3 link a arm suspension application. One more time.

[Yoshi]

Was there a discussion a while back on why people thought your 3rd. link wouldn't allow the suspension to cycle properly?  I seem to recall that at MB.net, but never joined in the conversation.  After seeing those pics though, I can see how it would have no issue cycling do to the forward mount being inline with the inner a-arm mounts. I like the idea of the forward link to take the stress off the inner mounts when the wheel tries to pull backward. When I thought about doing a rear a-arm setup on my rail, I didn't think about the 3rd. link so much as just making the a-arms that wide, which would basically be just like you have it, only not have the middle tube in the design, the forward link and the rear tubes would be attached to one another, but I wasn't sure about strength in having an a-arm that wide.........

[Rick S.]

Actually the point is not in line with the inner mounts. Vertically It falls between the mounts and can also vary up/down depending on how high you place the mount on the upright. Cross car is falls almost 2" outboard of the a arm pivots.
Cross car location will also vary depending on how far outboard you place the attachment on the upright.
I'll post up a drawing showing how this works with equilateral parallelogram arms. You can make the forward attachment point move wherever you need it in X,Y.& Z.

[Yoshi]

Actually the point is not in line with the inner mounts. Vertically It falls between the mounts and can also vary up/down depending on how high you place the mount on the upright. Cross car is falls almost 2" outboard of the a arm pivots.
Cross car location will also vary depending on how far outboard you place the attachment on the upright.
I'll post up a drawing showing how this works with equilateral parallelogram arms. You can make the forward attachment point move wherever you need it in X,Y.& Z.

It works like a control arm, as long as it is in the correct location, it will cycle properly, just like if a control rod is in the right location, you won't have bumpsteer.....

[Rick S.]

In this drawing I've exaggerated the conditions to show how this works.
I've used this concept for years in machine design. It's a clean and accurate way to rotate a mechanism, when you don't have room for a conventional pivot.
In the drawing the arms are 12". The attachment point on the upright moves on a 12" radius regardless of where you place it. Notice the origin of this radius is NOT in line with the a arm pivots. It's always dependant on where it's attached to the upright. If this attachment point were moved 1 mile out, it would still only travel on a 12" radius. But the origin of the radius would also move out 1 mile.

With unequal length arms you just need to plot the travel of the attachment point to determine the origin of the radius or arc. It's a little trickier, but the same concept.

[Yoshi]

In this drawing I've exaggerated the conditions to show how this works.
I've used this concept for years in machine design. It's a clean and accurate way to rotate a mechanism, when you don't have room for a conventional pivot.
In the drawing the arms are 12". The attachment point on the upright moves on a 12" radius regardless of where you place it. Notice the origin of thi radius is NOT in line with the a arm pivots. It's always dependant on where it's attached to the upright. If this attachment point were moved 1 mile out, it would still only travel on a 12" radius. But the origin of the radius would also move out 1 mile.

Just like a control arm.  If you left the outter mount, and moved the inner mount, you would have bind issues, but as long as you don't change the length of that link,  and you move the inner and outter mount on the same axis in any direction (since you have the same distance between upper and lower mounts for the inner and the outter), as you said, moving it a mile out wouldn't effect it...

[Rick S.]

Adding this link does more that just extra support for the a arms. It supports the upright as well. Wider spread on the a arms will not do this.

[Rick S.]

The length of the link in the fore/aft direction can be as long as you want.
once you have the points figured out in the rear view. Longer or shorter link will not bind once the rear view is set.

[Yoshi]

The length of the link in the fore/aft direction can be as long as you want.
once you have the points figured out in the rear view. Longer or shorter link will not bind once the rear view is set.

I agree, as long as the points are in the correct place, you could extend the inner link mount all the way to the nose of the rail making it 8 foot long (assuming it didn't hit anything as it cycled, or was bent in a way to not hit anything) and it still wouldn't bind the suspension, as long as the inner point were in the right location.  It's the 3 link setups like the drakart (or the blue rail ion the first page of this topic), that are mounted toward the outside of the vehicle, that would cause a bind issue, or in the drakarts case (or blue rail), a toe change...

[Doug Heim]

Your spot on Yoshi. And Rick I dont think you can explain it in any simpler way. Great informational thread!

[Rick S.]

Spot on? you been hanging around those OZ guys too much.

[Doug Heim]

thats right Bloke! I thought the same thing once I submit the post.

I get phone calls from the guys in the land of OZ all the time. Love talking with them! I really do.

Yeah maybe for too long!

I talk more like a Canadian than anything... Aye?

[artie on edge]

thats right Bloke! I thought the same thing once I submit the post.

I get phone calls from the guys in the land of OZ all the time. Love talking with them! I really do.

Yeah maybe for too long!

I talk more like a Canadian than anything... Aye?

Oh my.......

[artie on edge]

Spot on? you been hanging around those OZ guys too much.

Spot on mate! 

[Rick S.]

Yea, Doug really does talk like a Canadian. Or a Uper.

[Engineer]

Eng or anyone, can you give a formula for the calculation of the sweet spot/axis?

Rick's example above showed parallel, equal length arms.  Of course this is usually not what you are working with.  Also finding the sweet spot is exactly the same for finding the sweet spot for the inner tie rod mount to the rack. 

You are looking for the spot that causes no bind on the rear.  On the front because the spindle can rotate on the a-arms you won't get bind, but you will get toe in / out as the suspension cycles.

So, how to find the point?  In CAD terms.  I first draw the suspension like Rick's drawing above.  Then draw the upright in three positions: Full compression, mid travel, and Full droop.  The Tie rod location or the link mount location should be in all three of these positions.  Now draw a three point circle (you can define a circle by any thee points without knowing the center).  The center of the circle defined will be the sweet spot for the frame mount.

In the first picture you can see the suspension.  Unequal length arms, nonparallel.  If you can see the small red circle, that is the potential outer tie rod mount location.  It is outside of the axis that the spindle rotates on for Ackerman.



Now you have the suspension at the three travel locations.  Draw a circle with three points based on the little red circles.  You can see the large circle.  The radius of this circle is the tie rod length.  (As long as it's inner mount is fore/aft the same.)  You can now see the inner sweet spot point.




It makes sense that the sweet spot point is outboard of the suspension mounts because the outer point is outboard of the mounts.  It also makes sense that the vertical postion has a relationship to the outboard vertical position.  If the outer mount were moved up on the spindle, the inner point would move up as well.  However it is not a direct relationship because of the unequal length of the arms.

So to Trojan's question.  A formula would involve some pretty rough calculus.  That I don't remember how to do.   This is a way do do it.

If you were using CAD (Cardboard aided design TM Artie) you could draw it out like we have here, then experimentally draw radius's with the outer tie rod mounts as the center.  Once you found the one where the three intersected at the same point, you would have found the sweet spot and the tie rod length.

And for you 3D guys, you just learned the value of 2d Cad.