I am building an open source cable robot similar to this except constrained to two dimensions. I precisely know the lengths of all four cables, and from them I would like to derive the locations of the anchor points of the cables ($A,B,D$).
Essentially the known quantities are:
$$C = (0,0)$$ $$|\vec{AE}|$$ $$|\vec{BE}|$$ $$|\vec{CE}|$$ $$|\vec{DE}|$$
This is not enough information to constrain the positions of $A,B,D$, however I am able to move the robot to a new position giving us a second set of information.
So now we also know:
$$|\vec{AE'}|$$ $$|\vec{BE'}|$$ $$|\vec{CE'}|$$ $$|\vec{DE'}|$$
Is this enough information to solve for the positions of $A, B, C$? And if so how would I go about beginning to solve for them?
Edit: I think we may also need to arbitrarily constrain the whole system from rotating by saying that $Dy = 0$. Without that arbitrary constraint there would be infinite solutions where the whole system rotates around C...I think.
Edit 2: One more option that we have to constrain things further is to position E such that $|\vec{AE}|$ is parallel to $|\vec{DE}|$. If possible I would like to avoid using that unless it is necessary.
Thanks for taking the time to read all the way to the bottom.