Instantaneous Center Migration
August 14 — 2012
This is part 2 of a technical series talking about mountain bike suspension.
Words by: Joe Graney, SCB Engineering
Migration is defined by the American Heritage Dictionary as: "To change location periodically". For a bicycle suspension system, the Instantaneous Center (IC) is the point that the rear axle is rotating around at any given instant. On a single pivot suspension, the IC is the pivot - and it doesn't migrate. Other mechanisms can change the point that the rear axle is pivoting around as the suspension compresses. Most common in bicycle suspension is a four-bar linkage with the axle located on a link that is not connected directly to the front triangle. It's referred to as "instantaneous" because the pivot point can move, unlike the single pivot mechanism. Therefore, at any given point in the suspension motion the IC can be at a different location. IC Migration is the subject of several patents on bicycle suspension, some with detailed claims and some with more vague claims of the advantage of a particular system. Some patents don't say why its better, but simply protect something about the configuration of the mechanism. The IC can be determined by tracing lines through the first and third bars of the linkage (see figure 1).
The placement of the IC at any given point can play a big part in how the bike behaves with regard to chain tension (pedaling), and how much chain growth occurs. Imagine a single pivot bike with the pivot located along the centerline of the seat-tube. If that pivot is above the chain-line, the bike will exhibit anti-squat (the suspension extends)characteristics when the chain is under tension while pedaling. The opposite is true when the pivot is lower than the line of force in the chain. Additionally, the distance from the wheel axle to the pivot plays a part, by changing the bike's behavior under braking forces. Finally, squat - the pulsing acceleration of one's body that is timed with pedal strokes - has to be taken into consideration. You step on the pedals, the bike accelerates forward and the inertia from the mass of your body trying to stay put puts more force on the rear wheel which has a squat effect. The force acts through the contact patch of the tire to the ground, and acts around the IC or pivot.
There are a few major things going on when pedaling that affect the suspension in different ways: chain tension, the acceleration of rider mass, and the force of the tire pushing back on the ground to drive the bike forward. These forces all work around the IC of the frame, since that is the point that the rear wheel is moving around. When you apply the rear brake, there is the force of the tire on the ground; it also works around the IC. A braking force article might follow later, but remember for now that if anyone shows you a "braking demonstration" of their suspension without the tire on the ground they are excluding a key component of the physics, even if it looks convincing.
As always, there is a balance that comes into play. Chain tension is something that isn't constant, as different gears give different tension. Riders don't always pedal w/ the same force on the pedals either. Cranking up that steep ravine in the granny results in high chain tension and lots of pulsing rider mass acceleration, since you almost come to a stop between each pedal stroke. Contrast that to laying down some smooth big ring power on a flat XC track. Finding a system that performs well in both scenarios (and everything in-between) is challenging. Making it more difficult are different rider positions, because the center of mass of the rider/bike system changes. This complexity and balancing of forces is why we generally don't make blanket claims that "our bike has no bob" or believe that simply moving the IC near the chain-line relates directly to system efficiency.
So if the placement of the IC influences all of this behavior, why is everyone talking about axle path? As pointed out in the last article, there is only a small amount of chain growth allowable without tugging the pedals around a lot. Within that range of axle paths however, there are an infinite number of IC migration paths possible. The IC can move up, down, back and forth. It can also change its rate of motion as the suspension compresses. These things all profoundly influence the way the suspension behaves in different conditions.
Sorry it's not simple, but that's what's going on. The mechanisms also relate to bump absorption, aka plushness, but we'll save that one for the next article in December's newsletter which will be about shock rate - including "floating" shock mounts and why they're not all that exciting.
Bonus Section - The "5 bar" linkage:
Complicating things further, there are several systems being introduced into the marketplace that include a second degree of freedom for rear axle motion. This can be done by adding an extra link which allows the axle to move in a "zone" rather than following a single trajectory. Presumably, the axle moves in a more preferable way under different conditions. We call this type of mechanism an "envelope" bike, since the axle can move in an area or "envelope" of allowable motions. This sort of thing comes up in our brainstorm sessions all the time, but we haven't figured out the advantage the additional complexity would be justified by. Additional dampers that can change the suspension based on the rate of motion of the rear wheel gets pretty complex to control, as well as make tunable, serviceable, use commonly available parts, and all those boring things that are important if you want to have a reliable bike that can take years of abuse.