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I am trying to work out where to fit the pins on a gas strut for a 90 degree opening hinge. BTW - I am a farmer, not a maths person and this is my first post.

Strut details: Open length is $325mm$. Closed length is $205mm$. Hinge goes from $0^\circ$ degrees (fully closed) to $90^\circ$ degrees (fully open). The problem is where to drill the pins on each side of the hinge so it opens to the maximum length and closes to the shortest.

It seems such a simple problem, but I just cannot see how to solve it. The formula I have worked out is this (based on the squared rule for a right angle triangle):

$(x+y)^2 + y^2 = z^2$

So for my case, it is $(205 + y)^2 + y^2 = 325^2$

By substituting a few real-life values I can see the value for $y$ is about $103mm$, but that took about $4$ or $5$ high/low guesses to get to that.

Is there a mathematical way to work it out, or am I heading into integration/differentiation maths to get an answer?

Thanks
David

awkward
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user2991620
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1 Answers1

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Welcome to MSE!

you can solve the equation $(205+y)^2 +y^2=325^2$ through the quadratic equation formula or also, probably through pythagorean triples in some weird way.

I’de say maybe the most straight forward way would be to expand everything,

$$2y^2+410y-63600 =0$$

and then use $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ which will give you both solutions, where you have a polynomial of the form $ax^2+bx+c=0$

WolframAlpha gives $y=-\frac{205}{2}\pm\frac{5\sqrt{6769}}{2}$ with positive $y\approx 103.18$ and negative $y\approx -308.18$, but I’m pretty sure the positive $y$ is only useful to you.

It turns out you were pretty close to the right answer, only off by $0.18$

no lemon no melon
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  • OK - I can see how you expanded that out, thanks. I was expanding it out wrongly as: 2y^2=325^2 - 205^2 I've not heard of WolframAlpha - so I will do a bit of Googling on that. – user2991620 Mar 11 '21 at 07:21
  • yup you are missing the linear $y$ term, there are many tool available online that will do the whole thing for you, expand and give you the solutions, give WolframAlpha a try :) – no lemon no melon Mar 11 '21 at 07:24
  • If you are going to use WA, there is no need to do the preliminary simplification of the equation. You can just type in "solve (205+y)^2 + y^2 = 325^2 for y", and WA will solve the equation. Then click on the "approximate forms" button to get a numerical answer instead of the exact answer involving square roots. – awkward Mar 11 '21 at 13:25