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Faux-bar or four-bar?
Ginsu2000 asked a great question about rear suspension linkages that may be of interest to others. To paraphrase, he wants to clarify whether a design with the wheel attached to the chainstay / swingarm (often called a "faux-bar") is four-bar linkage. He further asks how flex-pivot and Horst designs fit in. Below is my response.
It's important to consider the purpose of the design. A four-bar system can decouple the movement of the wheel and brake from the element attached to the frame, which we can refer to as the chainstay or swingarm. Mounting the wheel and brake to this element removes valuable design freedoms offered by a four-bar system. A system with the wheel and brake attached to the swingarm is a single-pivot with linkage-actuated shock.
It's not incorrect to call it a four-bar, but it's misleading. If we allow such a system to be called a four-bar, we could add any number of elements to the shock linkage and call it an n-bar linkage, but it still behaves as a single-pivot with linkage-actuated shock. It would be like saying a line is a one-dimensional object … and also a two-dimensional object that doesn’t use the second dimension, and a third-dimensional object that doesn’t use the third dimension, and so on. While true, these are “trivial cases,” and trivial cases are typically ignored. Therefore, the best description is a single-pivot with linkage-actuated shock.
The Horst design is not the only true four-bar. A dw*link, for example, is the same as a Horst, but with the chainstay shrunken to become the lower link, the “seatstay” expanded to become the entire rear triangle, and the rocker often left unchanged. Same with VPP. Same with KS-Link. And Maestro. And MLink. And Lawwill. And ETS. And … take your pick; they’re all four-bar systems. Even Split Pivot and ABP are four-bars, since the brake is not attached to the swingarm. The ability of Split Pivot and ABP to decouple the braking instant centre from the swingarm pivot makes them more more closely related to a "true" four-bar design than a single-pivot with linkage-actuated shock.
A flex-pivot design with the flex mostly confined to the seatstay is a single-pivot with linkage-actuated shock. As before, the braking and pedaling instant centres are concentric with the swingarm pivot, so those properties behave the same as a single-pivot. Obviously, the linkage modifies the shock actuation, much as it would if there was a rotational element pivot.
A flex-pivot design with the flex mostly confined to the chainstay (ex. Cannondale, Spot), however, is equivalent to a four-bar.
It's important to consider the purpose of the design. A four-bar system can decouple the movement of the wheel and brake from the element attached to the frame, which we can refer to as the chainstay or swingarm. Mounting the wheel and brake to this element removes valuable design freedoms offered by a four-bar system. A system with the wheel and brake attached to the swingarm is a single-pivot with linkage-actuated shock.
It's not incorrect to call it a four-bar, but it's misleading. If we allow such a system to be called a four-bar, we could add any number of elements to the shock linkage and call it an n-bar linkage, but it still behaves as a single-pivot with linkage-actuated shock. It would be like saying a line is a one-dimensional object … and also a two-dimensional object that doesn’t use the second dimension, and a third-dimensional object that doesn’t use the third dimension, and so on. While true, these are “trivial cases,” and trivial cases are typically ignored. Therefore, the best description is a single-pivot with linkage-actuated shock.
The Horst design is not the only true four-bar. A dw*link, for example, is the same as a Horst, but with the chainstay shrunken to become the lower link, the “seatstay” expanded to become the entire rear triangle, and the rocker often left unchanged. Same with VPP. Same with KS-Link. And Maestro. And MLink. And Lawwill. And ETS. And … take your pick; they’re all four-bar systems. Even Split Pivot and ABP are four-bars, since the brake is not attached to the swingarm. The ability of Split Pivot and ABP to decouple the braking instant centre from the swingarm pivot makes them more more closely related to a "true" four-bar design than a single-pivot with linkage-actuated shock.
A flex-pivot design with the flex mostly confined to the seatstay is a single-pivot with linkage-actuated shock. As before, the braking and pedaling instant centres are concentric with the swingarm pivot, so those properties behave the same as a single-pivot. Obviously, the linkage modifies the shock actuation, much as it would if there was a rotational element pivot.
