Solving 4-Link Suspension Angles Without Knowing "Crap"

[Reed]

I want to do some math for 4-link suspension, and I soon realized I don't know crap. Say I take measurements of the lengths of the four connecting rods and one angle measurement. How do I find the values of the other three angles?

 

[uart]

Draw in one of the diagonals so as to form a triangle. Choose the digonal such that the one angle that you measured (or know) is at the apex of this triangle (and the diagonal the base of the triangle). You know two sides and the included angle so use the "cosine rule" to find the length of the diagonal. Once you've got hat it's easy to use the "sine rule" to find the other two angles of this first triangle.

Now you need to solve the second triangle. Here you now know all three sides (courtesy of solving the diagonal in the previous step) so just use the cosine rule to find anyone angle. Then use the sine rule to find a second angle and the 180 degree sum to find the remaining angle. Now you know everything.

 

[Reed]

Do the sine, cosine, and tangent functions not apply only to right triangles?

 

[uart]

Do the sine, cosine, and tangent functions not apply only to right triangles?

Yep that's right, but the "cosine rule" and "sine rule" apply to any triangle. If you haven't heard of them then do a google seach on "sine rule" or "cosine rule" and you're bound to turn something up at mathworld.

 

[cookiemonster]

Also known as the Law of Sines and Law of Cosines, just in case mathworld doesn't match it up with "rule."

cookiemonster

 

[Reed]

Say I have a triangle whose sides measure 17in, 16.5in, and 6in.

a=17
b=16.5
c=6
A=x


17^2 = 16.5^2 + 6^2 - 2(16.5)Cos X
289 = 272.25 + 36 - 33(Cos X)
-33(Cos X) = -19.25
Cos X = .583
X = 54.3 degrees?


I'm sure I'm making some gay mistake here...


Doing it that way would make B = 52 degrees and C = 73.7 degrees... which is crazy.

 

[Reed]

Doh! Got a mistyped formula from a crappy website. Mathworld shows that b AND c are multiplied with the cosine, which makes a lot more sense. Off to do some math (I mean work) again.

 

[Reed]

Four sides.

a = 6
b = 14
c = 9
d = 17

My rounded solutions output angle values of 117.45, 88.92, 78.57, and 75.03

That's exactly what I was looking for. Now time to apply it to some useful things. :) Thanks a lot, guys

 

[uart]

Doh! Got a mistyped formula from a crappy website. Mathworld shows that b AND c are multiplied with the cosine, which makes a lot more sense. Off to do some math (I mean work) again.

Yeah don't get confused with a's, b's and c's, it's always :

(Opposite_side)^2 = (Adjacent_side_1)^2 + (Adjacent_side_2)^2 - 2(Adjacent_side_1)(Adjacent_side_2) cos(theta)

I like to think of it (the cosine rule) as being a bit like Pythagoras thm but with the extra term to account for the fact that the angle is not generally 90 degrees. If the angle is 90 degrees then the opposite side is indeed the hypotenuse and since the cos of 90 is zero then you have exactly just Pythagoras. When the angle is acute then you get a negative adjustment, as the opposite side length is less then what you would have gotten with a right angle and Pythagoras, however when the angle is obtuse the cosine is negative and you get a positive adjustment.

It all makes sense, well kind of, that's how I like to remember it anyway.

 

[moshek]

This sound very bad " School me" !

still i say good luck with mathematics.

 

[Reed]

Yeah, the more I think about it, the more it makes sense. Good formula. I don't know why nobody taught me in high school. Anyways, sorry if "school me" sounded rude or anything. Just trying to keep a sense of humor in everything I do.

 

[moshek]

Reed: If it is really only Humor than it is a good one
Moshek