Hi,
Got this equation system to solve, and its just not going anywhere to me, keep banging a dead end... Hope you guys can help. The unknowns are d1 and d2, the rest is assumed as known.
Any help appreciated!
THNX!
$\displaystyle x_1 - d_1 \sin x_1= x_2 + d_2 \cos x_2 \rightarrow(1)$
$\displaystyle y_1 - d_1 \cos x_1= y_2 + d_2 \sin x_2 \rightarrow(2)$
Rearrange $\displaystyle (1): x_1 - x_2 - d_2 \cos x_2 = d_1 \sin x_1$
$\displaystyle \Rightarrow d_1 = \frac{x_1 - x_2 - d_2 \cos x_2}{\sin x_1} \rightarrow(3)$
Now sub $\displaystyle (3)$ into $\displaystyle (2)$ and solve for $\displaystyle d_2.$
Then, plug the $\displaystyle d_2$ you found into $\displaystyle (1)$ to find $\displaystyle d_1.$
$\displaystyle \frac{x_1 \cos x_1 - x_2 \cos x_1 - d_2 \cos x_1 \cos x_2}{\sin x_1} = y_2 - y_1 + d_2 \sin x_2$
$\displaystyle \implies x_1 \cos x_1 - x_2 \cos x_1 - d_2 \cos x_1 \cos x_2 = y_2 \sin x_1 - y_1 \sin x_1 + d_2 \sin x_2 \sin x_1$
$\displaystyle \implies x_1 \cos x_1 - x_2 \cos x_1 - y_2 \sin x_1 + y_1 \sin x_1 = d_2 \sin x_2 \sin x_1 + d_2 \cos x_1 \cos x_2 $
$\displaystyle \implies x_1 \cos x_1 - x_2 \cos x_1 - y_2\sin x_1 + y_1 \sin x_1 = d_2 (\sin x_2 \sin x_1 + \cos x_1 \cos x_2 )$
$\displaystyle \implies d_2 = \frac{x_1 \cos x_1 - x_2 \cos x_1 - y_2 \sin x_1 + y_1 \sin x_1}{\sin x_2 \sin x_1 + \cos x_1 \cos x_2}.$
Yeah it's ugly, but I'm not sure I see the issue...?
Change of situation!!!
If I assume that I know d1 and d2 but do not know alpha1 and alpha2 instead. From equation 1 I have expressed sina1 which results as (x1-x2-d2*cosa2)/d1. How do I change this in order to be able to substitute for cosa1 in equation 2? Or is there another way to solve it?