical Engineering Technology at Georgian College in Barrie. After spending a few years in the engineering departments of mining companies, he switched over to the bike industry. He now lives and works as a bike mechanic in Downtown Toronto.

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20 Comments

  1. Wow Matt. This is a really good read. I’ve been able to piece much of this together in the past but it’s great to have it all in one article.

  2. Thanks, Marc.

    This topic will inevitably invite some questions. Feel to free to throw out your queries and insight in the accompanying thread in our Tech Talk forum:

    https://www.ridingfeelsgood.com/topic/the-basics-of-anti-squat-and-pedal-kickback/

  3. Wow, thats pretty sweet! Definitely makes me question 1X setups on some bikes.

  4. Wow. I just quintupled my knowledge of suspension tech. Thanks for sharing, the videos helped a lot.

  5. No matter how many times I’ve heard “pedal kick” described, that video describes it a 1000 times better.

  6. All I can say is wow! Great article Matt!

  7. Great read!

  8. Nicely done Matt! I’ll be reading this one over and over!

  9. Hi, i just read the article and it left me with some questions: antisquat is given in procentage, i dont understand of what though. Force from riderinduced pedalbob?

    Pedal kickback is given by a 1 wich i dont understand at all. Please explain.

  10. Anti-squat is expressed as a percentage, but it doesn’t have a specific unit associated with it. 0% anti-squat means that the drive force does not have any affect on the suspension. 100% anti-squat means the drive force completely cancels out any pedal bob created from accelerating forces.

    Pedal kickback is expressed in degrees. The numbers you see on the side of the graph indicate how many degrees the pedals rotate backwards at a certain point in the suspension travel.

  11. Thanks for writing this! Best explanation I have found of anti squat an. pedal feedback/

  12. Would be much appreciated if you could provide the equations and assumptions used to graph these responses.

  13. All the graphs were created using the program Linkage. The geometric formulas are too involved for me to explain in a single post, but if you want to learn more about them you can check out the book “Race Tech’s Motorcycle Suspension Bible” by Paul Thede and Lee Parks

  14. it sounds like riding a 1x can potentially put you in an no-man’s-land for kinematics. If i have a 32t 1x on a Trance, and care more about small bump sensitivity on the downhills than eliminating pedal bob (I have a climb switch to help with that), what is my best move for getting the lowest anti-squat possible? Should I be running more sag, with a more progressive air spring to offset the lower air pressure? I would imagine this would push me further down the anti-squat curve, but of course, i’m losing a little bit of suspension travel.

  15. @1x ,

    There is no sense altering your sag to change the anti-squat properties. You will run into massive issues with your spring rate well before you gain any noticeable difference in the anti-squat performance. The only real solution is to change the size of your chainring.

  16. thanks for the reply! good to know

  17. Good explanation – something I didn’t figured out yet was the use of IGH anti-squat? Do these same physics apply here as well, since your basically having a huge 1x. Look forward hearing your opinion about this 😉

  18. The same physics apply to internally geared hubs, yes. Most of the texts on this topic are based on the motorcycle world, where pretty much everything is internally geared.

  19. I have a merida 140b. according to linkage designs it has very high anti-squat. even the lowest level (in large chainring on a double) is around 100%. This is consistent with my experiences – excellent climbing bike with no pedal bob even with the shock in “open”
    Given that I cannot reduce kickback by changing chainring, then, is there anything else I can do to give better performance on descents? I haven’t had enough experiences on other bikes to know what better small bump sensitivity feels like. Is it noticeable much?

  20. A very interesting read. Being a hardtail rider all my life, I have resisted the lure of full suspension. However, I have now reached the age where my back starts to suffer on longer rides and have started to look for a ride with a little more comfort. Information given hear will allow me to choose more wisely. Thank you!

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