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Shock linkage query


Guest cudgel

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Anybody know what the ratio is between the movement of the rear axle and the shock? If the axle moves up by 2 inches on a bump how far does the shock compress? Is the stock 'Bird spring around 950 lb/in? Thanks.

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Anybody know what the ratio is between the movement of the rear axle and the shock? If the axle moves up by 2 inches on a bump how far does the shock compress? Is the stock 'Bird spring around 950 lb/in? Thanks.

It's approximately a 3-1 ratio, though that changes throughout the travel of the linkage. An exact answer is beyond my math skills.

Stock rate is 16.8kg/mm, you can do the math, but 950 sounds close.

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Anything attached to the swingarm moves in arc. Getting back to trigonometry, the formula for arc length is s = rθ. Where s is arc length, r is the radius and θ is the angle of movement in radians. In our case, the angle the swingarm moves.

So for the rear axle:

2" = xθ. where x is distance from center of swingarm pivot bolt to center of rear axle (radius r). Let's rewrite this formula as θ = 2" / x

And for the rear linkage attachment point:

s = yθ, where y is distance from center of swingarm pivot bolt to center of linkage attachment point (LAP). We'll rewrite this formula as θ = s /y.

And since the rear axle and the LAP are both attached the swingarm, they both move through an arc of angle θ. So we can set our two formulas equal to each other, hence s /y = 2 " / x. So solving for s (arc length the LAP moves) is s = 2" * y / x. Go measure y and x, divided x into y and multiple by 2".

But that's just how much the LAP on the swingarm moves, next you'll have to use trigonometry to find the ratio of LAP movement to shock compression which is determined by the size of the linkage plates and the length of the shock, from the center of it's upper pivot point to the center of it's lower pivot point.

I think that's correct.

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Wow, that math hurts my head. You put your reply in while I was typing this-Make any sense? Looking at the swingarm and linkage is confusing and why I asked the question. The swingarm pivot to axle is about 20.75" and the swingarm pivot to shock centerline is about 3" giving a ratio of about 6.92-1. The triangle doodads and the link has me going but I don't see why they change the ratio of leverage. Looks like they just keep the shock level and centered as it moves. I'm probably missing something trying to understand this setup but the 950lb/in spring divided by 6.92 works out to an equivalent of 137lb/in and if you figure 3" travel you get a rear wheel load of about 412 lbs. Seems a reasonable figure for weight of part of the bike and part of rider. What am I not understanding?

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Those triangular plates and the associated "dog bone" are the key to the change in leverage. Like I said, I don't have the math. Matt did a good job of describing a linkageless system (KTM played around with those in the late 90's, or I suppose I should say went back to them briefly), but that linkage changes everything, as the bottom of the shock is moving in two axis and that changes the rate as it compresses.

The best way to understand it without taking advanced math classes is to get down there and watch it work as the arm moves up and down. Find a fat friend to bounce on it for you. :icon_lol:

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To both of you guys, thanks for the help. I can't come up to the level of your math so I have to do what I do. I'm going to make cardboard reps of the various parts and pin the pivots and measure how far the bottom mount of the shock moves in relation to the movement of the swingarm and am expecting to see a rising rate.

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I have software that has had a hard time extracitng the info in the shock rising rate ratio that cost 25,000 dollars. (FEA) Good try Matt. best i have seen. now go the rest of the way and do the linkage to shock ratos.

Why I went to a direct link.

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I have software that has had a hard time extracitng the info in the shock rising rate ratio that cost 25,000 dollars. (FEA) Good try Matt. best i have seen. now go the rest of the way and do the linkage to shock ratos.

Why I went to a direct link.

If I could remember exactly how the linkage / dogbone is configured, I'd try. Trouble is, there's no longer an XX in the garage for reference.
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I have software that has had a hard time extracitng the info in the shock rising rate ratio that cost 25,000 dollars. (FEA) Good try Matt. best i have seen. now go the rest of the way and do the linkage to shock ratos.

Why I went to a direct link.

If I could remember exactly how the linkage / dogbone is configured, I'd try. Trouble is, there's no longer an XX in the garage for reference.

I have the dimn's somewhere. maybe

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