A flex-pivot design with the flex mostly confined to the chainstay (ex. Cannondale, Spot), however, is equivalent to a four-bar.
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However, I tend to see the "structural" part of the layout, if that makes sense.
In that way, anything that have bearings (or a flexible element) near the rear axle would be on the same family.
They require the same triangulation, will have the same weight to strength ratio, will mostly suffer from the same bearing misalignment issue, "look" the same, will require equivalent manufacturing techniques. Even antisquat and kickback can be adjusted to be about the same.
That's why the distinction between single pivot and short links/ short links/four bar still makes sense, as it gives a good idea on what it'll look, how it will be manufactured, and what compromises will be made.
Similarly, consider the common motorcycle design of a swingarm with shock linkage (ex. www.youtube.com/watch?v=te7Q8V90bvo): the appearance and structural design are that of a simple swingarm design, but the kinematics are that of a single-pivot with linkage-actuated shock.
Kinematics, aesthetics, and structural design are three separate subjects. On the subject of kinematics, four-bars and faux-bars are different categories.
That said, the bikes that arise from these designs can be similar. As you noted, pedaling anti-squat and kickback from a four-bar vs. single-pivot are often similar. That's not coincidence: the acceptable range for these parameters is narrow for a direct drivetrain (i.e. without an idler sprocket or other such design). The brake squat (or "anti-rise") can be vary greatly, though, and it's an important distinction that four-bar designs can separate the braking kinematics from the pedaling kinematics, unlike a faux-bar (without the use of a floating brake linkage).
Faux bar and four bar are the same "structure", the only difference being where you put the dropout. they would have the same yoke, same tubes, same welds, same bearing sizes, same bearing lockout when side loaded...
The biggest difference in kinematics between both is brake squat, but that thing doesn't matter that much in my opinion, because the braking loads on the rear brake can't be that high. going from 0% to 100% brake squat will lead to a chassis movement difference about the same as going 1.5 or 2° less in head tube angle. Meaning brake squat isn't the indicator that should be segregating kinematics.
AS of a four bar has a big chance to be dropping, whatever it's aimed value, due to the chainstay's movement. a faux bar with a main pivot behind the chain ring "tangent point" (with the chain) can copy this behaviour 1:1. There is a bigger difference moving a SP pivot 4 cm forward, that to go from faux bar to four bar.
KB will have the same order of magnitudes in both if the AS are in the same order of magnitude.
So I think putting them in different categories don't makes much sens in first approach, when we have things like DW link , VPP's or MX links that will have totally different compromises and "structures".
I like to broadly classify four-bar configurations as LL (long and long links), LS (long and short), or SS. The kinematics of different systems, ex. LL and LS, can be more similar to each other than two of the same. For example, you could create LS and LL bikes with nearly identical curves for pedaling anti-squat, brake squat, and motion ratio, and you could create two LS bikes with vastly different values for each of these parameters. You could also create LS and LL bikes that connect to the front triangle in identical locations, or two LS bikes that connect in vastly different locations.
We can go further and say a faux-bar and a four-bar - any sort of four-bar - can be configured to have extremely similar kinematic properties and the ride feel of each may be indistinguishable, yet they are intrinsically different systems. There exists a wide range of tuning options, but the important thing is which parameters are linked and which are independent. The feel of the bike, the strength and stiffness of the chassis, the aesthetics - these are all important to the performance of the final product, but are not intrinsic differences that define the linkage types.
Similarly, it does not matter whether you think brake squat is important; what matters is that one type of linkage can vary this parameter independently of pedaling anti-squat, while the other cannot. That is an intrinsic difference between the systems; everything else is just a matter of how the designers have chosen to configure the systems.
More importantly, though, is that I discovered the converse of anal retentive (or "anal-retentive") is anal expulsive. I propose we refer to confidence, disorganization, generosity, or artistic inclinations as anal expulsiveness. If the anal expulsiveness is excessive, the cure is - obviously - cocaine. Or maybe that's the cure for having a crush on one's mother - I could never keep up with his theories.