I’m trying to figure out how long to make A and B here if I have linear actuator of length C (extended = 2C) in order to tilt my panels from completely horizontal to vertical so they avoid wind and shed snow respectively when I run up the actuator to the extremes respectively based on sensor input.
Is there a simple formula I can use to plug the length of whatever actuator I settle on to figure A and B out? I know it will have to be a certain minimum and maximum size to work properly and might have to experiment to get an idea of what works in the end, but I’d like a reasonable start point to purchase an appropriate actuator.
I’ve googled around and decided I’m not smart enough to even come up with the right search criteria, let alone figure this out myself since it’s been 35 years since I’ve used anything except the most basic trig.
This isn’t really homework except for the fact that I’m trying to make my home work right.
Edit: seems like if I select A=.75C and solve for B at horizontal, then it always works out. No idea why, but the couple examples I try seem to agree.
It’s a triangle, why not just use Pythagorean theorem? I don’t know if you can get the full 90 degree rotation from a liner actuator like that but it could get pretty close as long as A and B are long in relation to c’s minimum distance.
It’s only a right triangle at horizontal, so I’m not sure how I’d use that to figure out the lengths that give me anything for the vertical position. It’s easy enough for the fully retracted situation, but after that I’m lost figuring out how to get the angle to 0 at 2C.
Edit: OK, so you’re saying if the pole is 5’ long, pick an LA that’s close to half that length and just wing it. Which I could do, but I’d hoped to maybe figure it out approximately ahead of buying an expensive LA if I could get a smaller one for less.
Ok I understand better what you’re trying to do, this is a pretty basic trig problem there are a ton of triangle calculators out there that will give you a good idea of the lengths you want. This site even has some explanations of how sine and cosine can be used to find missing sides and angles. Also just a note, any triangle can be split to create 2 right angle triangles, it’s not the ideal way to solve these problems but can help simplify some concepts to make things easier to understand.
OK, so there’s some way to use the idea that at retracted, b^2 = a^2 + c^2 and at extended, 2C = A + B.
Since I have a 78" long panel I was going to hinge about 1/3 of the way from the top, it seems like a 60" tall post would be a reasonable height to work from. Just plugging random numbers in, if I have an LA of 24" and randomly select A=18, at horizontal B=30 and at vertical those add up to 2C=48.
It seems like if I make A=.75C and figure out B with pythagorean, then the second equation works out as well, ie: C=18 and A=13.5, then B=22.5 and it comes out right at 2C=36. Same with C=16 and A=12, B=20 and 12+20=32.
No clue how I make the above equations prove that, but seems to work.
Thanks for reviving that part of my brain. Now I can go back to killing those brain cells with alcohol.
There is a ton of ways to solve this, but I believe what might help you the most is a tool that allows you to a) solve these kinds of problems repeatedly, with variations in the setup and b) helps you re-learn the basic math.
Therefore, I suggest you setup your problem in Geogebra:
https://www.geogebra.org/math/angles
You can introduce an interactive slider to vary one or more parameters (e. g. extension of the linear rod) and immediately read all other values, like lengths and distances.
