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July 31st, 2013, 02:46 AM   #1
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triangle inequalities of four bar linkages

hello there
i am kinda learning about four-bar linkages, and im trying to find the length relationships of the four links

how do i combine these inequalities

L1 + L2 < L0 + L3
L0 < L2 - L1 + L3
L3 < L2 - L1 + L0

to form this

L1 + |L2 - L3| < L0 < L2 - L1 + L3



all are different variables, the links have different lengths

im kinda dumbfound abt it
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July 31st, 2013, 03:41 AM   #2
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Re: triangle inequalities of four bar linkages

Note that the second part of your inequality L0 < L2 - L1 + L3 is simply the second equation. So, all you have to show is:

L1 + I L2 - L3 I < L0

First, if L3 < L2, then I L2 - L3 I = L2 - L3. And, the inequality holds from looking at the first equation

L1 + L2 - L3 < L0, hence L1 + I L2 - L3 I < L0 (when L3 < L2)

If, however, L2 < L3, then I L2 - L3 I = L3 - L2. And, the inequality holds from the third equation:

L3 < L2 - L1 + L0 hence L1 + L3 - L2 < L0

And that's it.
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July 31st, 2013, 04:32 AM   #3
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Re: triangle inequalities of four bar linkages

thanks, i think i got it now
i confused myself with the absolute value signs
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