Hi, I am struggling with a trigonometry challenge and I hope some brains can help out.
3 points given. A, B and C. Point C is fixed, but A and B are movable. I am looking for a definition that returns two lines of equal lenth (a,b) whereby the blue line must have C as midpoint.
The system is like a scale with two equal springs finding their equilibrium.
I would like to solve this mathematically rather than with kangaroo.
Thanks a lot!
Thanks for that break-down into 90° triangles, I think this is a great approach
the blue and the white lengths are free ?
real physical springs will not have the same length !!
if A B C are fixed and the blue line is a stiff element,
the torque at both ends of the blue bar will be the same.
part of the force of the white springs will tear at C / will be directed towards this fixed point.
green: same torque
blue: radial force - captured by C
black / violett - different forces for both springs
… at least this is what i think.
But if they aren’t springs and the length of the blue line is given?
I’m trying to set up constraints but I could not figure out how to make the colinear and midpoint of the line between the two equal radii work.
Now if the midpoint of the in between line could be anchored, I’d be done.
Thants interesting Tom, I totally omitted the angular impact and resulting forces.
For clarification, The blue line’s lenth is defined. It can rotate about C.
For the positions of A and B respectively, the solution room is bounded.
fyi , here is the use case, a hinge (sorry, clip was deleted)
What is this used for?
flaps
What’s a flap?
A cabinet door that opens horizontally.
Actually, the geometric scetch, as decribed in the beginning could be done very easily in Solid Works. It must be possible in GH also… Thanks so far for your valuable input!
Interesting. I’ve done a fair bit of such constraints and hinges in GH. All of them with Kangaroo. I know how to do this in SW but somehow can’t get the rhino constraints to work, which is a bit frustrating.
Yes I feel you. You can`t just define two lines, circles etc. as equal without assigning a variable.
Still, your approach seems a good way to go. Everything blue is given or can be retrieved and the math behind the black stuff must yield the springs (puting aside Toms thoughts for the moment)
Allright, to close this: Tom you`re right. I checked some configurations with kangaroo and the springs end up with different lengths. That resonates well with your scetch - and also makes it easier for me.
Thank you all so much. It is so good to have this community!
Hello Ulrich Merz, a fun challenge to try to solve. Thank you.
As far as I can see there are always two solutions. One with crossed lines and one not crossed. But my knowledge of mathematics is far too limited to be able to prove this.
It is clear that in both solutions there is no movement in the system, due to the fixed location of point C and the fixed radius of C.
Here follows a Grashopper Definition that shows this challenge dynamically:
Rhinoforums Trigonometry Problem 11-3-25.gh (52.6 KB)
Hello Ed, this is awesome! How did you come up with these expressions. Chapeau
Thank you. I made them with “Geometry Expressions” (very old and sometimes clumsy software with bugs, but also unique. Takes a while to work with the flaws.) and Maple.
Maple gave 8 solutions, but as you can see in the program, it actually turns out to be only 4 solutions. I could have taken that out.
Nevertheless, there are areas where the solutions give a NaN. I am still looking into whether there is a way around that, I am working on it now, it will take a while before I know whether that is possible or not. I also do not know whether there are no solutions, or whether the expressions give a NaN (because of Sqrt(-x)).
If I do have a solution for NaN, I will post a new definition. I have already read up quite a bit on NaN here on the forum, so with that information I will see how far I get.
----Now without NaN, but it doesn’t matter for the solution. So there are probably areas where there is no solution, or my method is not complete. Here is Grasshopper definition without NaN (You need IAC plugin for the polynomial solver):
Rhinoforums Trigonometry Problem Wihout NaN 11-3-25.gh (53.3 KB)
